AI generatedStatisticsGCSE Higher

Estimating an interquartile range

Estimating an interquartile range.

  • 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 interquartile range to 1 d..

Straight-line interpolation between class-boundary points.102051015200
Straight-line interpolation between class-boundary points.
Lower-quartile positionRead Q₁ from one quarter of the total frequency.
Upper-quartile positionRead Q₃ from three quarters of the total frequency.
Subtract Q₁ from Q₃. Keep the unrounded graph-interpolation values until the end.

Example 2

Estimate the interquartile range to 1 d..

Straight-line interpolation between class-boundary points.10203040506051015200
Straight-line interpolation between class-boundary points.
Lower-quartile positionRead Q₁ from one quarter of the total frequency.
Upper-quartile positionRead Q₃ from three quarters of the total frequency.
Subtract Q₁ from Q₃. Keep the unrounded graph-interpolation values until the end.

Your turn

Question 1

Estimate the interquartile range to 1 d..

Straight-line interpolation between class-boundary points.1020305101520250
Straight-line interpolation between class-boundary points.
Check answer
Lower-quartile positionRead Q₁ from one quarter of the total frequency.
Upper-quartile positionRead Q₃ from three quarters of the total frequency.
Subtract Q₁ from Q₃. Keep the unrounded graph-interpolation values until the end.
Question 2

Estimate the interquartile range to 1 d..

Straight-line interpolation between class-boundary points.1020304050605101520250
Straight-line interpolation between class-boundary points.
Check answer
Lower-quartile positionRead Q₁ from one quarter of the total frequency.
Upper-quartile positionRead Q₃ from three quarters of the total frequency.
Subtract Q₁ from Q₃. Keep the unrounded graph-interpolation values until the end.
Question 3

Estimate the interquartile range to 1 d..

Straight-line interpolation between class-boundary points.102030405101520250
Straight-line interpolation between class-boundary points.
Check answer
Lower-quartile positionRead Q₁ from one quarter of the total frequency.
Upper-quartile positionRead Q₃ from three quarters of the total frequency.
Subtract Q₁ from Q₃. Keep the unrounded graph-interpolation values until the end.
Question 4

Estimate the interquartile range to 1 d..

Straight-line interpolation between class-boundary points.10203040506051015200
Straight-line interpolation between class-boundary points.
Check answer
Lower-quartile positionRead Q₁ from one quarter of the total frequency.
Upper-quartile positionRead Q₃ from three quarters of the total frequency.
Subtract Q₁ from Q₃. Keep the unrounded graph-interpolation values until the end.
Question 5

Estimate the interquartile range to 1 d..

Straight-line interpolation between class-boundary points.10205101520250
Straight-line interpolation between class-boundary points.
Check answer
Lower-quartile positionRead Q₁ from one quarter of the total frequency.
Upper-quartile positionRead Q₃ from three quarters of the total frequency.
Subtract Q₁ from Q₃. Keep the unrounded graph-interpolation values until the end.
← All Statistics cardsReport a mistake