0 votes
558 views
in Statistics by (27.3k points)
closed by

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

1 Answer

+1 vote
by (26.1k points)
selected by
 
Best 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)  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

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...