Plot points at the upper class boundary
A cumulative frequency point is plotted at the end of each class (the upper boundary), against the running total — never at the midpoint.
Read quartiles at n/2, n/4, 3n/4
On a cumulative frequency graph: median at , lower quartile at , upper quartile at ; go up to the curve, then across.
IQR is a subtraction
Interquartile range . A box plot shows min, LQ (lower quartile), median, UQ (upper quartile), max — range .
Drawn from real examiner reports.
Plotting at midpoints or drawing bars
Plotting cumulative frequency at the mid-interval value instead of the upper boundary, or drawing bars instead of a curve.
Reported on June 2024 Paper 2H (Q13) and Nov 2024 Paper 2H (Q13).
Adding the quartiles instead of subtracting
Giving UQ (upper quartile) + LQ (lower quartile) for the interquartile range rather than UQ − LQ.
June 2024 Paper 1HR (Q10): students added the quartiles rather than finding the difference.
Confusing the median with a quartile
Reading the lower quartile value when the median is asked for, or finding ¼ and ¾ of n rather than reading the curve.
June 2024 Papers 2H/1HR (Q13/Q10).
"More than X": subtract from the total
For "how many weigh more than X", read the cumulative frequency at X and subtract from the total (and give a whole number).
Nov/June 2024 Paper 2H (Q13d).
n/2 for a curve, (n+1)/2 for a list
On a cumulative frequency curve read the median at n/2, and the quartiles at n/4 and 3n/4. The (n+1)/2 position rule is only for a short ordered list — mixing the two costs the read-off marks.
Box edges are quartiles, not min/max
On a box plot the ends of the box are the lower and upper quartiles; the whisker ends are the minimum and maximum. Reading the box edges as the smallest and largest values gives a wrong range.
Show your read-off lines on the graph
Draw the construction lines up to the curve and across to the axis — they earn method marks even if the final read-off slips.
Mark n/4, n/2, 3n/4 before reading
Work out these three heights before you touch the curve, then draw across to the curve and down to the axis. Reading from the correct cumulative frequency values avoids picking the wrong quartile.
Sense-check LQ < median < UQ
The three quartiles must increase in order. If your lower quartile is not below the median, or the upper quartile not above it, you have read the graph at the wrong height — re-read.
Cumulative frequency is a running total. Plot each point at the upper boundary of the class against the running total, then join with a smooth curve.
To read statistics off the curve (with values), go up to the curve then across:
Formula for the interquartile range?
For the ordered data (which has values), find the median, the lower and upper quartiles, and the interquartile range.
