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	11	10	7	4	4

Answer 1

The class mark (\(x_i\)) for each interval is calculated using the formula: Class mark (\(x_i\)) = \( \frac{\text{Upper \,limit + Lower \,limit}}{2} \).

The class size (h) of the data is 10.

With 70 designated as the assumed mean (a), \(d_i\), \(u_i\), and \(f_iu_i\) are computed as follows.

Literacy rate (in %)	Number of cities \(f_i\)	\(x_i\)	\(d_i = x_i -70\)	\(u_i = \frac{d_i}{10}\)	\(f_iu_i\)
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

The table provides the following sums:

\(\sum f_i = 35\)
\(\sum f_iu_i = -2\)

The mean is calculated using the formula: \(\overset{-}{x} = a + (\frac{\sum f_iu_i}{\sum f_i}) \times h\)

Substituting the values: x = \(70 + (-\frac{2}{35})\times (10)\)

x = 70 - \(\frac{20}{35}\)

x = 70 - \(\frac{4}{5}\)

x = 70 - 0.57
x = 69.43

The mean literacy rate is 69.43%.