# The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate. Literacy rate (in %): 45 - 55, 55 - 65

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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

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We may calculate class marks (xi) for each interval by using the relation

xi $=\frac{Upper\,class\,limit+lower\,class\,limit}{2}$

Class size (h) for this data = 10

Now taking 70 as assumed mean (A) we can calculate as follows:

 Literacy rate (in %) Number of cities (fi) xi di = xi - 70 ui = $\frac{di}{10}$ 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 N = 35 $\sum$fiui = -2

Mean (x̅) = A + $\frac{\sum f_iu_i}{N}\times h$

$=70+\frac{-2}{35}\times10$

$=70-0.57$

$69.43$

So,

mean literacy rate is 69.437