Question

Find the mean and variance for the data

\(x_i\)	62	93	97	98	102	104	106
\(f_i\)	3	2	3	2	6	3	3

Answer 1

The data is obtained in tabular form as follows.

\(x_i\)	\(f_i\)	\(fx_i\)	\((x_i-\bar{x})\)	\((x_i-\bar{x})^2\)	\(f_i(x_i-\bar{x})^2\)	\(f_i(x_i-\bar{x})\)
92	3	276	8	64	192	192
93	2	186	7	49	98	98
97	3	291	3	9	27	27
98	2	196	2	4	8	8
102	6	612	2	4	24	24
104	3	312	4	16	48	48
109	3	327	9	81	243	243
	32	2200			640	640

Here, N = 22, \(\sum_{i=1}^7f_ix_i=2200\)

\(∴\bar{x}=\frac{1}{N}\frac{\sum_{i=1}^7f_ix_i}{n}=\frac{1}{22}×2200=100\)

Variance(σ²) = \(\frac{1}{n}\sum_{i=1}^7f_i(x_i-\bar{x})^2=\frac{1}{22}×640=29.09\)