Question

if mean of 29 onder various is 33 and on adding one more international the new mean becomes 34.what is the value of the 30th observation?

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Answer 1

Given :- if mean of 29 observations is 33 and on adding one more observation the new mean becomes 34. what is the value of the 30th observation ?

Solution :-

given that, mean of 29 observations is 33 .

So,

→ mean = (sum of observations) / (total number of observation)

→ 33 = (sum of observations) / 29

→ sum of observations = 33 * 29 = 957.

now, let us assume that, the new observation added is x.

Than,

→ sum of 30 observations = sum of 29 observations + new added observation = (957 + x).

given that, new mean becomes 34.

Therefore,

→ mean = (sum of observations) / (total number of observation)

→ 34 = (957+ x) /30

→ 34 * 30 = 957+x

→ x + 957 = 1020

→ x = 1020 - 957

→ x = 63. (Ans.)

Hence the value of the 30th observation is 63.

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Answer 2

$\underline{\textsf{Given:}}$

$\textsf{Mean of 29 observations is 33 and}$

$\textsf{on adding one more observation the new mean becomes 34}$

$\underline{\textsf{To find:}}$

$\textsf{Value of the 30th observation}$

$\underline{\textsf{Solution:}}$

$\textsf{Mean of 29 observations is 33}$

$\textsf{Sum of 29 observations}\,\mathsf{=29{\times}33=957}$

$\textsf{When adding one more observation, the mean becomes 34}$

$\implies\textsf{Sum of 30 observations}\,\mathsf{=30{\times}34=1020}$

$\textsf{Now,}$

$\textsf{Value of 30 th observation}$

$=\textsf{Sum of 30 observations}-\textsf{Sum of 29 observations}$

$\mathsf{=1020-957}$

$\mathsf{=63}$

$\underline{\textsf{Answer:}}$

$\textsf{Value of the 30 th observation is 63}$

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