33:I[196793,["/_next/static/chunks/39xwo21u32kk3.js?dpl=nogit-1790936776","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790936776","/_next/static/chunks/13_9hjun60hj-.js?dpl=nogit-1790936776","/_next/static/chunks/3mz725-y91ph6.js?dpl=nogit-1790936776","/_next/static/chunks/3idr5td_y0l2x.js?dpl=nogit-1790936776","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790936776","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790936776","/_next/static/chunks/2bxmml65nu49g.js?dpl=nogit-1790936776","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790936776","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790936776","/_next/static/chunks/1v3yeqs4syiu6.js?dpl=nogit-1790936776","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790936776","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790936776","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790936776","/_next/static/chunks/19ijf68pshdcn.js?dpl=nogit-1790936776","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790936776","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790936776","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790936776","/_next/static/chunks/30ejopwuj9-ez.js?dpl=nogit-1790936776","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790936776","/_next/static/chunks/0viymfxbftnxg.js?dpl=nogit-1790936776","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790936776","/_next/static/chunks/3lz9pr5v38m4h.js?dpl=nogit-1790936776","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1790936776","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790936776","/_next/static/chunks/1_p5v4n7583_r.js?dpl=nogit-1790936776","/_next/static/chunks/3fht_ul1qhe08.js?dpl=nogit-1790936776","/_next/static/chunks/3hy4f5dlm3hqf.js?dpl=nogit-1790936776","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790936776","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790936776","/_next/static/chunks/04pw9vpn2wezi.js?dpl=nogit-1790936776","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790936776","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790936776","/_next/static/chunks/37oe4_azebkh6.js?dpl=nogit-1790936776","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790936776","/_next/static/chunks/0r7hf3r-7wi-w.js?dpl=nogit-1790936776","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790936776","/_next/static/chunks/0k3581c5est85.js?dpl=nogit-1790936776","/_next/static/chunks/2uzea6b173htc.js?dpl=nogit-1790936776","/_next/static/chunks/03ff00u5689yw.js?dpl=nogit-1790936776","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1790936776","/_next/static/chunks/3jia3kgen87vp.js?dpl=nogit-1790936776","/_next/static/chunks/13gj59kzq50t_.js?dpl=nogit-1790936776","/_next/static/chunks/2tom8_rk-gmeh.js?dpl=nogit-1790936776","/_next/static/chunks/3x_-spr91qs0c.js?dpl=nogit-1790936776","/_next/static/chunks/1u4k5v04xsltr.js?dpl=nogit-1790936776","/_next/static/chunks/1d7tjnrc0fv5y.js?dpl=nogit-1790936776","/_next/static/chunks/2ywjv53bqy6tq.js?dpl=nogit-1790936776","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790936776","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790936776","/_next/static/chunks/37eine4sgbepr.js?dpl=nogit-1790936776","/_next/static/chunks/0z_oky3704907.js?dpl=nogit-1790936776","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790936776","/_next/static/chunks/1_mai2ew48jvc.js?dpl=nogit-1790936776","/_next/static/chunks/3ybwgs28on6c8.js?dpl=nogit-1790936776","/_next/static/chunks/2leuonyicz6gk.js?dpl=nogit-1790936776","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790936776","/_next/static/chunks/0_e0vb210svk3.js?dpl=nogit-1790936776","/_next/static/chunks/1hnuhh5t7cfaj.js?dpl=nogit-1790936776","/_next/static/chunks/2u1q43gtwo_9f.js?dpl=nogit-1790936776"],"Gingerbread"] 35:I[647935,["/_next/static/chunks/39xwo21u32kk3.js?dpl=nogit-1790936776","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790936776","/_next/static/chunks/13_9hjun60hj-.js?dpl=nogit-1790936776","/_next/static/chunks/3mz725-y91ph6.js?dpl=nogit-1790936776","/_next/static/chunks/3idr5td_y0l2x.js?dpl=nogit-1790936776","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790936776","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790936776","/_next/static/chunks/2bxmml65nu49g.js?dpl=nogit-1790936776","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790936776","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790936776","/_next/static/chunks/1v3yeqs4syiu6.js?dpl=nogit-1790936776","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790936776","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790936776","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790936776","/_next/static/chunks/19ijf68pshdcn.js?dpl=nogit-1790936776","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790936776","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790936776","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790936776","/_next/static/chunks/30ejopwuj9-ez.js?dpl=nogit-1790936776","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790936776","/_next/static/chunks/0viymfxbftnxg.js?dpl=nogit-1790936776","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790936776","/_next/static/chunks/3lz9pr5v38m4h.js?dpl=nogit-1790936776","