Question

Approximate the mean of the frequency distribution for the ages of the residents of a town.

Age Frequency ​0-9 40 ​10-19 30 ​20-29 18 ​30-39 24 ​40-49 33 ​50-59 53 ​60-69 41 ​70-79 16 ​80-89 3

The approximate mean age is nothing years. ​(Round to one decimal place as​ needed.)

Answer 1

Solution-

Approximate mean of the frequency distribution for the ages of the residents of a town is

= 40.0   (rounded)

• Calculations-

The grouped data information provided, with the corresponding frequencies is shown in the table below: Classes Frequency (f) 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 For each of the grouped classes we need to compute the midpoint (M), by calculating the average between the lower and upper value of the class. Then, the following table si obtained: Classes M Mof M2. f 0-9 4.5 180 810 10-19 14.5 435 6307.5 20-29 24.5 441 10804.5 30-39 34.5 828 28566 40-49 44.5 1468.5 65348.25 50-59 54.5 2888.5 157423.25 60-69 64.5 2644.5 170570.25 70-79 74.5 1192 88804 80-89 84.5 253.5 21420.75 Sum = 10331 550054.5

From the table, we compute the sample mean X as follows: 8= + (¿M-5.) = 2 (1031) = 40.043 2= Also, the sample variable is calculated as follows: n warf(x) = +i (3M *-*(SMS)) - 2+1 (59543 - 198) = 540 695 var(X) = Mifi 550054.5 - 103312 258 = 530.638 N -1 N 258 – 1 Vi=1 Therefore, the sample sandartd deviation s is directly computed by taking the square root from the sample variance. s = V 92 = 1530.638 = 23.036

-----------

Thank you..!!

Please like..