CDS 2026 (I) Elementary Mathematics, question 39

Topic: Statistics

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Q39

The sum of the deviations of a set of $n$ numbers $x_{1},x_{2},x_{3},\ldots,x_{n}$ measured from $15$ is $-90$ and the sum of the deviations of the same numbers measured from $-3$ is $54$ . What is the arithmetic mean ?

(a) $3.25$
(b) $3.50$
(c) $3.75$ Correct answer
(d) $4.25$

Solution.

Answer: (c) $3.75$

Let S be the total.
The two deviation sums give $S - 15n = - 90$ and $S + 3n = 54$ .
Subtracting yields $18n = 144$ , so $n = 8$ .
Then $S = 54 - 24 = 30$ , and the mean is $30/8 = 3.75$ .