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Each bar’s height represents the amount associated with one category."},{"text":"intervals","correct":false,"explanation":"Intervals are continuous ranges and are more commonly associated with grouped data or histograms. Separate bars on a bar chart represent different categories."},{"text":"measurements","correct":false,"explanation":"Measurements are the numerical amounts represented by bar heights, not the groups being compared. Those separate groups are called categories."},{"text":"frequencies","correct":false,"explanation":"Frequencies can determine the heights of the bars, but they are not necessarily the groups along the horizontal axis. Bar charts compare different categories."}]},{"id":"a0490d79-93dc-cbfc-60da-8a9031c105d7","cardType":"basic","points":1,"front":"If one bar is taller than another, what does that show?","back":"The taller bar has the bigger value.","mcqOptions":[{"text":"The taller bar has the bigger value.","correct":true,"explanation":"Bar height represents the value for a category, so a taller bar reaches a larger number on the vertical scale and therefore has the bigger value."},{"text":"The taller bar has the smaller value.","correct":false,"explanation":"This reverses the relationship between height and value. A taller bar reaches higher on the vertical scale, so it has the bigger value."},{"text":"The two bars have the same value.","correct":false,"explanation":"Equal values would normally produce bars of equal height. If one bar is taller, it represents a bigger value than the other bar."},{"text":"The wider bar has the bigger value.","correct":false,"explanation":"Bar width does not usually represent the value in a standard bar chart. The taller bar, rather than the wider bar, has the bigger value."}]},{"id":"1bc051de-82da-53c3-ef84-717eff7232c7","cardType":"cloze","points":null,"front":"On a usual bar chart, the horizontal axis shows [ ] and the vertical axis shows [ ].","back":"On a usual bar chart, the horizontal axis shows categories and the vertical axis shows numbers.","mcqOptions":[{"text":"On a usual bar chart, the horizontal axis shows categories and the vertical axis shows numbers.","correct":true,"explanation":"A usual bar chart places the groups being compared along the horizontal axis. Numerical values are shown on the vertical axis and determine the bars’ heights."},{"text":"On a usual bar chart, the horizontal axis shows numbers and the vertical axis shows categories.","correct":false,"explanation":"This swaps the usual roles of the axes. Categories normally appear along the horizontal axis, while numbers are displayed on the vertical axis."},{"text":"On a usual bar chart, the horizontal axis shows categories and the vertical axis shows bars.","correct":false,"explanation":"Bars are drawn within the chart rather than used as vertical-axis labels. The horizontal axis shows categories and the vertical axis shows numbers."},{"text":"On a usual bar chart, the horizontal axis shows bar heights and the vertical axis shows numbers.","correct":false,"explanation":"Bar heights are read using the vertical scale, not listed on the horizontal axis. The horizontal axis shows categories and the vertical axis shows numbers."}]},{"id":"d8719a18-02a9-c1ad-3079-9894eee67417","cardType":"basic","points":2,"front":"Why should you check the vertical scale before reading a bar?","back":"It may increase by more than 1.","mcqOptions":[{"text":"It may increase by more than 1.","correct":true,"explanation":"Consecutive marks on the vertical axis do not always differ by one. Checking the scale prevents a bar’s height from being read as the wrong value."},{"text":"It always increases by exactly 1.","correct":false,"explanation":"Assuming every scale rises in ones is a common reading error. The vertical scale may increase by more than 1 between consecutive marks."},{"text":"It shows which bar is widest.","correct":false,"explanation":"The vertical scale is used to read bar values, not widths. It must be checked because consecutive marks may increase by more than 1."},{"text":"It determines the order of the categories.","correct":false,"explanation":"Category order is normally shown along the horizontal axis, not determined by the vertical scale. The scale needs checking because it may rise by more than 1."