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