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Measures of Dispersion
Average daily wage of 50 workers of a factory was Rs. 200 with a standard deviation of Rs. 40. Each worker is given a raise of Rs. 20. What is the new average daily wage and standard deviation? Have the wages become more or less uniform?
Increase in each worker wages = Rs. 20
Total increase in wages = 50 × 20 = Rs. 1000
Total of wages before increase worker in wages = 50 × 200 = Rs. 10,000
Total wages after increase in wages
Hence, mean wages will be affected but standard deviation will not be affected as the standard deviation is independent of origin. Have the wages become or less uniform? In order to calculate uniformity wages, we will have to calculate co-efficient of variation.
Afterwards
Now more uniformity in wages has taken place.
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Which measure of dispersion is the best and how?
Some measures of dispersion depend upon the spread of values whereas some calculate the variation of values from a central value. Do you agree?
In a town 25% of the persons earned more than Rs. 45000, whereas 75% earned more than Rs. 18000. Calculate the absolute and relative values of dispersion.
A batsman is to be selected for a cricket team. The choice is between X and Y on the basis of their five previous scores which are:
|
X |
Y |
|
25 |
50 |
|
85 |
70 |
|
40 |
65 |
|
80 |
45 |
|
120 |
80 |
Which batsman should be selected if we want
(i) a higher run getter, or
(ii) a more reliable batsman in the team?
To check the quality of two brands of lightbulbs, their life in burning hours was estimated as under for 100 bulbs of each brand.
|
Life (in hrs) |
No. of bulbs |
||
|
Brand A |
Brand B |
||
|
0–50 |
15 |
2 |
|
|
50–100 |
20 |
8 |
|
|
100–150 |
18 |
60 |
|
|
150–200 |
25 |
25 |
|
|
200–250 |
22 |
5 |
|
|
100 |
100 |
||
(i) Which brand gives higher life?
(ii) Which brand is more dependable?Average daily wage of 50 workers of a factory was Rs. 200 with a standard deviation of Rs. 40. Each worker is given a raise of Rs. 20. What is the new average daily wage and standard deviation? Have the wages become more or less uniform?
In the previous question, calculate the relative measures of variation and indicate the value, which in your opinion is more reliable.
If in the previous question, each worker is given a hike of 10% in wages, how are the mean and standard deviation values affected?
The sum of 10 values is 100 and the sum of their squares is 1090. Find the coefficient of variation.
Calculate the mean deviation about mean and standard deviation for the following distribution:
|
Classes |
Frequencies |
|
20–40 |
3 |
|
40–80 |
6 |
|
80–100 |
20 |
|
100–120 |
12 |
|
120–140 |
9 |
|
50 |
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