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- Cumulative frequency and box plots
Cumulative frequency and box plots
Cumulative frequency graphs and box plots show how data is spread, and let you compare groups.
Cumulative frequency
A running total of the frequencies. Plot each total at the upper end of its group and join with a smooth curve.
Reading the graph
With n values:
Median: read across at n2.
Lower quartile (LQ): at n4. Upper quartile (UQ): at 3n4.
Interquartile range (IQR) = UQ − LQ
Median: read across at n2.
Lower quartile (LQ): at n4. Upper quartile (UQ): at 3n4.
Interquartile range (IQR) = UQ − LQ
Box plots and comparing
A box plot shows minimum, LQ, median, UQ and maximum.
To compare groups, compare an average (median) and a spread (IQR), in context.
To compare groups, compare an average (median) and a spread (IQR), in context.
For 80 values, the LQ is 23 and the UQ is 41. Find the IQR.
- IQR = UQ − LQ = 41 − 23
Answer: 18
Plot cumulative frequency at upper class boundaries. Median at n/2, quartiles at n/4 and 3n/4. IQR = UQ − LQ. Compare a median and an IQR, in context.
Check you have got it
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