Question

The following table shows th
lowing table shows the frequency table of literacy rate (in percentage) of
ties Find the mean literacy rate by assumed mean method :
Heracy rate (in percentage) 45 – 55 55 – 65 65 – 75 75 – 85 85 – 95
Number of cities
3 10 11 8 3
|
Take 70 as the assumed mean. Find mean up to two places of decimal.​

Answer 1

Answer:

Mean = 69.43

Step-by-step explanation:

We are given below the following table that shows the frequency table of literacy rate (in percentage) of  cities;

  Literacy rate(in %)       Number of cities (f)     X        d = $\frac{X-A}{h}$        f * d

    45 - 55                                    3                        50           -2               -6            

    55 - 65                                   10                        60           -1               -10

    65 - 75                                    11                        70            0                0

    75 - 85                                    8                         80            1                8

    85 - 95                                    3                         90           2                6        

                                             ∑ f = 35                                             ∑f*d = -2     

Here, X is calculated as (Upper limit + Lower limit) ÷ 2 .

Assumed Mean method formula is given by;

        Mean = $A+\frac{\sum fd}{\sum f} * h$   where, A = assumed mean = 70

                                                         h = width of class interval = 10

        Mean = $70+\frac{-2}{35} * 10$

                   = 70 - $\frac{4}{7}$ = 69.43

Therefore, mean literacy rate by assumed mean method is 69.43 .