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

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

#### Solution

To find the class marks, the following relation is used.

x_i  = ("Upper class limit + Lower class limit")/2

Class size (h) for this data = 10

Taking 70 as assumed mean (a), diui, and fiui are calculated as follows

 Literacy rate (in %) Number of cities fi xi di = xi − 70 ui = 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 Total 35 − 2

From the table, we obtain

sumf_i = 35

sumf_iu_i = -2

"Mean " barx = a+ ((sumf_iu_i)/(sumf_i))xxh

=70+(-2/35)xx(10)

= 70-20/35

=70-4/7

= 70 - 0.57

= 69.43

Therefore, mean literacy rate is 69.43%.

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#### APPEARS IN

NCERT Class 10 Maths
Chapter 14 Statistics
Exercise 14.1 | Q 9 | Page 272
RD Sharma Class 10 Maths
Chapter 15 Statistics
Exercise 15.3 | Q 25 | Page 24