Question

8. The mean of five numbers is 27. If one number is excluded, their mean is 25. Find the
excluded observation.
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Answer 1

Given :

• The mean of five numbers is 27.
• One number is excluded, their mean is 25.

To find :

• The excluded observation =?

Step-by-step explanation :

Firstly we have to find the sum of 5 numbers:

As We know that,

Mean of 5 numbers = 27

So, Sum of 5 numbers = 27 x 5 = 135

Now,

We have to find the sum of the 4 numbers:

So,

Mean of the 4 numbers = 25

Sum of the 4 numbers = 4 x 25 = 100

Now, the excluded observation = Sum of 5 numbers - Sum of 4 numbers.

= 135 - 100

= 35

Therefore, the excluded observation = 35.

Answer 2

★ QUESTION :

The mean of five numbers is 27. If one number is excluded, their mean is 25. Find the excluded observation.

GIVEN :

• The mean of five numbers = 27

• After excluding one number, we got here the mean = 25

TO FIND :

• The excluded observation = ?

STEP-BY-STEP EXPLAINATION :

➠ Mean of five numbers = 27 (GIVEN)

Here, now we will have to find the sum of five numbers, for finding the sum ; we will how how to multiply 5 and mean of 5 numbers.

➠ Sum = 5 × Mean of 5 numbers

Substituting the value as per the given formula :

➠ Sum = 5 × 27 = 135

Therefore, here we got the sum of 5 numbers as 135.

Now, we will have to find again the sum of 4 Numbers, so that we will able to find the excluded number.

➠ Mean of four numbers = 25 (GIVEN)

➠ Sum = 4 × mean of 4 numbers

➠ Sum = 4 × 25 = 100

Hence, here we got the sum 4 numbers as 100.

We will find here now, the excluded number :

➠ Excluded no. = Sum of 4 no's – Sum of 5 no's

substituting the given value as per the given formula :

⟹ Excluded no. = 135 - 100

⟹ Excluded no. = 35

Hence, we got here the excluded number / observation = 35