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1790936776","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790936776","/_next/static/chunks/1_p5v4n7583_r.js?dpl=nogit-1790936776","/_next/static/chunks/3fht_ul1qhe08.js?dpl=nogit-1790936776","/_next/static/chunks/3hy4f5dlm3hqf.js?dpl=nogit-1790936776","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790936776","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790936776","/_next/static/chunks/04pw9vpn2wezi.js?dpl=nogit-1790936776","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790936776","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790936776","/_next/static/chunks/37oe4_azebkh6.js?dpl=nogit-1790936776","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790936776","/_next/static/chunks/0r7hf3r-7wi-w.js?dpl=nogit-1790936776","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790936776","/_next/static/chunks/0k3581c5est85.js?dpl=nogit-1790936776","/_next/static/chunks/2uzea6b173htc.js?dpl=nogit-1790936776","/_next/static/chunks/03ff00u5689yw.js?dpl=nogit-1790936776","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1790936776","/_next/static/chunks/3jia3kgen87vp.js?dpl=nogit-1790936776","/_next/static/chunks/13gj59kzq50t_.js?dpl=nogit-1790936776","/_next/static/chunks/2tom8_rk-gmeh.js?dpl=nogit-1790936776","/_next/static/chunks/3x_-spr91qs0c.js?dpl=nogit-1790936776","/_next/static/chunks/1u4k5v04xsltr.js?dpl=nogit-1790936776","/_next/static/chunks/1d7tjnrc0fv5y.js?dpl=nogit-1790936776","/_next/static/chunks/2ywjv53bqy6tq.js?dpl=nogit-1790936776","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790936776","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790936776","/_next/static/chunks/37eine4sgbepr.js?dpl=nogit-1790936776","/_next/static/chunks/0z_oky3704907.js?dpl=nogit-1790936776","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790936776","/_next/static/chunks/1_mai2ew48jvc.js?dpl=nogit-1790936776","/_next/static/chunks/3ybwgs28on6c8.js?dpl=nogit-1790936776","/_next/static/chunks/2leuonyicz6gk.js?dpl=nogit-1790936776","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790936776","/_next/static/chunks/0_e0vb210svk3.js?dpl=nogit-1790936776","/_next/static/chunks/1hnuhh5t7cfaj.js?dpl=nogit-1790936776","/_next/static/chunks/2u1q43gtwo_9f.js?dpl=nogit-1790936776"],"RecordResourceResume"] 36:I[830476,["/_next/static/chunks/39xwo21u32kk3.js?dpl=nogit-1790936776","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790936776","/_next/static/chunks/13_9hjun60hj-.js?dpl=nogit-1790936776","/_next/static/chunks/3mz725-y91ph6.js?dpl=nogit-1790936776","/_next/static/chunks/3idr5td_y0l2x.js?dpl=nogit-1790936776","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790936776","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790936776","/_next/static/chunks/2bxmml65nu49g.js?dpl=nogit-1790936776","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790936776","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790936776","/_next/static/chunks/1v3yeqs4syiu6.js?dpl=nogit-1790936776","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790936776","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790936776","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790936776","/_next/static/chunks/19ijf68pshdcn.js?dpl=nogit-1790936776","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790936776","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790936776","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790936776","/_next/static/chunks/30ejopwuj9-ez.js?dpl=nogit-1790936776","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790936776","/_next/static/chunks/0viymfxbftnxg.js?dpl=nogit-1790936776","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790936776","/_next/static/chunks/3lz9pr5v38m4h.js?dpl=nogit-1790936776","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1790936776","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790936776","/_next/static/chunks/1_p5v4n7583_r.js?dpl=nogit-1790936776","/_next/static/chunks/3fht_ul1qhe08.js?dpl=nogit-1790936776","/_next/static/chunks/3hy4f5dlm3hqf.js?dpl=nogit-1790936776","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790936776","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790936776","/_next/static/chunks/04pw9vpn2wezi.js?dpl=nogit-1790936776","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790936776","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790936776","/_next/static/chunks/37oe4_azebkh6.js?dpl=nogit-1790936776","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790936776","/_next/static/chunks/0r7hf3r-7wi-w.js?dpl=nogit-1790936776","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790936776","/_next/static/chunks/0k3581c5est85.js?dpl=nogit-1790936776","/_next/static/chunks/2uzea6b173htc.js?dpl=nogit-1790936776","/_next/static/chunks/03ff00u5689yw.js?dpl=nogit-1790936776","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1790936776","/_next/static/chunks/3jia3kgen87vp.js?dpl=nogit-1790936776","/_next/static/chunks/13gj59kzq50t_.js?dpl=nogit-1790936776","/_next/static/chunks/2tom8_rk-gmeh.js?dpl=nogit-1790936776","/_next/static/chunks/3x_-spr91qs0c.js?dpl=nogit-1790936776","/_next/static/chunks/1u4k5v04xsltr.js?dpl=nogit-1790936776","/_next/static/chunks/1d7tjnrc0fv5y.js?dpl=nogit-1790936776","/_next