Question

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Literacy rate (in %)	45 − 55	55 − 65	65 − 75	75 − 85	85 − 95
Number of cities	3	10	11	8	3

Answer 1

To find the class marks, the following relation is used.

`x_i  = ("Upper class limit + Lower class limit")/2`

Class size (h) for this data = 10

Taking 70 as the assumed mean (a), d_i, u_i, and f_iu_i are calculated as follows:

Literacy rate (in %)	Number of cities fi	xi	di = xi − 70	ui = di/10	fiui
45 − 55	3	50	−20	−2	−6
55 − 65	10	60	−10	−1	−10
65 − 75	11	70	0	0	0
75 − 85	8	80	10	1	8
85 − 95	3	90	20	2	6
Total	35				−2

From the table, we obtain

`sumf_i = 35`

`sumf_iu_i = -2`

`"Mean"  barx = a+ ((sumf_iu_i)/(sumf_i))xxh`

= `70+(-2/35)xx(10)`

= `70-20/35`

= `70-4/7`

= 70 − 0.57

= 69.43

Therefore, the mean literacy rate is 69.43%.