Question

The mean of the following frequency table is 10. Find the value of a.

$x_i$	$f_i$
10	10
12	5
14	a
15	2
5	8

• A.
  10
• B.
  7
• C.
  5
• D.
  8

Answer 1

The correct option is C

5
Calculating the arithmetic mean from the given frequency table:

$x_i$	$f_i$	$f_i{x}_i$
10	10	100
12	5	60
14	a	14a
15	2	30
5	8	40
	$\sum f_i$ = 25 + a	$\sum f_i{x}_i$ = 230 + 14a

Given, mean=10
$\Rightarrow$ mean=$\frac{\sum f_i{x}_i}{\sum f_i}$=$\frac{230+14a}{25+a}$ =10
$\Rightarrow$ 230 + 14a = 250 + 10a
$\Rightarrow$ 4a = 20
$\Rightarrow$ a = 5