Question

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?​

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

$\textbf{Given:}$

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

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

$\textbf{To find:}$

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

$\textbf{Solution:}$

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

$\textbf{Sum of 29 observations}\,\mathrm{=29{\times}33=957}$

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

$\implies\textbf{Sum of 30 observations}\,\mathrm{=30{\times}34=1020}$

$\text{Now,}$

$\textbf{Value of 30 th observation}$

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

$\mathrm{=1020-957}$

$\mathrm{=63}$

$\textbf{Answer:}$

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

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