Question

The standard deviation of 25 observations is 4 and their mean is 25 .if each observation is increased by 10 what are the new mean and ew standard deviation

Answer 1

ORIGINAL MEAN
=X1+X2+X3......X25/25
NEW MEAN
=(X1+10)+(X2+10).......(X25+10)/25
Split the terms
=X1+X2+X3.....+X25/25 +
10+10+10+10.....25 TIMES/25
=original mean +25(10)/25
=25+10
=35

Standard deviation will remain unchanged(Properties of Mean,variance,standard deviation)
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Answer 2

Given :- The standard deviation of 25 observations is 4 and their mean is 25 .if each observation is increased by 10 what are the new mean and ew standard deviation ?

Solution :-

we know that,

• Mean = (sum of observations)/(Total number of observations .

so,

→ 25 = (sum of observations) / 25

→ sum of observations = 25 * 25 = 625 .

now, given that, 10 is added in each observation .

then,

→ Total sum increased = 10 * 25 = 250 .

therefore,

→ New mean = (sum of observations)/(Total number of observations = (625 + 250) / 25 = (875/25) = 35 (Ans.)

Now, we know that,

• If a number is added to each number in a set of data, standard deviation will be unaltered. (since the spread of the data will be unchanged).

Hence, New standard deviation will be 4 .

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