Question

Find the mean and median of all the multiples of 5 which lies in between 101 and 201​

Answer 1

The median is 150

The mean is 150

Step-by-step explanation:

The multiples of 5 between 101 and 201 are

105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195

These are arranged in ascending order

The number of terms = 19

Which is an odd number

Therefore, the median will be 10th term

Thus, median = 150

If sum of all the numbers is S

Then mean = S/19

Now the sequence is an AP with common difference 5

The sum of this AP

$S=\frac{n}{2}[\text{First term}+\text{Last term}]$

$S=\frac{19}{2}[105+195]$

$S=\frac{19\times 300}{2}$

$S=19\times 150$

Therefore mean = $\frac{19\times 150}{19}=150$

Hope this answer is helpful.

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Answer 2

Given that,

Multiples = 5

The multiples of 5 which lies in between 101 and 201​

105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195.

We know that,

First digit a = 105

difference d = 5

Last digit l = 195

We need to find the value of n

Using formula of AP series

$a_{n}=a+(n-1)d$

Put the value into the formula

$195=105+(n-1)\times5$

$195-105=(n-1)\times5$

$90=5n-5$

$5n=90+5$

$n=\dfrac{95}{5}$

$n=19$

We need to calculate the sum of the all number

Using formula of sum

$S_{n}=\dfrac{n}{2}(a+l)$

Put the value into the formula

$S_{n}=\dfrac{19}{2}(105+195)$

$S_{n}=2850$

We need to calculate the mean

Using formula of mean

$mean=\dfrac{S_{n}}{n}$

Put the value into the formula

$mean = \dfrac{2850}{19}$

$mean=150$

We know that,

The median is the middle digit in the series.

We need to find the median

Using formula of median

So, The median is 150.

Hence, The mean is 150 and median is 150.