AQA · Mathematics · 8300
GCSE Maths: Graphs: cumulative frequency (draw)
Statistics · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions and answers for Graphs: cumulative frequency (draw) (Corbettmaths Video 153), 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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How do you find the median from a cumulative frequency graph?
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Find the value at half the total frequency (n/2) on the cumulative frequency axis, then read across and down to find the corresponding data value.
What is the first step in drawing a cumulative frequency graph?
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Complete a cumulative frequency table by adding up frequencies progressively (running total) for each class interval.
On a box plot, what does the line inside the box represent?
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The median of the data set.
The ? measures the spread of the middle 50% of the data.
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interquartile range
How do you estimate the lower quartile (Q1) from a cumulative frequency graph?
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Find the value at one quarter of the total frequency (n/4) on the cumulative frequency axis, then read across and down.
How do you estimate the upper quartile (Q3) from a cumulative frequency graph?
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Find the value at three quarters of the total frequency (3n/4) on the cumulative frequency axis, then read across and down.
How do you estimate how many data values fall below a specific threshold using a cumulative frequency graph?
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Find the threshold value on the horizontal axis, read up to the curve, then across to the cumulative frequency axis to read off the number.
What five values are needed to draw a box plot?
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Minimum, lower quartile (Q1), median, upper quartile (Q3), and maximum.
How do you calculate the range of a data set from a box plot?
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Subtract the minimum value from the maximum value (Range = Maximum - Minimum).
How do you find the interquartile range from a cumulative frequency graph?
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Subtract the lower quartile value (at 25% of total frequency) from the upper quartile value (at 75% of total frequency).
What relationship is stated between range and interquartile range in the supermarket employee survey?
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The range is twice the interquartile range.
If 40% of students spent less than X minutes revising, at what cumulative frequency value on a graph of 75 students would you find X?
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At cumulative frequency 30 (because 40% of 75 = 30).
If 20% of students spent longer than Y minutes revising, at what cumulative frequency value on a graph of 75 students would you find Y?
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At cumulative frequency 60 (because 80% of 75 = 60, since 20% spent longer means 80% spent less).
What percentage of students scored more than the upper quartile mark?
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25%. The upper quartile is at the 75th percentile, so 25% score above it.
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), while the range is sensitive to them.
What fraction of employees take between the median and upper quartile travel time?
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One quarter (25%). The median is at 50% and the upper quartile is at 75%.
What is a cumulative frequency graph used to show?
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How many data points lie at or below each value in a distribution.
On a cumulative frequency graph, what does the y-axis represent?
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The cumulative frequency (running total of data points at or below each value).
If a cumulative frequency graph shows 80 boys scored 40 marks or less out of 100 total, how many scored over 40?
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20 boys (100 - 80 = 20).
What feature on a cumulative frequency graph indicates a steeper rate of increase in data?
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A steeper slope on the curve indicates more data points are concentrated in that score range.
When comparing two cumulative frequency graphs, what does it mean if one graph is consistently higher than the other?
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The group with the higher graph has more lower scores (more of their data lies at or below each value).
What does the maximum value on the cumulative frequency axis represent?
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The total number of data points in the dataset.
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