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Measures of Dispersion
Prove that mean deviation calculated about mean will be greater than that calculate about median.
In order to prove the statement given in the question we calculate mean deviation about mean and mean deviation from median and compare what is greater:
2, 4, 7, 8 and 9.
Mean deviation about Mean
|
X |
D |
|
2 |
4 |
|
4 |
2 |
|
7 |
1 |
|
8 |
2 |
|
9 |
3 |
|
ΣX = 30 |
ΣD = 12 |
|
X |
D (X–7) |
|
2 |
5 |
|
4 |
3 |
|
7 |
0 |
|
8 |
1 |
|
9 |
2 |
|
N = 5 |
ID = 11 |
Mean deviation about mean is 2.4. and mean deviation about median is 2.2. Hence, proved that mean deviation about mean is greater than mean deivation about median.
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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 |
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.
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