}]},{"id":"ee455e12-1cb8-74e2-7dde-4365c8b43c1b","cardType":"basic","points":1,"front":"A vertical scale is labelled 0, 2, 4, 6, 8. What is each labelled step worth?","back":"2.","mcqOptions":[{"text":"2.","correct":true,"explanation":"The difference between consecutive labels is $2$, as shown by $2-0=2$ and $4-2=2$. Therefore, each labelled step is worth 2."},{"text":"1.","correct":false,"explanation":"Counting each labelled jump as one ignores the numbers printed on the scale. Consecutive labels differ by $2$, so each labelled step is worth 2."},{"text":"4.","correct":false,"explanation":"Using $4$ confuses two labelled steps with one: moving from 0 to 4 crosses two steps. A single labelled step is worth 2."},{"text":"8.","correct":false,"explanation":"The value 8 is the highest label shown, not the value of one step. Consecutive labels differ by 2, so each step is worth 2."}]},{"id":"2da5cd25-98df-5724-e8f5-f68df866e47a","cardType":"basic","points":1,"front":"With a scale of 1°C per unit, what height should an October bar for 15°C reach?","back":"15°C.","mcqOptions":[{"text":"15°C.","correct":true,"explanation":"At 1°C per unit, a temperature of 15°C corresponds directly to a height of 15 units. The bar should therefore reach 15°C on the scale."},{"text":"14°C.","correct":false,"explanation":"This is one unit too low, usually from stopping before the fifteenth scale interval. At 1°C per unit, 15°C requires a height of 15 units."},{"text":"16°C.","correct":false,"explanation":"This is one unit too high, usually from counting both zero and the first interval. At 1°C per unit, the bar should reach 15°C."},{"text":"150°C.","correct":false,"explanation":"Multiplying by 10 incorrectly treats each unit as 10°C. Since the scale is 1°C per unit, a 15°C bar should reach 15°C."}]},{"id":"6e0c9cf6-d078-9058-2686-d4a551e43d35","cardType":"cloze","points":null,"front":"The range is the [ ] minus the [ ].","back":"The range is the biggest value minus the smallest value.","mcqOptions":[{"text":"The range is the biggest value minus the smallest value.","correct":true,"explanation":"The range measures the full spread of a data set. It is calculated by subtracting the smallest observed value from the biggest observed value."},{"text":"The range is the smallest value minus the biggest value.","correct":false,"explanation":"This reverses the subtraction and would produce a negative result when the values differ. The range is the biggest value minus the smallest value."},{"text":"The range is the biggest value minus the second-smallest value.","correct":false,"explanation":"Using the second-smallest value ignores part of the data’s spread. The range uses both extremes: the biggest value minus the smallest value."},{"text":"The range is the total value minus the smallest value.","correct":false,"explanation":"The total is used when finding a mean, not a range. To measure the full spread, subtract the smallest value from the biggest value."}]},{"id":"bbce9f57-055e-a22c-218e-11005c71614b","cardType":"basic","points":1,"front":"Temperatures are 6°C, 8°C, 12°C, 17°C and 20°C. What is the range?","back":"14°C.","mcqOptions":[{"text":"14°C.","correct":true,"explanation":"The highest temperature is 20°C and the lowest is 6°C. Subtracting the lowest from the highest gives a range of $20-6=14$°C."},{"text":"12°C.","correct":false,"explanation":"This uses 8°C rather than the actual minimum of 6°C. The range must use both extremes, giving $20-6=14$°C."},{"text":"26°C.","correct":false,"explanation":"Adding the highest and lowest temperatures does not calculate the range. Subtract the minimum from the maximum instead: $20-6=14$°C."},{"text":"8°C.","correct":false,"explanation":"This subtracts the middle value, 12°C, from 20°C and ignores the minimum. The range uses the smallest value: $20-6=14$°C."}]},{"id":"b047b7c1-a8a7-1b26-c19e-8733e32cd111","cardType":"basic","points":2,"front":"Why is using the last bar minus the first bar unreliable for the range?","back":"Range uses the biggest and smallest values.","mcqOptions":[{"text":"Range uses the biggest and smallest values.","correct":true,"explanation":"The range measures the full spread of the data, so it is calculated by subtracting the smallest value from the biggest value, regardless of bar order."