Question

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

Day	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Rainfall (in mm)	$0.0$	$12.2$	$2.1$	$0.0$	$20.5$	$5.3$	$1.0$

On how many days was the rainfall less than the mean rainfall?

Answer 1

In this question, we have to find out the correct option from the given particulars.
We need to first consider the definition of mean of a set of data then using the formula of mean we can calculate the mean rainfall of the given particular.
The mean (or average) of observations, is the sum of the values of all the observations divided by the total number of observations.
Then we need to find out the days in which it is less than mean rainfall and calculating the number of days will give the required solution.

Complete step-by-step solution:
It is given that, the rainfall (in mm) in a city on $7$ days of a certain week was recorded as follows:

Day	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Rainfall (in mm)	$0.0$	$12.2$	$2.1$	$0.0$	$20.5$	$5.3$	$1.0$

We need to find out the number of days in which the rainfall was less than the mean rainfall.
Mean rainfall is given by dividing the total rainfall of the given data by the number of days.
Here, the total rainfall in the city is
$\Rightarrow \left( {0.0 + 12.2 + 2.1 + 0.0 + 20.5 + 5.5 + 1.0} \right)$
Adding the terms,
$\Rightarrow 41.3$
By using the formula for mean rainfall we get,
Mean rainfall =Total rainfall/the number of days.
$\Rightarrow \dfrac{{41.3}}{7}$
Hence,
$\Rightarrow 5.9$
Hence we get, the rainfall (in mm) less than mean rainfall are $0.0$,$2.1$,$0.0$,$5.3$,$1.0$.

Therefore on $5$ days the rainfall was less than the mean rainfall.

Note: We have known that there are several kinds of mean in mathematics, especially in statistics. For a data set, the arithmetic mean, also called the expected value or average, is the central value of a discrete set of numbers specifically, the sum of the values divided by the number of values.
m = Sum of the terms/number of terms.