Question

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

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

By using the above table find the mean rainfall (in mm).

Answer 1

Hint: First find total rainfall (in mm) and then divide by number of days which is nothing but the mean rainfall (in mm).

Complete step-by-step answer:
As we know, the mean of certain independent quantities is the ratio of total sum of quantities and number of quantities.
Here the quantity is rainfall (in mm).
So Mean = $\dfrac{\text{total rainfall }\left( \text{in mm} \right)}{\text{total number of days}}$…..(1)
First we need to find total rainfall (in mm) = 0.0 + 12.2 + 2.1 + 0.0 + 20.5 + 5.5 + 1.0
Total rainfall (in mm) = $\dfrac{122}{10}$+ $\dfrac{21}{10}$+ $\dfrac{205}{10}$+ $\dfrac{55}{10}$+ $\dfrac{10}{10}$
Total rainfall (in mm) =$\dfrac{122\text{ }+\text{ }21\text{ }+\text{ }205\text{ }+\text{ }55\text{ }+\text{ }10}{10}$
We know that 122 + 21 + 205 + 55 + 10 = 413.
So by substituting the value, we get:
Total rainfall (in mm) = $\dfrac{413}{10}$
So, Total rainfall (in mm) = 41.3
Total number of days = 7.
Mean rainfall (in mm) = $\dfrac{41.3}{7}$
By multiplying and dividing by 10, we get:
Mean rainfall (in mm) = $\dfrac{413}{70}$
As 413 is written as:
413 = 59 $\times$7
By simplifying, we get:
Mean rainfall (in mm) = $\dfrac{59\times 7}{10\times 7}$
By cancelling 7, we get:
Mean rainfall (in mm) = $\dfrac{59}{10}$ = 5.9
So, the Mean rainfall (in mm) is 5.9mm.
$\therefore$The Mean rainfall (in mm) of a given city on 7 days of a certain week is 5.9mm.

Note: Students tend to confuse between mean and median. Mean is as said above, the total sum of quantities by number of quantities and whereas median is the quantity which occurs in the middle of the data collection.