Question

If the algebraic sum of deviations of 20 observations measured from 23 is 70, what is the mean of these observations?

• A. 24
• B. 25
• C. 26
• D. None of these

Hint:

Use mean = assumed value + (sum of deviations / number of observations).

Answer 1

The Correct Option is D

Here is another way to reach 26.5, by rebuilding the actual total instead of using the shortcut formula directly.

Deviation of each observation $x_i$ from 23 is $d_i = x_i - 23$. Summing over all 20 observations, $\sum d_i = \sum x_i - 20 \times 23$.

We are told $\sum d_i = 70$, and $20 \times 23 = 460$. So $\sum x_i = 70 + 460 = 530$.

The mean is the total sum divided by the count: mean $= \frac{530}{20} = 26.5$.

Let's summarize:

• Total of all 20 observations: 530
• Mean: $\frac{530}{20} = 26.5$

Since 26.5 does not match 24, 25, or 26, option D, None of these, is correct.