Rainfall Records for the School
A class records daily rainfall in millimetres for one week: Monday 12, Tuesday 0, Wednesday 8, Thursday 15, Friday 5, Saturday 20, Sunday 10. The class wants to display this as a bar chart and to describe the 'typical' rainfall. One learner says the mean is the best description because it uses all the data. Another says the median is better. A third learner wants to know how spread out the rainfall was.
1. Calculate the mean, median, mode and range of the rainfall figures.
Read the worked answer
Data: 12, 0, 8, 15, 5, 20, 10.
Mean: sum = 12 + 0 + 8 + 15 + 5 + 20 + 10 = 70. There are 7 days, so mean = 70 ÷ 7 = 10 mm.
Median: order the values: 0, 5, 8, 10, 12, 15, 20. The middle (4th) value is 10 mm.
Mode: every value appears once, so there is no mode.
Range: highest − lowest = 20 − 0 = 20 mm.
2. Which measure best describes a typical day's rainfall here, and what does the range tell us? Justify your choice.
Read the worked answer
Here the mean and median are both 10 mm, so either gives the same 'typical' value. The mean uses all seven readings, which is a strength, but it can be pulled by extreme values. The median is resistant to extremes.
Since mean = median = 10 mm, there is no conflict, and 10 mm is a fair summary of a typical day.
The range is 20 mm (from 0 mm on Tuesday to 20 mm on Saturday). This shows the rainfall was quite variable: some days had no rain and one day had 20 mm. A single average hides this spread, so the range is important to report alongside the average.
3. The class decides to draw a bar chart. The tallest bar is 20 mm. If 1 cm on the chart represents 4 mm of rainfall, how tall should the Saturday bar be, and what is a sensible scale for the vertical axis?
Read the worked answer
Saturday rainfall is 20 mm. Using 1 cm = 4 mm, the bar height = 20 ÷ 4 = 5 cm.
Check other bars with the same scale: Monday 12 mm → 3 cm; Wednesday 8 mm → 2 cm; Thursday 15 mm → 3.75 cm; Friday 5 mm → 1.25 cm; Sunday 10 mm → 2.5 cm; Tuesday 0 mm → 0 cm.
A sensible vertical axis would go from 0 to 20 mm, marked in steps of 4 mm (0, 4, 8, 12, 16, 20), so each step is 1 cm on the chart. This keeps all bars readable and the Saturday bar at 5 cm fits within a reasonable chart height.