/static/chunks/2ywjv53bqy6tq.js?dpl=nogit-1790936776","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790936776","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790936776","/_next/static/chunks/37eine4sgbepr.js?dpl=nogit-1790936776","/_next/static/chunks/0z_oky3704907.js?dpl=nogit-1790936776","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790936776","/_next/static/chunks/1_mai2ew48jvc.js?dpl=nogit-1790936776","/_next/static/chunks/3ybwgs28on6c8.js?dpl=nogit-1790936776","/_next/static/chunks/2leuonyicz6gk.js?dpl=nogit-1790936776","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790936776","/_next/static/chunks/0_e0vb210svk3.js?dpl=nogit-1790936776","/_next/static/chunks/1hnuhh5t7cfaj.js?dpl=nogit-1790936776","/_next/static/chunks/2u1q43gtwo_9f.js?dpl=nogit-1790936776"],"FlashcardAccessBranch"] 37:I[315438,["/_next/static/chunks/39xwo21u32kk3.js?dpl=nogit-1790936776","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790936776","/_next/static/chunks/13_9hjun60hj-.js?dpl=nogit-1790936776","/_next/static/chunks/3mz725-y91ph6.js?dpl=nogit-1790936776","/_next/static/chunks/3idr5td_y0l2x.js?dpl=nogit-1790936776","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790936776","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790936776","/_next/static/chunks/2bxmml65nu49g.js?dpl=nogit-1790936776","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790936776","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790936776","/_next/static/chunks/1v3yeqs4syiu6.js?dpl=nogit-1790936776","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790936776","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790936776","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790936776","/_next/static/chunks/19ijf68pshdcn.js?dpl=nogit-1790936776","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790936776","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790936776","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790936776","/_next/static/chunks/30ejopwuj9-ez.js?dpl=nogit-1790936776","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790936776","/_next/static/chunks/0viymfxbftnxg.js?dpl=nogit-1790936776","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790936776","/_next/static/chunks/3lz9pr5v38m4h.js?dpl=nogit-1790936776","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1790936776","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790936776","/_next/static/chunks/1_p5v4n7583_r.js?dpl=nogit-1790936776","/_next/static/chunks/3fht_ul1qhe08.js?dpl=nogit-1790936776","/_next/static/chunks/3hy4f5dlm3hqf.js?dpl=nogit-1790936776","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790936776","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790936776","/_next/static/chunks/04pw9vpn2wezi.js?dpl=nogit-1790936776","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790936776","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790936776","/_next/static/chunks/37oe4_azebkh6.js?dpl=nogit-1790936776","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790936776","/_next/static/chunks/0r7hf3r-7wi-w.js?dpl=nogit-1790936776","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790936776","/_next/static/chunks/0k3581c5est85.js?dpl=nogit-1790936776","/_next/static/chunks/2uzea6b173htc.js?dpl=nogit-1790936776","/_next/static/chunks/03ff00u5689yw.js?dpl=nogit-1790936776","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1790936776","/_next/static/chunks/3jia3kgen87vp.js?dpl=nogit-1790936776","/_next/static/chunks/13gj59kzq50t_.js?dpl=nogit-1790936776","/_next/static/chunks/2tom8_rk-gmeh.js?dpl=nogit-1790936776","/_next/static/chunks/3x_-spr91qs0c.js?dpl=nogit-1790936776","/_next/static/chunks/1u4k5v04xsltr.js?dpl=nogit-1790936776","/_next/static/chunks/1d7tjnrc0fv5y.js?dpl=nogit-1790936776","/_next/static/chunks/2ywjv53bqy6tq.js?dpl=nogit-1790936776","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790936776","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790936776","/_next/static/chunks/37eine4sgbepr.js?dpl=nogit-1790936776","/_next/static/chunks/0z_oky3704907.js?dpl=nogit-1790936776","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790936776","/_next/static/chunks/1_mai2ew48jvc.js?dpl=nogit-1790936776","/_next/static/chunks/3ybwgs28on6c8.js?dpl=nogit-1790936776","/_next/static/chunks/2leuonyicz6gk.js?dpl=nogit-1790936776","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790936776","/_next/static/chunks/0_e0vb210svk3.js?dpl=nogit-1790936776","/_next/static/chunks/1hnuhh5t7cfaj.js?dpl=nogit-1790936776","/_next/static/chunks/2u1q43gtwo_9f.js?dpl=nogit-1790936776"],"TopicFlashcardRunner"] 24:[["$","$L33",null,{"feature":"flashcards"}],"$L34",["$","$L35",null,{"href":"/as-level/maths/edexcel/as-statistics-box-plots/flashcards","label":"3.2 Box Plots","subjectCode":"as_level_maths","surface":"flashcards"}],["$","$L36",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L37",null,{"decks":[{"id":"6f98b429-8e6c-46ab-9ab5-4b50479f5f8d","title":"Box Plots Flashcards","topicId":"1996c83d-31d1-4b00-9509-d28a8d3a34b6","topicSlug":"as-statistics-box-plots","cards":[{"id":"4499c9fc-95db-4b84-85d6-31b27bdd83ef","cardType":"basic","points":2,"front":"List the five values required to build the main box and whiskers of a box plot.","back":"

