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Measures of Dispersion
Prove that mean deviation is based on all values. A change in even one value will effect of.
In order to prove the statement given in the question, we calculate the mean deviation of the following data: 2, 4, 7, 8, 9.
|
X |
D |
|
2 |
4 |
|
4 |
2 |
|
7 |
1 |
|
8 |
2 |
|
9 |
3 |
|
ΣX = 30 |
ΣD = 12 |
Now change one value i.e. we take 14 in place of 9.
|
X |
D |
|
2 |
5 |
|
4 |
3 |
|
7 |
0 |
|
8 |
1 |
|
14 |
7 |
|
ΣX = 35 |
ΣD = 16 |
In this way we see that mean deviation changes with a change in even one value. Earlier, the mean deviation was 2.4. After the change in one value it is 3.2.
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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.
How is coefficient of quartile deviation calculated?
Define mean deviation.
Define standard deviation.
Give formula to calculate standard deviation of a frequency destribution series by direct method.
Sponsor Area
Sponsor Area