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Measures of Dispersion
Why should we measure dispersion about some particular value?
We should measure dispersion about some particular value because in that case (i) We can assess how precise is the central tendency as the representative value of all the observations in the series. Greater value of dispersion implies lesser representativeness of the central tendency and vice versa.
(ii) We can precisely asses how scattered are the actual observation from their representative value.
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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 |
A measure of dispersion is a good .supplement to the central value in understanding a frequency distribution. Comment
Define dispersion.
How many methods are there to calculate dipersion?
Define range.
Define quartile deviation.
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