},{"text":"Range uses the first and last values.","correct":false,"explanation":"This assumes the bars are arranged in numerical order, which they may not be. The range uses the biggest and smallest values in the entire data set."},{"text":"Range uses the tallest and shortest bars.","correct":false,"explanation":"Bar heights may represent frequencies rather than the data values themselves. The range is found from the biggest and smallest values, not automatically from bar heights."},{"text":"Range uses the most common and least common values.","correct":false,"explanation":"This confuses range with frequency. How often values occur does not determine the range, which is the difference between the biggest and smallest values."}]},{"id":"9af23752-994a-7d6f-0716-be31f405a3cc","cardType":"cloze","points":null,"front":"A grouped bar chart has [ ] next to each other for each category.","back":"A grouped bar chart has two or more bars next to each other for each category.","mcqOptions":[{"text":"two or more bars","correct":true,"explanation":"Grouped bar charts place two or more bars beside one another within each category, allowing the values for different groups to be compared directly."},{"text":"one continuous bar","correct":false,"explanation":"A single continuous bar does not display separate groups side by side. A grouped bar chart has two or more bars next to each other for each category."},{"text":"two or more sectors","correct":false,"explanation":"Sectors are used in pie charts, not grouped bar charts. Each category in a grouped bar chart contains two or more separate bars."},{"text":"several stacked sections","correct":false,"explanation":"Stacked sections describe a stacked bar chart, where values share one bar. A grouped bar chart instead places two or more separate bars next to each other."}]},{"id":"d851a499-1907-3a69-4232-7e79614b22ae","cardType":"basic","points":1,"front":"In a grouped bar chart, why is a key needed?","back":"It shows which colour, shading or pattern belongs to each group.","mcqOptions":[{"text":"It shows which colour, shading or pattern belongs to each group.","correct":true,"explanation":"Each group is represented using a particular visual style. The key links every colour, shading or pattern to the group it represents."},{"text":"It shows which bar height or scale belongs to each group.","correct":false,"explanation":"Bar heights are read using the vertical scale rather than the key. The key identifies which colour, shading or pattern represents each group."},{"text":"It shows which category label or number belongs to each group.","correct":false,"explanation":"Categories and numbers are normally displayed on the chart’s axes. The key explains which colour, shading or pattern has been assigned to each group."},{"text":"It shows which frequency, range or mode belongs to each group.","correct":false,"explanation":"A key does not calculate statistical measures or state frequencies. It matches each group with its colour, shading or pattern so the bars can be identified."}]},{"id":"a13e2081-e3b1-8fc8-24bb-22b4aebd488f","cardType":"basic","points":1,"front":"Aisha ran 4 miles and Ben ran 7 miles. How much further did Ben run?","back":"3 miles.","mcqOptions":[{"text":"3 miles.","correct":true,"explanation":"The difference is found by subtracting Aisha’s distance from Ben’s distance: $7-4=3$. Therefore, Ben ran 3 miles further."},{"text":"11 miles.","correct":false,"explanation":"Adding $4+7$ gives the total distance both people ran, not how much further Ben ran. Subtracting gives $7-4=3$ miles."},{"text":"4 miles.","correct":false,"explanation":"This repeats Aisha’s distance instead of finding the difference. Ben’s extra distance is calculated using $7-4=3$, so he ran 3 miles further."},{"text":"28 miles.","correct":false,"explanation":"Multiplying the two distances does not measure how much further Ben ran. The required comparison is subtraction: $7-4=3$ miles."}]},{"id":"99d14a31-fae2-1b11-daa3-45c91273c2e2","cardType":"basic","points":1,"front":"Maya has run 22 miles and Liam has run 27 miles. Liam will not run again. How many miles must Maya run to match him?","back":"5 miles.","mcqOptions":[{"text":"5 miles.","correct":true,"explanation":"Maya must close the difference between 22 miles and 27 miles. Subtracting gives $27-22=5$, so she must run another 5 miles."