Question

Consider the following statements:
1. The algebraic sum of the deviations of a set of $n$ values from its arithmetic mean is zero.
2. In the case of frequency distribution, mode is the value of the variable which corresponds to maximum frequency.
Which of the statements given above is/are correct?

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

The correct option is C Both 1 and 2

Now let the values be $a_1,a_2,a_3,.......a_n$

Mean $=\frac{a_1+a_2+a_3+.......a_n}{n}$

Algebraic sum of deviations from mean

$=(a_1-\frac{a_1+a_2+a_3+.......a_n}{n})+(a_2-\frac{a_1+a_2+a_3+.......a_n}{n})+.........(a_n-\frac{a_1+a_2+a_3+.......a_n}{n})$

$=a_1+a_2+.....a_n-n\left(\frac{a_1+a_2+a_3+.......a_n}{n}\right)$

$=0$

Mode is the value of the variable which corresponds to maximum frequency, this is the definition of mode.

So both the statements are correct.

Hence, option C is correct.