Question

Solve the following questions according to statistics.
Given value : 11,10,22,31,8,9,26,9,19,65,74.
Calculate
1.mean
2.median
3.mode
4.range
5.variance
6.standard deviation
7.mean deviation
8.median deviation
9.mode deviation
10.coefficient of range
11.coefficient of variance
12.coefficient of mean deviation
13.coefficient of median deviation
14.coefficient of mode deviation

Answer 1

1. Mean = (11+10+22+31+8+9+26+9+19+65+74) / 11 = 215 / 11 = 19.54

2. Median = 22

3. Mode = 9

4. Range = 74 - 8 = 66

5. Variance = [(11-19.54)^2 + (10-19.54)^2 + (22-19.54)^2 + (31-19.54)^2 + (8-19.54)^2 + (9-19.54)^2 + (26-19.54)^2 + (9-19.54)^2 + (19-19.54)^2 + (65-19.54)^2 + (74-19.54)^2] / 11
Variance = 4707.82

6. Standard deviation = sqrt(Variance) = sqrt(4707.82) = 68.62

7. Mean deviation = (|11-19.54| + |10-19.54| + |22-19.54| + |31-19.54| + |8-19.54| + |9-19.54| + |26-19.54| + |9-19.54| + |19-19.54| + |65-19.54| + |74-19.54|) / 11
Mean deviation = 24.25

8. Median deviation = (|22-22| + |22-22| + |22-22| + |31-22| + |22-22| + |22-22| + |26-22| + |22-22| + |22-22| + |65-22| + |74-22|) / 11
Median deviation = 12

9. Mode deviation = (|11-9| + |10-9| + |22-9| + |31-9| + |8-9| + |9-9| + |26-9| + |9-9| + |19-9| + |65-9| + |74-9|) / 11
Mode deviation = 21.09

10. Coefficient of range = (74 - 8) / (74 + 8) = 0.83

11. Coefficient of variance = Standard deviation / Mean = 68.62 / 19.54 = 3.51

12. Coefficient of mean deviation = Mean deviation / Mean = 24.25 / 19.54 = 1.24

13. Coefficient of median deviation = Median deviation / Median = 12 / 22 = 0.55

14. Coefficient of mode deviation = Mode deviation / Mode = 21.09 / 9 = 2.34