},{"text":"49 miles.","correct":false,"explanation":"Adding $22+27$ finds the combined distance, not the extra distance Maya needs. She must cover the difference, which is $27-22=5$ miles."},{"text":"27 miles.","correct":false,"explanation":"This uses Liam’s total as the additional distance Maya must run. Maya already has 22 miles, so she needs only $27-22=5$ more miles."},{"text":"6 miles.","correct":false,"explanation":"This is an off-by-one subtraction error. Counting from 22 up to 27 gives five steps, so Maya must run exactly 5 more miles."}]},{"id":"16d22990-1067-7a9b-9ab4-46b76bd27a63","cardType":"cloze","points":null,"front":"Frequency means how many [ ] something happens.","back":"Frequency means how many times something happens.","mcqOptions":[{"text":"times","correct":true,"explanation":"Frequency is the number of times an event or value occurs. For example, a frequency of 6 means that it happened six times."},{"text":"categories","correct":false,"explanation":"Categories are the groups into which data is organised, not the number of occurrences. Frequency means how many times something happens."},{"text":"groups","correct":false,"explanation":"Groups can be used to organise or compare data, but they do not define frequency. Frequency is the number of times something occurs."},{"text":"days","correct":false,"explanation":"Days could be a unit in a particular data set, but frequency is not limited to time. It means the number of times something happens."}]},{"id":"c9f56ccd-c63f-7025-d430-0f01dfa2f9da","cardType":"basic","points":1,"front":"On a frequency bar chart, how do you identify the mode?","back":"Choose the category with the tallest bar.","mcqOptions":[{"text":"Choose the category with the tallest bar.","correct":true,"explanation":"The mode is the category occurring most frequently. On a frequency bar chart, the greatest frequency is represented by the tallest bar."},{"text":"Choose the category with the shortest bar.","correct":false,"explanation":"The shortest bar represents the lowest frequency, not the mode. The modal category has the greatest frequency and therefore the tallest bar."},{"text":"Choose the category with the first bar.","correct":false,"explanation":"A bar’s position does not determine whether its category is the mode. The mode is identified by finding the category with the tallest bar."},{"text":"Choose the category with the last bar.","correct":false,"explanation":"The final category is not necessarily the most frequent one. The modal category is shown by whichever bar is tallest on the chart."}]},{"id":"c9c4af9a-85f5-0403-f89b-1976af8f79d3","cardType":"basic","points":1,"front":"A goals frequency chart shows 0 goals: 5, 1 goal: 9, 2 goals: 7, 3 goals: 4. What is the modal number of goals?","back":"1 goal.","mcqOptions":[{"text":"1 goal.","correct":true,"explanation":"The mode is the result with the highest frequency. One goal occurred 9 times, which is more frequent than 0, 2 or 3 goals."},{"text":"0 goals.","correct":false,"explanation":"Zero goals has a frequency of 5, but this is not the greatest frequency. One goal has the highest frequency of 9, so it is the mode."},{"text":"2 goals.","correct":false,"explanation":"Two goals occurred 7 times, which is less than the frequency of 9 for one goal. Therefore, the modal number is 1 goal."},{"text":"3 goals.","correct":false,"explanation":"Three goals has the lowest frequency, occurring only 4 times. The highest frequency is 9 for one goal, making 1 goal the mode."}]},{"id":"a17e9e06-9796-5732-c031-9d5f89a66f20","cardType":"basic","points":1,"front":"If a team scored 3 goals in 4 matches, how many goals is that in total?","back":"12 goals.","mcqOptions":[{"text":"12 goals.","correct":true,"explanation":"The team scored 3 goals in each of 4 matches, so multiplying $3 \\times 4$ gives a total of 12 goals."},{"text":"7 goals.","correct":false,"explanation":"Adding 3 goals and 4 matches mixes different quantities and gives 7. The total is found by multiplying $3 \\times 4$, giving 12 goals."},{"text":"9 goals.","correct":false,"explanation":"This accounts for only three of the four matches. Multiplying 3 goals per match by all 4 matches gives $3 \\times 4 = 12$ goals."