IGCSE Mathematics (0580)

Averages and measures of spread

What this topic tests, the mistakes that cost marks, and one exam-style question worked through step by step.

Key ideas and common mistakes

For an odd number of ordered values, the median is the value at position (n + 1) ÷ 2.
Common mistake: A common mistake is to average the two middle values or miscount the position.
To find the mean from a frequency table, multiply each value by its frequency, sum these products, and divide by the total frequency.
Common mistake: Students often mistakenly average the values or frequencies alone instead of using this weighted method.
To read a value from a scatter diagram, locate the given value on the correct axis, find the corresponding plotted point, and then read the associated value from the other axis.
Common mistake: Students often mix up which axis represents which variable or misread the axes.
To plot a point from a data pair on a scatter diagram, match the first value to the horizontal axis and the second to the vertical axis.
Common mistake: Students often reverse the axes and plot (x, y) as (y, x) instead.
Identifying positive correlation means recognizing that as one variable increases, the other also increases.
Common mistake: Students often confuse this with negative correlation or no correlation if the points are not perfectly aligned.
The median in a box-and-whisker diagram is represented by the line inside the box, not by the ends of the box or whiskers.
Common mistake: Students often mistakenly choose the lower or upper quartile instead.

Find the median height.

Try it first, then show the working

Answer: 160 cm

26 exam-style questions on Averages and measures of spread, each marked to the scheme.