Question

The value of appropriate measure of dispersion for the following distribution of daily wages
Wages (')
Below 30
30-39
40-49
50-59
60-79
Above 80
No. of workers
5
7
18
32
28
10
a) 11.03 b) 10.50 c) 11.68 d) 11.68​

Answer 1

Given that,

Wages x= below 30, 30-39, 40-49, 50-59,60-79, above 80

Number of workers f = 5, 7, 18, 32, 28, 10

Total number of workers = 100

We need to write the middle digit of wages

Using given data

$m=30, 34.5, 44.5, 54.5, 69.5, 80$

We need to calculate the fx

Using given data

$fx=150, 241.5, 8016, 1744, 1946, 800$

$Total\ of fx=5682.5$

We need to calculate the fx²

Using given data

$fx^2=4500, 8331.75, 35644.5, 95048, 135247, 64000$

$Total\ of fx^2=342771.25$

We need to calculate the mean wage

Using formula of mean wage

$mean\ wage=\dfrac{\sum{fx}}{\sum{f}}$

Put the value into the formula

$mean\ wage=\dfrac{5682.5}{100}$

$mean\ wage=56.825$

We need to calculate the standard deviation

Using formula of standard deviation

$S.D=\sqrt{\dfrac{\sum{fx^2}}{\sum{f}}-(\dfrac{\sum{fx}}{\sum{f}})^2}$

Put the value into the formula

$S.D=\sqrt{\dfrac{342771.25}{100}-(56.825)^2}$

$S.D=14.0$

We need to calculate the daily wages

Using formula of daily wages

$daily\ wages=2\times S.D$

Put the value into the formula

$daily\ wages=2\times14.0$

$daily\ wages=28$

Hence, The daily wages are 28.

Answer 2

8.71

Step-by-step explanation:

Q1=46.72 Q3=64.14 then QD which Is appropriate measure Is Q3-Q1/2= 64.14-46.72/2 = 8.71