},{"text":"16 goals.","correct":false,"explanation":"This incorrectly uses 4 goals for each of the 4 matches. The stated rate is 3 goals per match, so the total is 12 goals."}]},{"id":"a1a97e87-8ace-037b-0426-05edba1a1df6","cardType":"cloze","points":null,"front":"To find a total from a frequency bar chart, multiply each [ ] by its [ ], then add.","back":"To find a total from a frequency bar chart, multiply each value by its frequency, then add.","mcqOptions":[{"text":"To find a total from a frequency bar chart, multiply each value by its frequency, then add.","correct":true,"explanation":"Each value contributes to the total once for every time it occurs. Therefore, multiplying each value by its frequency and adding the products gives the overall total."},{"text":"To find a total from a frequency bar chart, multiply each frequency by its frequency, then add.","correct":false,"explanation":"Squaring each frequency ignores the values represented by the bars. The correct method is to multiply each value by its frequency, then add all the products."},{"text":"To find a total from a frequency bar chart, multiply each value by its cumulative frequency, then add.","correct":false,"explanation":"Cumulative frequencies are running totals, so using them repeatedly overcounts the data. Each value must instead be multiplied by its ordinary frequency before the products are added."},{"text":"To find a total from a frequency bar chart, multiply each class width by its frequency density, then add.","correct":false,"explanation":"Class width and frequency density are used to recover frequencies from histograms, not totals from frequency bar charts. Here, multiply each value by its frequency, then add."}]},{"id":"729da605-49a2-a27d-c21a-4ca76994f5db","cardType":"basic","points":2,"front":"A team scored 0 goals in 3 matches, 1 in 5 matches, 2 in 4 matches, and 3 in 2 matches. What was the total number of goals?","back":"19 goals.","mcqOptions":[{"text":"19 goals.","correct":true,"explanation":"Weighting each score by its frequency gives $(0 \\times 3) + (1 \\times 5) + (2 \\times 4) + (3 \\times 2) = 19$ goals."},{"text":"14 goals.","correct":false,"explanation":"Adding $3+5+4+2$ counts the number of matches, not the goals scored. Weighting each score by its frequency gives a total of 19 goals."},{"text":"20 goals.","correct":false,"explanation":"This is an arithmetic slip when adding the weighted scores. The products are 0, 5, 8 and 6, which sum to 19 goals."},{"text":"22 goals.","correct":false,"explanation":"This overcounts the goals by failing to match each score with its correct frequency. The correct calculation is $0+5+8+6=19$ goals."}]},{"id":"3a203d76-92e7-00fa-ddfd-5d05c8dcf0db","cardType":"basic","points":2,"front":"Why is adding only the frequencies wrong when finding total goals?","back":"Frequencies count matches, not total goals.","mcqOptions":[{"text":"Frequencies count matches, not total goals.","correct":true,"explanation":"A frequency records how many matches produced each score. Adding the frequencies therefore gives the number of matches, while total goals require each score to be multiplied by its frequency."},{"text":"Frequencies count total goals, not matches.","correct":false,"explanation":"This reverses the meaning of frequency. Frequencies count how many matches had each score, so adding them gives matches; total goals require multiplying scores by frequencies."},{"text":"Each frequency already includes the goals scored.","correct":false,"explanation":"A frequency contains only the number of occurrences, not the score attached to them. Each score must be multiplied by its frequency to find its contribution to total goals."},{"text":"Adding frequencies counts each match twice.","correct":false,"explanation":"Adding frequencies counts each match once, not twice, but it still gives only the number of matches. Total goals come from multiplying each score by its frequency."}]},{"id":"bb3556ea-0ff9-45b3-22c0-4fb926a71ced","cardType":"cloze","points":null,"front":"Tallies are usually grouped in [ ].","back":"Tallies are usually grouped in fives.","mcqOptions":[{"text":"fives","correct":true,"explanation":"Tallies are grouped in fives because the fifth stroke crosses the previous four, making larger frequencies quicker and easier to count accurately."