Question

Question 10. The weights of 15 participants (kg) are shown below:

51.2, 70.5, 61.4, 67.0, 83.0, 61.1, 82.4, 94.4, 62.6, 78.4, 63.9, 89.6, 71.4, 58.4, 79.2

Calculate the following descriptive statistics:

1. Mean
2. Median
3. Variance
4. Standard deviation

Answer 1

Given 15 participants weights are 51.2,
70.5, 61.4, 67.0, 83.0, 61.1, 82.4, 94.4,62.6, 78.4, 63.9, 89.6, 71.4, 58.4, 79.2

Mean:

Mean = (70.5 + 61.4 +  67.0 +  83.0 +  61.1 + 82.4 + 94.4 + 62.6 + 78.4 + 63.9 + 89.6 + 71.4 + 58.4 + 79.2)/15

= 71.63

Median:

First arrange the weights in ascending order.

51.2, 58.4, 61.1, 61.4, 62.6, 63.9, 67, 70.5, 71.4, 78.4, 79.2, 82.4, 83, 89.6, 94.4.

Median is middle element.

Therefor median = 70.5

Variance:

variance =

Where x_i is mean of the given weights

x	x-xi	(x-xx)2
51.2	-20.43	417.43
70.5	-1.13	1.28
61.4	-10.23	104.66
67	-4.63	21.44
83	11.37	129.28
61.1	-10.53	110.89
82.4	10.77	116
94.4	22.77	518.48
62.6	-9.03	81.55
78.4	6.77	45.84
63.9	-7.73	59.76
89.6	17.97	322.93
71.4	-0.23	0.06
58.4	-13.23	175.04
79.2	7.57	57.31

variance =

= 417.39+1.28+104.66+21.44+129.28+110.89+116+518.48+81.55+45.84+59.76+322.93+0.06+175.04+57.31)/15

= 2161.91/15

= 144.127

Standard deviation:

  Standard deviation = squareroot(variance)

= squareroot(144.127)

= 12.005

  

Note:

For sample variance the formula is

Accordingly standard deviation value will be changed