Given :- The standard deviation for the set of numbers 1,4,5,7,8, is 2.45 nearly. If 10 is added TOEACH number then new standard deviation ?

Solution :-

→ given set of numbers = 1, 4, 5 , 7 , 8 = Total 5 .

→ sum of numbers = 1 + 4 + 5 + 7 + 8 = 25

So,

→ MEAN of given numbers = (sum of numbers) / (Total number)

→ mean = (25 / 5) = 5 .

Now, given that, 10 is added in each number .

So,

→ New set of numbers = 1+10, 4+10, 5+10 , 7+10 , 8+10 = 11, 14, 15, 17 , 18 = Total 5 .

→ sum of new numbers = 11 + 14 + 15 + 17 + 18 = 75

So,

→ mean of new numbers = (sum of numbers) / (Total number)

→ mean = (75 / 5) = 15 .

As, we can see now, The mean for the original set of numbers is 5 and for the new set of numbers is 15..

The change in the mean is 10 , which is equal to number we added in each number.

Now, we know that,

• In statistical terms the set is affected by the number which affects the mean.

Here, when we add the set of numbers by 10, the mean of the set ALSO gets affected by an increase of 10.

Therefore, we can conclude that,

Their will be no change in the standard deviation for the set of numbers .

Hence,

→ standard deviation of new numbers = Original standard deviation ≈ 2.45 . (Ans.)

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