},{"text":"tens","correct":false,"explanation":"Groups of ten would be harder to recognise and count quickly. Standard tally notation groups marks in fives, with the fifth mark crossing the first four."},{"text":"threes","correct":false,"explanation":"Groups of three are not the standard tally convention and make larger totals less efficient to read. Tallies are normally arranged in recognisable groups of five."},{"text":"pairs","correct":false,"explanation":"Pairing tally marks would create many small groups and slow down counting. Tallies are conventionally grouped in fives so totals can be identified quickly."}]},{"id":"1946f3f8-dde5-8fc6-489d-dfe53b402b36","cardType":"basic","points":1,"front":"In the list Blue, Red, Blue, Black, Blue, Red, White, Black, Blue, White, what is the frequency of Blue?","back":"4.","mcqOptions":[{"text":"4.","correct":true,"explanation":"Blue appears in the first, third, fifth and ninth positions in the list. Counting these four occurrences gives Blue a frequency of 4."},{"text":"3.","correct":false,"explanation":"This misses one occurrence of Blue. Blue appears in the first, third, fifth and ninth positions, so its frequency is 4."},{"text":"5.","correct":false,"explanation":"This includes one item that is not Blue, possibly confusing Blue with Black. There are exactly four occurrences of Blue in the list."},{"text":"6.","correct":false,"explanation":"This likely combines the frequencies of Blue and Black. Blue occurs four times, while Black occurs twice, so Blue’s frequency alone is 4."}]},{"id":"afb8d459-56d0-1115-d0a1-1b6e716f999a","cardType":"cloze","points":null,"front":"Bars in a bar chart should have [ ] and [ ] between them.","back":"Bars in a bar chart should have equal widths and clear gaps between them.","mcqOptions":[{"text":"Bars in a bar chart should have equal widths and clear gaps between them.","correct":true,"explanation":"Equal widths prevent visual distortion, while clear gaps show that the categories are separate. These features make a bar chart accurate and easy to interpret."},{"text":"Bars in a bar chart should have equal widths and no gaps between them.","correct":false,"explanation":"Bars without gaps suggest continuous data, as in a histogram. A bar chart represents separate categories, so its equal-width bars should have clear gaps between them."},{"text":"Bars in a bar chart should have different widths and clear gaps between them.","correct":false,"explanation":"Different widths can exaggerate some categories and make comparisons misleading. Bar-chart bars should have equal widths as well as clear gaps between the separate categories."},{"text":"Bars in a bar chart should have different widths and no gaps between them.","correct":false,"explanation":"This confuses a bar chart with features associated with histograms and also distorts comparisons. Bar-chart bars should have equal widths and clear gaps between categories."}]},{"id":"50eb3da3-cdae-cc07-3388-c224f470dad9","cardType":"basic","points":1,"front":"What is wrong with a vertical scale labelled 0, 5, 12, 20, 30?","back":"The scale is uneven.","mcqOptions":[{"text":"The scale is uneven.","correct":true,"explanation":"The intervals are 5, 7, 8 and 10 rather than a constant amount. A numerical axis must increase by equal values at equally spaced points."},{"text":"The scale starts at zero.","correct":false,"explanation":"Starting at zero is not the problem and is often appropriate for a bar chart. The error is that the intervals between labels are unequal."},{"text":"The scale has too many labels.","correct":false,"explanation":"Five labels are not excessive for an axis. The actual problem is that the increases are 5, 7, 8 and 10, so the scale is uneven."},{"text":"The scale is increasing.","correct":false,"explanation":"A vertical scale should normally increase upwards, so increasing values are appropriate. The fault is that the values do not rise in equal intervals."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Unit 1"},"heading":"Bar Charts","title":"Bar Charts Flashcards","topbar":{"backHref":"/gcse/maths/wjec/flashcards"},"topicSidebar":"$L37"}]}],"topicId":"5d3ee263-685e-8811-0599-eb74d1d57c66","walled":"$L38"}],"$L39","$L3a"]