Question

Find the mean and variance for the data

$x_i$	6	10	14	18	24	28	30
$f_i$	2	4	7	12	8	4	3

Answer 1

The data is obtained in tabular form as follows.

$x_i$	$f_i$	$fx_i$	$(x_i-\bar{x})$	$(x_i-\bar{x})^2$	$f_i(x_i-\bar{x})^2$
6	2	12	-13	169	338
10	4	40	-9	81	324
14	7	98	-5	25	175
18	12	216	-1	1	12
24	8	192	5	25	200
28	4	112	9	81	324
30	3	90	11	121	363
40	760			1736

Here, N = 40, $\sum_{i=1}^7f_ix_i=760$

$∴\bar{x}=\frac{\sum_{i=1}^7f_ix_i}{n}=\frac{760}{40}=19$

Variance=(σ2) = $\frac{1}{n}\sum_{i=1}^7f_i(x_i-\bar{x})^2=\frac{1}{40}×1736=43.4$