Smallest non-outlier value
Lower Quartile ($Q_1$)
Median
Upper Quartile ($Q_3$)
Largest non-outlier value

","mcqOptions":[{"text":"

Smallest non-outlier value
Lower Quartile ($Q_1$)
Median
Upper Quartile ($Q_3$)
Largest non-outlier value

","correct":true,"explanation":"These are the five-number summary used by a box plot: the box shows the quartiles and median, while the whiskers extend to the extreme non-outlier values."},{"text":"

Smallest non-outlier value
Lower Quartile ($Q_1$)
Mean
Upper Quartile ($Q_3$)
Largest non-outlier value

","correct":false,"explanation":"The mean does not determine any part of a standard box plot. The central line represents the median, alongside the two quartiles and the extreme non-outlier values."},{"text":"

Smallest non-outlier value
Lower Quartile ($Q_1$)
Median
Interquartile Range
Largest non-outlier value

","correct":false,"explanation":"The IQR measures the box’s width but is not itself one of its five plotted positions. The upper boundary of the box must be $Q_3$."},{"text":"

Lower outlier fence
Lower Quartile ($Q_1$)
Median
Upper Quartile ($Q_3$)
Upper outlier fence

","correct":false,"explanation":"The fences are calculated thresholds for classifying outliers, not necessarily observed data values. Whiskers end at the smallest and largest actual non-outlier values."}]},{"id":"20be1efb-4bb5-4633-81c4-3d229f11a838","cardType":"cloze","points":null,"front":"To find the lower quartile ($Q_1$) of an ordered data set, calculate the [ ] of the lower half of the data.","back":"To find the lower quartile ($Q_1$) of an ordered data set, calculate the median of the lower half of the data.","mcqOptions":[{"text":"median","correct":true,"explanation":"The lower quartile is the central value of the ordered lower half, so it is found by calculating that half’s median."},{"text":"mean","correct":false,"explanation":"Using the mean confuses quartiles with averages based on every value’s magnitude. The lower quartile is the median of the ordered lower half."},{"text":"mode","correct":false,"explanation":"The mode identifies the most frequent value and does not locate the quarter-way position. The required calculation is the median of the lower half."},{"text":"range","correct":false,"explanation":"The range measures the difference between extreme values rather than a central position. The lower quartile is obtained from the median of the lower half."}]},{"id":"c9ce2f07-1d87-46c0-bbc7-89027bf23478","cardType":"cloze","points":null,"front":"To find the lower quartile ($Q_1$) of an ordered data set, calculate the median of the [ ] of the data.","back":"To find the lower quartile ($Q_1$) of an ordered data set, calculate the median of the lower half of the data.","mcqOptions":[{"text":"lower half","correct":true,"explanation":"After ordering and dividing the data around the overall median, $Q_1$ is found by taking the median of the lower half."},{"text":"upper half","correct":false,"explanation":"The median of the upper half gives $Q_3$, not $Q_1$. The lower quartile is the median of the lower half of the data."},{"text":"entire set","correct":false,"explanation":"Taking the median of the entire set gives the overall median, $Q_2$. For $Q_1$, take the median of the lower half."},{"text":"middle half","correct":false,"explanation":"The middle half is the interval between $Q_1$ and $Q_3$, so its median does not define $Q_1$. Use the lower half instead."}]},{"id":"c4509f85-d9a0-47c1-ab79-ef6ca962d67d","cardType":"basic","points":1,"front":"When finding quartiles for an odd number of data values, how is the overall median treated?","back":"It is excluded from both the lower and upper halves of the data.","mcqOptions":[{"text":"It is excluded from both the lower and upper halves of the data.","correct":true,"explanation":"Under this quartile convention, the overall median separates the ordered data but belongs to neither half, ensuring equal-sized lower and upper subsets."},{"text":"It is included in both the lower and upper halves of the data.","correct":false,"explanation":"Including the overall median in both halves uses a different quartile convention. Here it is excluded from both halves before their medians are calculated."},{"text":"It is included in the lower half but excluded from the upper half of the data.","correct":false,"explanation":"Placing the overall median only in the lower half makes the two halves unequal and treats them inconsistently. It should be excluded from both halves."},{"text":"It is excluded from the lower half but included in the upper half of the data.","correct":false,"explanation":"Placing the overall median only in the upper half makes the division asymmetric. Under the stated method, it is excluded from both halves of the data."}]},{"id":"3f3eb77e-c2b4-482e-8aea-58b33716289a","cardType":"basic","points":1,"front":"State the formula for calculating the Interquartile Range (IQR).","back":"$$$IQR = Q_3 - Q_1$$","mcqOptions":[{"text":"$$$IQR = Q_3 - Q_1$$","correct":true,"explanation":"The IQR measures the spread of the middle 50% of the data, extending from the lower quartile $Q_1$ to the upper quartile $Q_3$."},{"text":"$$$IQR = Q_1 - Q_3$$","correct":false,"explanation":"Reversing the subtraction usually produces a negative result, which cannot represent a spread. The upper quartile must be reduced by the lower quartile: $Q_3-Q_1$."},{"text":"$$$IQR = Q_3 + Q_1$$","correct":false,"explanation":"Adding the quartiles depends on their location and does not measure the distance between them. The IQR is the difference $Q_3-Q_1$."},{"text":"$$$IQR = Q_3 - Q_2$$","correct":false,"explanation":"Subtracting the median $Q_2$ measures only the upper half of the box. The full interquartile range extends from $Q_1$ to $Q_3$."}]},{"id":"aaaeacdc-78bf-4e60-ad16-02142daf567e","cardType":"basic","points":1,"front":"What does a smaller IQR indicate about the data distribution?","back":"The middle 50% of the data are more tightly clustered (greater consistency).","mcqOptions":[{"text":"The middle 50% of the data are more tightly clustered (greater consistency).","correct":true,"explanation":"The IQR is the width of the interval containing the middle 50%. A smaller width means those central observations are closer together and therefore more consistent."},{"text":"The middle 50% of the data are more widely spread (lower consistency).","correct":false,"explanation":"A more widely spread middle 50% would produce a larger IQR, not a smaller one. A smaller IQR indicates tighter central clustering and greater consistency."