AI generatedStatisticsGCSE Higher

Estimating a median from cumulative frequency

Estimating a median from cumulative frequency.

  • Cumulative frequency is a running total. Plot it at the upper class boundary.
  • Read the median at N/2, Q₁ at N/4 and Q₃ at 3N/4.
  • The interquartile range is Q₃ − Q₁. Graph readings are estimates.

Example 1

Estimate the median from the graph, to 1 d..

Straight-line interpolation between class-boundary points.102051015200
Straight-line interpolation between class-boundary points.
Median positionStart halfway up the cumulative-frequency scale. Go across to the graph, then down to .

Example 2

Estimate the median from the graph, to 1 d..

Straight-line interpolation between class-boundary points.10203040506051015200
Straight-line interpolation between class-boundary points.
Median positionStart halfway up the cumulative-frequency scale. Go across to the graph, then down to .

Your turn

Question 1

Estimate the median from the graph, to 1 d..

Straight-line interpolation between class-boundary points.1020305101520250
Straight-line interpolation between class-boundary points.
Check answer
Median positionStart halfway up the cumulative-frequency scale. Go across to the graph, then down to .
Question 2

Estimate the median from the graph, to 1 d..

Straight-line interpolation between class-boundary points.1020304050605101520250
Straight-line interpolation between class-boundary points.
Check answer
Median positionStart halfway up the cumulative-frequency scale. Go across to the graph, then down to .
Question 3

Estimate the median from the graph, to 1 d..

Straight-line interpolation between class-boundary points.102030405101520250
Straight-line interpolation between class-boundary points.
Check answer
Median positionStart halfway up the cumulative-frequency scale. Go across to the graph, then down to .
Question 4

Estimate the median from the graph, to 1 d..

Straight-line interpolation between class-boundary points.10203040506051015200
Straight-line interpolation between class-boundary points.
Check answer
Median positionStart halfway up the cumulative-frequency scale. Go across to the graph, then down to .
Question 5

Estimate the median from the graph, to 1 d..

Straight-line interpolation between class-boundary points.10205101520250
Straight-line interpolation between class-boundary points.
Check answer
Median positionStart halfway up the cumulative-frequency scale. Go across to the graph, then down to .