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GCSE cumulative frequency questions: graph reading drill

The GCSE cumulative frequency drill has 6 practice questions, each with a worked answer.

Finishing times of 80 runners
Time, tt (minutes)FrequencyCumulative frequency
0<t≤100 < t \le 1044
10<t≤2010 < t \le 201216
20<t≤3020 < t \le 302440
30<t≤4030 < t \le 402262
40<t≤5040 < t \le 501274
50<t≤6050 < t \le 60680
Cumulative frequency graph
010203040506001020304050607080Time (minutes)Cumulative frequency

Estimate the median finishing time.

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Questions people ask

How do you find the median from a cumulative frequency graph?

Halve the total frequency, go across from that value on the cumulative frequency axis to the graph, then down to the horizontal axis. For 80 values, read across from 40.

How do you find the interquartile range?

Read the lower quartile at a quarter of the total and the upper quartile at three quarters, then subtract: upper quartile minus lower quartile.

Where do you plot the points?

At the upper end of each class, against the running total. The point for 20 < t ≤ 30 goes at t = 30.

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How we work this out

What it does

Read the median, quartiles and percentiles from a cumulative frequency graph, then check why each one is an estimate.

Edexcel GCSE Maths Higher: drawing and reading cumulative frequency graphs, quartiles, interquartile range and percentiles. The data and questions are original.

Method

  1. The graph is drawn from the table: each point sits at the upper end of its class, joined with straight lines.
  2. Readings use straight-line interpolation between plotted points, so the key is the value a careful reading gives.