},{"text":"The middle 50% of the data are centred at a lower value (smaller median).","correct":false,"explanation":"The IQR measures spread rather than location, so it cannot show whether the centre is lower. A smaller IQR means the middle 50% are more tightly clustered."},{"text":"The whole data set is more tightly clustered (smaller overall range).","correct":false,"explanation":"A small IQR describes only the middle 50%; extreme values may still be far apart. It therefore indicates tighter central clustering, not necessarily a smaller overall range."}]},{"id":"77672a6d-ed1c-46df-8df8-495890d22fef","cardType":"basic","points":1,"front":"State the formula for the lower fence used to identify outliers.","back":"$$$Q_1 - 1.5 \\times IQR$$","mcqOptions":[{"text":"$$$Q_1 - 1.5 \\times IQR$$","correct":true,"explanation":"The lower outlier threshold is found by moving $1.5$ interquartile ranges below $Q_1$. Values below this fence are classified as potential outliers."},{"text":"$$$Q_1 + 1.5 \\times IQR$$","correct":false,"explanation":"Adding moves the threshold inside or above the box rather than below it. The lower fence subtracts $1.5$ interquartile ranges from $Q_1$."},{"text":"$$$Q_3 - 1.5 \\times IQR$$","correct":false,"explanation":"This starts from the upper quartile and moves downward, so it is not the standard lower fence. The lower fence starts at $Q_1$."},{"text":"$$$Q_1 - 0.5 \\times IQR$$","correct":false,"explanation":"The standard outlier rule uses $1.5$ interquartile ranges, not $0.5$. The lower fence is therefore $Q_1-1.5\\times IQR$."}]},{"id":"60f15c38-30d6-4419-a368-967f9dffcba5","cardType":"basic","points":1,"front":"State the formula for the upper fence used to identify outliers.","back":"$$$Q_3 + 1.5 \\times IQR$$","mcqOptions":[{"text":"$$$Q_3 + 1.5 \\times IQR$$","correct":true,"explanation":"The upper outlier threshold is found by moving $1.5$ interquartile ranges above $Q_3$. Values above this fence are classified as potential outliers."},{"text":"$$$Q_3 - 1.5 \\times IQR$$","correct":false,"explanation":"Subtracting moves the threshold below $Q_3$, potentially into the main distribution. The upper fence adds $1.5$ interquartile ranges to $Q_3$."},{"text":"$$$Q_1 + 1.5 \\times IQR$$","correct":false,"explanation":"The upper fence must start from the upper quartile rather than the lower quartile. Its formula is $Q_3+1.5\\times IQR$."},{"text":"$$$Q_3 + 0.5 \\times IQR$$","correct":false,"explanation":"The standard rule places the fence $1.5$ interquartile ranges beyond $Q_3$, not $0.5$. Using $0.5$ would incorrectly classify too many values as outliers."}]},{"id":"e23a770d-ec3d-4ae3-a391-28b7297c5402","cardType":"cloze","points":null,"front":"A value is considered an outlier if it is [ ] the lower fence or greater than the upper fence.","back":"A value is considered an outlier if it is smaller than the lower fence or greater than the upper fence.","mcqOptions":[{"text":"smaller than","correct":true,"explanation":"The lower fence is the cutoff for unusually small values, so a value must lie strictly below it to be classified as an outlier."},{"text":"equal to","correct":false,"explanation":"Equality with the lower fence does not make a value an outlier; it must be strictly below the lower fence, while values above the upper fence are also outliers."},{"text":"greater than","correct":false,"explanation":"This reverses the lower-tail condition: unusually small values are outliers below the lower fence, whereas unusually large values are above the upper fence."},{"text":"at least as large as","correct":false,"explanation":"The lower-tail rule is not based on being large or equal to the fence. The correct condition is being strictly below the lower fence."}]},{"id":"3c327455-7a03-496d-b6c5-396efc0780e4","cardType":"cloze","points":null,"front":"A value is considered an outlier if it is smaller than the lower fence or [ ] the upper fence.","back":"A value is considered an outlier if it is smaller than the lower fence or greater than the upper fence.","mcqOptions":[{"text":"greater than","correct":true,"explanation":"The upper fence marks the boundary for unusually large values, so a value is an outlier only when it lies strictly above that fence."},{"text":"equal to","correct":false,"explanation":"A value exactly on the upper fence is not an outlier because the rule requires it to be strictly above the fence; equality is included within the non-outlier range."},{"text":"less than","correct":false,"explanation":"This describes the lower-tail direction rather than the upper-tail condition. Values above the upper fence are outliers, while values below the lower fence form the other tail."},{"text":"at most","correct":false,"explanation":"Being no greater than the upper fence does not identify an upper outlier. The correct rule requires a value to be strictly above the upper fence."}]},{"id":"dc112a4d-9693-4533-88c6-cad47ce31d65","cardType":"basic","points":1,"front":"If a data value is exactly equal to the upper fence, is it classified as an outlier?","back":"No; it must be strictly greater than the fence.","mcqOptions":[{"text":"No; it must be strictly greater than the fence.","correct":true,"explanation":"The upper-fence rule uses a strict inequality. A value equal to the fence remains within the non-outlier range, and only a value greater than it is an outlier."},{"text":"Yes; it is at the boundary of the outlier region.","correct":false,"explanation":"The boundary itself is not classified as an outlier because the condition is strictly greater than the upper fence. Equality is therefore still treated as non-outlying."},{"text":"Yes; all values at or above the fence are outliers.","correct":false,"explanation":"Including the boundary changes the strict inequality into an inclusive one. Only values above the upper fence count as outliers, not values equal to it."},{"text":"No; it must be strictly less than the fence.","correct":false,"explanation":"The conclusion is right but the direction is wrong: upper outliers lie above the fence. Values equal to it are not outliers, while values greater than it are."}]},{"id":"15f3e0ad-b0ea-4e2c-9abb-bd008cb2d11e","cardType":"basic","points":1,"front":"Where must the whiskers of a box plot end if outliers are present?","back":"At the smallest and largest non-outlier values.","mcqOptions":[{"text":"At the smallest and largest non-outlier values.","correct":true,"explanation":"When outliers are excluded, each whisker extends from the box to the most extreme remaining value: the smallest non-outlier on one side and the largest on the other."},{"text":"At the smallest and largest values.","correct":false,"explanation":"Using the overall minimum and maximum would make the whiskers reach outliers. They should stop at the smallest and largest values that are not classified as outliers."