☰
Measures of Dispersion
Calculate the standard deviation of the following values by following methods:
(i) Actual Mean Method, (ii) Assumed Mean Method, (iii) Direct Method, (iv) Step Deviation Method.
5, 10, 25, 30, 50.
(i) Calculation of Standard Deviation by Actual Mean Method :
|
X |
d |
d2 |
|
5 |
–19 |
361 |
|
10 |
–14 |
196 |
|
25 |
+1 |
1 |
|
30 |
+6 |
36 |
|
50 |
+26 |
676 |
|
ΣX = 120 |
0 |
Σd2 = 1270 |
(ii) Calculation of Standard Deviation by Assumed Mean Method :
|
X |
d |
d2 |
|
5 |
–20 |
400 |
|
10 |
–15 |
225 |
|
25 |
0 |
0 |
|
30 |
+5 |
25 |
|
50 |
+25 |
625 |
|
–5 |
1275 |
(iii) Calculation of Standard Deviation by Direct Method : Standard Deviation can also be calculated from the values directly, i.e., without taking deviations, as shown below :
|
X |
x2 |
|
5 |
25 |
|
10 |
100 |
|
25 |
625 |
|
30 |
900 |
|
50 |
2500 |
|
ΣX = 120 |
ΣX2 = 4150 |
(iv) Calculation of Standard Deviation by Step Deviation Method : The values are divisible by a common factor, they can be so divided and standard deviation can be calculated from the resultant values as follows :
Since all the five values are divisible by a common factor 5, we divide and get the following values :
|
x |
x2 |
d |
d2 |
|
5 |
1 |
–3.8 |
14.44 |
|
10 |
2 |
–2.8 |
7.84 |
|
25 |
5 |
+0.2 |
0.04 |
|
30 |
6 |
+1.2 |
1.44 |
|
50 |
10 |
+5.2 |
27.04 |
|
N = 5 |
0 |
50.80 |
Alternative Method : Alternatively, instead of dividing the values by a common factor, the deviations can be divided by a common factor. Standard Deviation can be calculated as shown below :
|
x |
d |
d' |
d2 |
|
5 |
–20 |
–4 |
16 |
|
10 |
–15 |
–3 |
9 |
|
25 |
0 |
0 |
0 |
|
30 |
+5 |
+1 |
1 |
|
50 |
+25 |
+5 |
25 |
|
N = 5 |
–1 |
51 |
Deviations have been calculated from an arbitrary value 25. Common factor of 5 has been used to divide deviations.
Sponsor Area
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.
How is coefficient of quartile deviation calculated?
Define mean deviation.
Sponsor Area
Sponsor Area
