AQA · Mathematics · 8300
GCSE Maths: Graphs: box plots (compare)
Statistics · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise, practice questions and answers for Graphs: box plots (compare) (Corbettmaths Video 150), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What are the five key values needed to draw a box plot?
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Minimum, lower quartile, median, upper quartile, and maximum.
How do you calculate the interquartile range (IQR) from a box plot?
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Upper quartile minus lower quartile.
How do you calculate the range from a box plot?
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Maximum value minus minimum value.
What percentage of data values lie within the box (between the quartiles) of a box plot?
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50% (the middle 50% of the data).
What percentage of data values lie below the lower quartile in a box plot?
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25%
What percentage of data values lie above the upper quartile in a box plot?
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25%
When comparing two box plots, what does a larger interquartile range indicate?
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Greater spread or variability in the middle 50% of the data.
The ? is the line inside the box of a box plot.
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median
What percentage of data values lie below the median in a box plot?
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50%
On a cumulative frequency graph, what value corresponds to the median?
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The median corresponds to the value at 50% of the cumulative frequency (i.e., n/2, where n is the total number of data points).
On a cumulative frequency graph for n data points, at what cumulative frequency value is the upper quartile (Q3) found?
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At 3n/4 (75% of the total cumulative frequency).
What percentage of students scored more than the upper quartile mark in any distribution?
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25%. The upper quartile marks the point where 75% scored below, so 25% scored above.
Why is the interquartile range often a better measure of spread than the range?
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The IQR is not affected by extreme values (outliers), whereas the range depends entirely on the minimum and maximum values.
When comparing two distributions using box plots, what two aspects should you typically comment on?
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Central tendency (e.g., median) and spread (e.g., range or interquartile range).
If 20% of students spent longer than Y minutes revising, what percentile does Y represent?
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The 80th percentile. If 20% spent longer, then 80% spent Y minutes or less.
How do you estimate the probability of a value falling within a specific range using a cumulative frequency graph?
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Read the cumulative frequencies at both boundary values from the graph, subtract the lower from the higher to find the count in that range, then divide by the total number of data points.
When finding a ratio of counts from different ranges on a cumulative frequency graph, what operation gives you the number in each category?
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Subtract consecutive cumulative frequencies. For example, if you want counts for ranges A, B, and C, subtract: (CF at end of A), (CF at end of B minus CF at end of A), (CF at end of C minus CF at end of B).
How do you estimate the probability that both of two independent random selections meet a condition using cumulative frequency graphs?
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Find the probability for each selection separately from their respective graphs, then multiply the two probabilities together.
How do you estimate the number of data points above a threshold value using a cumulative frequency graph?
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Read the cumulative frequency at the threshold from the graph, then subtract that value from the total number of data points.
What percentage of a dataset lies between the median and the upper quartile?
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25% (one quarter). The median is at the 50th percentile and the upper quartile is at the 75th percentile.
On a cumulative frequency graph with n data points, the lower quartile is found at the ? cumulative frequency position.
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25%
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