},{"text":"At the lower and upper quartiles.","correct":false,"explanation":"The quartiles form the edges of the box, not the whisker endpoints. With outliers present, whiskers continue to the smallest and largest non-outlier values."},{"text":"At the lower and upper fences.","correct":false,"explanation":"Fences are calculated boundaries used to identify outliers, not necessarily observed data values. Whiskers end at the extreme observed values that remain non-outliers."}]},{"id":"058a937f-968e-45c7-8db3-c744dd113506","cardType":"basic","points":1,"front":"How are outliers represented on a box plot?","back":"Separately using crosses.","mcqOptions":[{"text":"Separately using crosses.","correct":true,"explanation":"Outliers are plotted as individual symbols away from the whiskers, commonly crosses, so they are visibly distinguished from the main spread of the data."},{"text":"Separately using dots.","correct":false,"explanation":"Individual marks can suggest separate plotting, but in this convention outliers are represented by crosses. The whiskers then stop at the extreme non-outliers."},{"text":"As part of the whiskers.","correct":false,"explanation":"Including outliers in the whiskers would hide their unusual status. Whiskers end at the smallest and largest non-outlier values, with outliers shown separately."},{"text":"Inside the box.","correct":false,"explanation":"The box displays the middle 50% of the data, so outliers are not placed there. They are plotted separately beyond the whiskers to show their distance from the main distribution."}]},{"id":"d44594c6-3877-4d7b-8aca-31431927837e","cardType":"cloze","points":null,"front":"In a box plot, the box itself represents the middle [ ] of the data, while each whisker represents approximately 25%.","back":"In a box plot, the box itself represents the middle 50% of the data, while each whisker represents approximately 25%.","mcqOptions":[{"text":"50%","correct":true,"explanation":"The box extends from the lower quartile to the upper quartile, containing the middle half of the ordered data. Each remaining quarter lies approximately in a whisker."},{"text":"25%","correct":false,"explanation":"A quarter of the data lies between the minimum and lower quartile, and another quarter lies between the upper quartile and maximum. The box itself contains both central quarters."},{"text":"75%","correct":false,"explanation":"The upper quartile marks the point below which about 75% of values lie, but the box covers only the interval from the lower to upper quartile, which contains 50%."},{"text":"100%","correct":false,"explanation":"The entire data range is represented by the full plot, including whiskers and any outliers. The box alone represents only the central half of the data."}]},{"id":"0ba87097-f20f-44f7-a1fb-46c20e466263","cardType":"cloze","points":null,"front":"In a box plot, the box itself represents the middle 50% of the data, while each whisker represents approximately [ ].","back":"In a box plot, the box itself represents the middle 50% of the data, while each whisker represents approximately 25%.","mcqOptions":[{"text":"25%","correct":true,"explanation":"The box covers the middle 50%, leaving approximately one quarter of the data below it and one quarter above it. Each whisker therefore represents about 25%."},{"text":"50%","correct":false,"explanation":"The central box, not each individual whisker, represents 50% of the data. The remaining data are split into two approximately equal quarters, one for each whisker."},{"text":"75%","correct":false,"explanation":"A value such as the upper quartile corresponds to a cumulative position near 75%, but the upper whisker represents only the final quarter beyond that point."},{"text":"10%","correct":false,"explanation":"A standard box plot divides the ordered data into four quarters. Since the box contains two quarters, each whisker accounts for approximately one of the remaining quarters."}]},{"id":"7739951b-354b-49ae-82c3-1b35fe19a888","cardType":"basic","points":1,"front":"In a box plot, which specific feature represents the time by which 75% of a group has finished a task?","back":"The Upper Quartile ($Q_3$).","mcqOptions":[{"text":"The Upper Quartile ($Q_3$).","correct":true,"explanation":"The upper quartile is the value below which approximately 75% of the observations lie. It therefore represents the time by which 75% of the group has finished."},{"text":"The Lower Quartile ($Q_1$).","correct":false,"explanation":"The lower quartile marks the point by which approximately 25% have finished, not 75%. The 75% completion point is the upper quartile, $Q_3$."},{"text":"The Median ($Q_2$).","correct":false,"explanation":"The median divides the data into two equal halves, representing approximately 50% completion. The point associated with 75% is the upper quartile, $Q_3$."},{"text":"The Interquartile Range ($\\text{IQR}$).","correct":false,"explanation":"The interquartile range measures the spread between the lower and upper quartiles; it is not a completion time or cumulative percentage. The relevant feature is the upper quartile, $Q_3$."}]},{"id":"5d82304e-0e81-4893-9034-fff7eab67b70","cardType":"basic","points":1,"front":"When comparing two distributions, which statistic should be used to compare average location?","back":"The median.","mcqOptions":[{"text":"The median.","correct":true,"explanation":"The median is the middle value when the data are ordered, so it represents the central or average location of a distribution and is directly read from a box plot."},{"text":"The mode.","correct":false,"explanation":"The mode identifies the most frequent value, not the central location of an ordered distribution. For box plots, the median is used to compare average location."},{"text":"The Interquartile Range (IQR).","correct":false,"explanation":"The IQR measures the spread of the middle 50% of values, rather than location. The median should be used to compare the average location of two distributions."},{"text":"The range.","correct":false,"explanation":"The range measures total spread from minimum to maximum and says nothing directly about central location. The median is the appropriate statistic for comparing average location."}]},{"id":"b3c8d6a0-688e-48bf-af15-ac175b01d2ec","cardType":"basic","points":1,"front":"When comparing two distributions, which statistic should be used to compare consistency (spread of the middle 50%)?","back":"The Interquartile Range (IQR).","mcqOptions":[{"text":"The Interquartile Range (IQR).","correct":true,"explanation":"The IQR is the difference between the upper and lower quartiles, so it measures the spread of the middle 50% and is suitable for comparing consistency."