Question:

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

Literacy rate (in %)45 - 5555 - 6565 - 75 75 - 85 85 - 95
Number of cities

11

10

7

4

4

Updated On: Nov 8, 2023
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Solution and Explanation

To find the class mark (xix_i) for each interval, the following relation is used.  

Class mark  (xi)(x_i) = Upper limit + Lower limit2\frac {\text{Upper \,limit + Lower \,limit}}{2}

class size (h) of the data = 10

Taking 70 as assumed mean (a), did_iuiu_i, and fiuif_iu_i can be calculated as follows.   

Literacy rate (in %)       Number of cities fi\bf{f_i}               xi\bf{x_i}       di=xi70\bf{d_i = x_i -70}ui=di10\bf{u_i = \frac{d_i}{10}}       fiui\bf{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

From the table, We obtain

fi=35\sum f_i = 35
fiui=2\sum f_iu_i = -2

Mean, x=a+(fiuifi)×h\overset{-}{x} = a + (\frac{\sum f_iu_i}{\sum f_i}) \times h 

x = 70+(235)×(10)70 + (-\frac{2}{35})\times (10) 

x = 70 - 2035\frac{20}{35} 

x = 70 - 45\frac{4}5

x = 70 - 0.57
x = 69.43

Therefore, mean literacy rate is 69.43%.  

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