Question

The rainfall (in mm) in a city on $7$ days of a certain week was recorded as follows:

$\begin{array}{cc}\text{Days}& \text{Rain fall (in mm)}\\ \text{Monday}& 0.0\\ \text{Tuesday}& 12.2\\ \text{Wednesday}& 2.1\\ \text{Thursday}& 0.0\\ \text{Friday}& 20.5\\ \text{Saturday}& 5.5\\ \text{Sunday}& 1.0\end{array}$

(i) Find the range of the 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.

Answer 1

Given data:

$\begin{array}{cc}\text{Days}& \text{Rain fall (in mm)}\\ \text{Monday}& 0.0\\ \text{Tuesday}& 12.2\\ \text{Wednesday}& 2.1\\ \text{Thursday}& 0.0\\ \text{Friday}& 20.5\\ \text{Saturday}& 5.5\\ \text{Sunday}& 1.0\end{array}$

(i)

Range $=$ Maximum value $-$ Minimum value

So, Range $=(20.5-0.0)mm$

$=20.5mm$

(ii)

Mean $\left(\overline{x}\right)=\frac{\text{Sum of all the observations}}{\text{Number of observations}}$

Since, in given data $7$ number of days.

Mean rainfall $=\frac{0.0+12.2+2.1+0.0+20.5+5.5+1.0}{7}$

$=\frac{41.3}{7}$

$=5.9$

Hence, Mean is $5.9mm$

(iii)

Since, Mean $=5.9mm$

Now by observing the data,

For $5$ days (i.e., Monday, Wednesday, Thursday, Saturday, Sunday), the rainfall was less than the average rainfall.

$\begin{array}{cc}\text{Days}& \text{Rain fall (in mm)}\\ \text{Monday}& 0.0\\ \text{Wednesday}& 2.1\\ \text{Thursday}& 0.0\\ \text{Saturday}& 5.5\\ \text{Sunday}& 1.0\end{array}$