},{"text":"The median.","correct":false,"explanation":"The median measures the central location of a distribution, not the spread of its middle half. The IQR is required when comparing consistency in this way."},{"text":"The range.","correct":false,"explanation":"The range measures the spread of all values and can be dominated by extreme observations. The IQR specifically measures the spread of the middle 50%."},{"text":"The mode.","correct":false,"explanation":"The mode is the most common value and does not measure spread. Consistency in the middle 50% is compared using the IQR."}]},{"id":"0308ed20-f7b9-4d56-ab6d-ad57164ab87c","cardType":"basic","points":2,"front":"A box plot shows a median of 13 and an IQR of 8. Another shows a median of 15 and an IQR of 5. Which set is more consistent?","back":"The second set, because it has a lower IQR.","mcqOptions":[{"text":"The second set, because it has a lower IQR.","correct":true,"explanation":"A lower IQR means the middle 50% of values are more tightly grouped. Since 5 is less than 8, the second set is more consistent."},{"text":"The first set, because it has a higher IQR.","correct":false,"explanation":"A higher IQR means the middle 50% are more spread out, indicating less consistency. The second set is more consistent because its IQR is lower, at 5."},{"text":"The second set, because it has a higher IQR.","correct":false,"explanation":"The second set has an IQR of 5, which is lower rather than higher than 8. Smaller IQR values indicate greater consistency in the middle 50%."},{"text":"The first set, because it has a lower IQR.","correct":false,"explanation":"The first set has an IQR of 8, while the second has an IQR of 5. The smaller IQR makes the second set more consistent."}]},{"id":"1ef7c868-8f5d-4d4e-a4ef-bd1de8c4d475","cardType":"basic","points":1,"front":"Identify the median position in an ordered list of 11 values.","back":"The 6th value.","mcqOptions":[{"text":"The 6th value.","correct":true,"explanation":"For 11 ordered values, the median position is $(n+1)\\/2 = 12\\/2 = 6$, so the median is the 6th value."},{"text":"The 5th value.","correct":false,"explanation":"Using $(n-1)\\/2$ gives 5, but the median position for an odd number of values is $(n+1)\\/2$. Therefore, the correct position is the 6th value."},{"text":"The 7th value.","correct":false,"explanation":"The 7th value is one position beyond the centre of the list. With 11 ordered values, $(11+1)\\/2$ gives the 6th position."},{"text":"The 11th value.","correct":false,"explanation":"The 11th value is the maximum, not the central value. Ordering 11 values places the median at position $(11+1)\\/2$, which is the 6th value."}]},{"id":"79d85489-2fda-4fc5-b77a-808c9c887b21","cardType":"cloze","points":null,"front":"When drawing a box plot, the [ ] is drawn as a vertical line inside the box.","back":"When drawing a box plot, the median is drawn as a vertical line inside the box.","mcqOptions":[{"text":"median","correct":true,"explanation":"The median is the central value of the data and is represented by a line inside the box, separating the lower and upper halves of the middle 50%."},{"text":"lower quartile","correct":false,"explanation":"The lower quartile forms the left-hand edge of a standard horizontal box, rather than the internal line. The median is drawn as the line inside the box."},{"text":"interquartile range","correct":false,"explanation":"The IQR is a numerical measure of spread, calculated as upper quartile minus lower quartile. It is not a positional line drawn inside the box."},{"text":"range","correct":false,"explanation":"The range measures the distance between the minimum and maximum values and is represented by the full whisker span. The internal line represents the median."}]},{"id":"0e104de4-db1c-4005-b070-415df576a8dc","cardType":"cloze","points":null,"front":"When drawing a box plot, the median is drawn as a [ ] inside the box.","back":"When drawing a box plot, the median is drawn as a vertical line inside the box.","mcqOptions":[{"text":"vertical line","correct":true,"explanation":"The median is shown by a vertical line inside a standard horizontal box plot, marking the central value between the lower and upper quartiles."},{"text":"horizontal line","correct":false,"explanation":"A horizontal line would not mark the median in the usual horizontal box plot orientation. The median is represented by a vertical line inside the box."},{"text":"diagonal line","correct":false,"explanation":"A diagonal line is not part of the standard box plot convention and does not clearly identify the central position. The median is shown with a vertical line."},{"text":"vertical box","correct":false,"explanation":"The box represents the interquartile range, not the median itself. The median is indicated by a vertical line drawn inside that box."}]},{"id":"e387c6dc-81b8-4f8d-9e21-f8295e11a38b","cardType":"basic","points":2,"front":"Why is the IQR often preferred over the range when discussing spread?","back":"The range is significantly affected by extreme values (outliers), whereas the IQR focuses on the central values.","mcqOptions":[{"text":"The range is significantly affected by extreme values (outliers), whereas the IQR focuses on the central values.","correct":true,"explanation":"The range uses the minimum and maximum, so one unusual value can change it greatly. The IQR uses the quartiles and therefore describes the central 50% more reliably."},{"text":"The IQR is significantly affected by extreme values (outliers), whereas the range focuses on the central values.","correct":false,"explanation":"This reverses the properties of the two measures. The range depends on the extremes, while the IQR is resistant to outliers because it focuses on the central 50%."},{"text":"The range is significantly affected by central values, whereas the IQR focuses on the extreme values (outliers).","correct":false,"explanation":"The range is determined by the two extreme endpoints, not by central values. The IQR excludes the tails and focuses on the central values."},{"text":"The range is significantly unaffected by extreme values (outliers), whereas the IQR focuses on the central values.","correct":false,"explanation":"Because the range uses the minimum and maximum, it is directly affected by extreme values. The IQR is the measure that is comparatively resistant to outliers."}]},{"id":"659a7a1d-ba5e-4978-a139-87d9d91ac219","cardType":"basic","points":2,"front":"If $n=15$, which value is the median, and how many values are in the lower half?","back":"

