Question

The rainfall (in mm) in a city on $7$ days of a certain week was recorded as follows. (i) Find the range of rainfall in the above data. (ii) Find the mean rainfall for the week. (iii) On how many days was the rainfall less than the mean rainfall.

Day	Mon	Tue	Wed	Thurs	Fri	Sat	Sun
Rainfall(in mm)	$0.0$	$12.2$	$2.1$	$0.0$	$20.5$	$5.5$	$1.0$

Answer 1

Step 1. Find the range.

From the given data

Range of rainfall $=$ Highest rainfall $–$ Lowest rainfall

$$\begin{gathered} =20.5–0.0 \\ =20.5\mathrm{mm} \end{gathered}$$

Step 2. Calculate the mean.

$$\begin{gathered} \mathrm{Mean}\mathrm{of}\mathrm{rainfall}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{all}\mathrm{observations}}{\mathrm{Number}\mathrm{of}\mathrm{observation}} \\ =\frac{(0.0+12.2+2.1+0.0+20.5+5.5+1.0)}{7} \\ =\frac{41.3}{7} \\ =5.9\mathrm{mm} \end{gathered}$$

Step 3. Find the number of days.

From the table we observe that for five days the rainfall was less than average.

Monday, Wednesday, Thursday, Saturday and Sunday the rainfall was less than the average rainfall.

Hence,

(i).Range of rainfall is $20.5\mathrm{mm}$

(ii).Mean rainfall for the week is $5.9\mathrm{mm}$

(iii) For five days was the rainfall less than the mean rainfall.