.5.3 Data presentation and interpretation Flashcards","topicId":"9376d013-2b7b-4030-9487-9bb192f01f46","topicSlug":"data-presentation-and-interpretation-4","cards":[{"id":"d02d4a95-116e-45cd-aadc-96c8acc46d4a","cardType":"basic","front":"What does a larger standard deviation indicate?","back":"Values are more widely dispersed around the mean.","points":1,"mcqOptions":null},{"id":"0edfe6d2-6eac-44f1-b4af-1ffca6b20b0c","cardType":"basic","front":"Why can two data sets with the same mean have different standard deviations?","back":"The mean measures centre, while standard deviation measures spread.","points":2,"mcqOptions":null},{"id":"f2809cb7-53d7-44c4-99b8-4fe52a927c89","cardType":"cloze","front":"The deviation of a value $x$ from the sample mean is $\\text{[...]}$.","back":"The deviation of a value $x$ from the sample mean is $\\boxed{x-\\bar{x}}$.","points":null,"mcqOptions":null},{"id":"92564585-f9cf-4c18-8814-f9193d2377aa","cardType":"basic","front":"Why are deviations squared when calculating variance?","back":"Squaring prevents positive and negative deviations cancelling.","points":2,"mcqOptions":null},{"id":"133e8ebd-343f-44e1-8c29-05fca25b356c","cardType":"cloze","front":"For any data set, the sum of deviations from its mean is $\\text{[...]}$.","back":"For any data set, the sum of deviations from its mean is $\\boxed{0}$.","points":null,"mcqOptions":null},{"id":"84baf056-cbf2-450a-adc1-61d332b5eb1f","cardType":"basic","front":"When is the standard deviation zero?","back":"When every data value is identical.","points":1,"mcqOptions":null},{"id":"430106a8-494e-4e0a-8891-fadf2f4a311a","cardType":"basic","front":"If data are measured in cm, what are the units of the variance?","back":"cm²","points":1,"mcqOptions":null},{"id":"33ba319a-7a60-4de6-83bb-ec9d887a5ba6","cardType":"basic","front":"If data are measured in cm, what are the units of the standard deviation?","back":"cm","points":1,"mcqOptions":null},{"id":"f56d9be0-27a2-4fa0-a71c-4abbc7f62983","cardType":"basic","front":"If the observations form the complete group of interest, should they be treated as a population or sample?","back":"A population.","points":1,"mcqOptions":null},{"id":"f6291f12-5bb6-434d-bd2e-c90c9b370eb0","cardType":"basic","front":"Why does sample variance use $n-1$ rather than $n$?","back":"It corrects the sample's tendency to underestimate population variation.","points":2,"mcqOptions":null},{"id":"0fa46adf-5ca2-4e4f-a871-cdea3c6e86ca","cardType":"basic","front":"Which calculator outputs give population and sample standard deviation?","back":"

$\\sigma_x$: population standard deviation
$s_x$: sample standard deviation

","points":3,"mcqOptions":null},{"id":"98c1e079-c955-4f30-a6c3-0961015fa633","cardType":"cloze","front":"For a population of size $N$, the variance is $\\text{[...]}$.","back":"For a population of size $N$, the variance is $\\boxed{\\sigma^2=\\frac{\\sum(x-\\mu)^2}{N}}$.","points":null,"mcqOptions":null},{"id":"2fcfd9bd-8b1d-4763-a5c5-dc26cbe2a228","cardType":"cloze","front":"For a sample of size $n$, the variance is $\\text{[...]}$.","back":"For a sample of size $n$, the variance is $\\boxed{s^2=\\frac{\\sum(x-\\bar{x})^2}{n-1}}$.","points":null,"mcqOptions":null},{"id":"4662a246-11e5-4241-bc86-28c106d440ad","cardType":"basic","front":"How is standard deviation obtained from variance?","back":"Take the positive square root of the variance.","points":1,"mcqOptions":null},{"id":"50f4223f-028d-47d2-aa3c-cb0ad4170863","cardType":"cloze","front":"Using population summary statistics, $\\text{[...]}$.","back":"Using population summary statistics, $\\boxed{\\sigma^2=\\frac{\\sum x^2}{n}-\\left(\\frac{\\sum x}{n}\\right)^2}$.","points":null,"

2.5.3 Data presentation and interpretation Flashcards

2.5.3 Data presentation and interpretation Flashcards