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

Step 1: Recall the assumed mean method.
When deviations are measured from an assumed value \(A\), the actual mean is \(A + \frac{\sum d_i}{n}\), where \(\sum d_i\) is the sum of deviations and \(n\) is the number of observations. Here \(A = 23\), \(\sum d_i = 70\), and \(n = 20\).

Step 2: Compute the average deviation.
Average deviation \(= \frac{70}{20} = 3.5\).

Step 3: Add this to the assumed mean.
Actual mean \(= 23 + 3.5 = 26.5\).

Step 4: Check the given options.
Option A, 24, option B, 25, and option C, 26, are all close guesses but none equals 26.5 exactly, so none of them can be the mean. Only "None of these" fits.

Final Answer:
The mean of the 20 observations is 26.5, which is not listed among A, B, or C, so the answer is \[ \boxed{\text{Option D, None of these}} \]