Find the arithmetic mean of the five observations 14, 56, 23, 44, 23 where the assumed mean is given as 30.

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Solution

The correct option is B 32
Data given: 14, 56, 23, 44, 23

Assumed mean = 30

Arithmetic mean = $A s s u m e d m e a n + \frac{S u m o f t o t a l d e v i a t i o n s}{N u m b e r o f o b s e r v a t i o n s}$

$A r i t h m e t i c m e a n = A s s u m e d m e a n + \frac{Σ (x i - A)}{N}$

$A r i t m e t i c m e a n = 30 + \frac{(14 - 30) + (56 - 30) + (23 - 30) + (44 - 30) + (23 - 30)}{5} A r i t m e t i c m e a n = 30 + \frac{(- 16) + 26 + (- 7) + 14 + (- 7)}{5} A r i t h m e t i c m e a n = 30 + \frac{10}{5} A r i t h m e t i c m e a n = 30 + 2 = 32$

So, the arithmetic mean is 32.

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