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

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 |

(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?

(i) Now,

We have to find the range of the given data.

And,

We know that,

Highest rainfall = 20.5mm

Lowest rainfall = 0.0mm

Thus,

Range = Highest value – Lowest value

Hence,

Range of the given data can be calculated as follows:

Range = highest rainfall – lowest rainfall

= 20.5 – 0.0

= 20.5 mm

(ii) Here,

We have to find the mean of the rainfall for the week

Now,

At first,

We’ll find the sum of all the observations

Thus,

Sum of all the observations = 0.0 + 12.2 + 2.1 + 0.0 + 20.5 + 5.5 + 1.0

= 41.3

Now,

Total number of observations = 7

Hence,

Mean rainfall =

=

= 5.9 mm

(iii) Here,

As per the question,

We have to find that,

The number of days when the rainfall was less than the mean rainfall

Hence,

We can observe that,

For total five days the rainfall was less than the mean rainfall

Now,

These days are as follows:

Monday, Wednesday, Thursday, Saturday and Sunday

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