Question

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

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

Answer 1

The Correct Option is D

To find the mean of the given 20 observations, we start by noting that the algebraic sum of deviations of these observations from 23 is given as 70. Using the formula for the mean and the property of deviations, we can derive a solution.

Let the observations be \(x_1, x_2, x_3, \ldots, x_{20}\).

The mean \(\bar{x}\) is calculated using the formula:

\(\displaystyle \bar{x} = \frac{\sum_{i=1}^{20} x_i}{20}\)

Given that the sum of deviations from 23 is 70, we express this as:

\(\displaystyle \sum_{i=1}^{20} (x_i - 23) = 70\)

Expanding the sum, we have:

\(\displaystyle \sum_{i=1}^{20} x_i - 20 \times 23 = 70\)

\(\displaystyle \sum_{i=1}^{20} x_i = 70 + 460\)

\(\displaystyle \sum_{i=1}^{20} x_i = 530\)

Now, substituting this back into the formula for the mean, we get:

\(\displaystyle \bar{x} = \frac{530}{20} = 26.5\)

The calculated mean is 26.5. The options provided do not include 26.5, so the correct answer is "None of these".