Median: 8th value
Lower half: 7 values

","mcqOptions":[{"text":"

Median: 8th value
Lower half: 7 values

","correct":true,"explanation":"With 15 ordered values, the median is at position $(15+1)\\/2 = 8$. Removing it leaves seven values below and seven values above, so the lower half contains 7 values."},{"text":"

Median: 7th value
Lower half: 7 values

","correct":false,"explanation":"The 7th value would leave eight values at or above the centre. For 15 values, $(15+1)\\/2$ gives the 8th value, with 7 values in the lower half."},{"text":"

Median: 8th value
Lower half: 8 values

","correct":false,"explanation":"Although the median is the 8th value, it is not included in the lower half when the halves are split around the median. Therefore, the lower half has 7 values."},{"text":"

Median: 7th value
Lower half: 8 values

","correct":false,"explanation":"Both entries result from mishandling the central value in an odd-sized list. The 8th value is the median, and the seven values before it form the lower half."}]}]}],"examCountdown":{"examDate":"2027-05-13","paperLabel":"Paper 1"},"heading":"3.2 Box Plots","title":"Box Plots Flashcards","topbar":{"backHref":"/as-level/maths/edexcel/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"1996c83d-31d1-4b00-9509-d28a8d3a34b6","walled":"$L39"}],"$L3a","$L3b"]

3.2 Box Plots Flashcards

3.2 Box Plots Flashcards