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

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Solution

To find the class mark $(x_{i})$ for each interval, using the following relation:
$(x_{i}) = \frac{U p p e r c l a s s l i m i t + L o w e r c l a s s l i m i t}{2}$
Class size $(h)$ for this data $= 10$
Taking 70 as assumed mean $(a)$ , calculating $d_{i}, u_{i}, f_{i} u_{i}$ :
From the table:
$\sum f_{i} = 35$
$\sum f_{i} u_{i} = - 2$
Mean, $¯ x = a + (\frac{\sum f_{i} u_{i}}{\sum f_{i}}) \times h$
$= 70 + (\frac{- 2}{35}) \times 10$
$= 70 - \frac{20}{35}$
$= 70 - \frac{4}{7}$
$= 70 - 0.57$
$= 69.43$
Therefore, mean literacy rate is $69.43$ %

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