AQA · Mathematics · 8300
GCSE Maths: Graphs: cumulative frequency (reading)
Statistics · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions and answers for Graphs: cumulative frequency (reading) (Corbettmaths Video 154), 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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On a cumulative frequency graph, how do you estimate the median?
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Find the value corresponding to n/2 on the cumulative frequency axis, where n is the total frequency.
What does the median represent on a box plot?
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The middle line inside the box, representing the value that divides the data in half.
How do you calculate the range from a box plot?
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Subtract the minimum value (leftmost point) from the maximum value (rightmost point).
How do you calculate the interquartile range?
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Subtract the lower quartile from the upper quartile (IQR = Q3 - Q1).
On a cumulative frequency graph, how do you estimate the upper quartile?
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Find the value corresponding to 3n/4 on the cumulative frequency axis, where n is the total frequency.
On a cumulative frequency graph, how do you estimate the lower quartile?
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Find the value corresponding to n/4 on the cumulative frequency axis, where n is the total frequency.
On a box plot, the ? is represented by the right edge of the box.
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upper quartile
What is the first step in constructing a cumulative frequency graph?
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Complete a cumulative frequency table by adding up frequencies progressively for each class interval.
How do you estimate the number of data values below a certain threshold using a cumulative frequency graph?
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Read the cumulative frequency value at the point on the graph corresponding to that threshold value.
What five values are needed to construct a box plot?
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Minimum, lower quartile, median, upper quartile, and maximum.
The lower quartile corresponds to the ? percentile in a cumulative frequency diagram.
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25th
If 40% of students spent less than X minutes revising, what cumulative frequency value would you use to find X from a graph of 75 students?
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30 students (40% of 75 = 0.4 × 75 = 30).
If 20% of students spent longer than Y minutes revising, what percentile does Y represent?
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The 80th percentile (100% - 20% = 80%).
What percentage of students scored more than the upper quartile mark?
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25%. The upper quartile is the 75th percentile, so 100% - 75% = 25% scored higher.
Why is the interquartile range a better measure of spread than the range?
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The interquartile range is not affected by extreme values (outliers), whereas the range is.
What proportion of data values lie within the interquartile range?
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The middle 50% of the data (from the 25th percentile to the 75th percentile).
To find the number of values between two data points on a cumulative frequency graph, what calculation do you perform?
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Subtract the cumulative frequency at the lower value from the cumulative frequency at the higher value.
How do you estimate the probability of a value falling within a certain range using a cumulative frequency graph?
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Find the number of values in that range (difference in cumulative frequencies), then divide by the total number of values.
On a cumulative frequency graph, how do you estimate the number of values above a certain threshold?
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Read the cumulative frequency at that threshold, then subtract from the total number of values.
What does a cumulative frequency graph plot on the y-axis?
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The running total of frequencies up to each value (or the number of data points below or equal to each value).
When comparing two cumulative frequency distributions, what two aspects should you typically compare?
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A measure of central tendency (like the median) and a measure of spread (like the range or interquartile range).
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