1.

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: 3101183

Answer»

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) xidi = xi - 70ui = \(\frac{di}{10}\) fiui
 45 - 55350-20-2-6
 55 - 651060-10-1-10
 65 - 751170000
 75 - 858801018
 85 - 953902026
 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


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