Question

Calcuate:

Dispersion measures

Tailedness measures

15 - 27 14.5 - 27.5            7
28 - 40   27.5 - 40.5        13
41 - 53    40.5 - 53.5         16
54 - 66    53.5 - 66.5         21
67 - 79   66.5 - 79.5         15
80 - 92   79.5 - 92.5          6
93 - 105 92.5 - 105.5       2

Answer 1

The measures of dispersion are Range, Standard deviation, Quartile deviation, Mean Deviation etc. and the measures of tailedness is kurtosis.

Range = highest value- lowest value

Range = 93-(-105.5) = 198.5

To calculate standard deviation:

15	17.71429	313.7959
28	30.71429	943.3673
41	43.71429	1910.939
54	56.71429	3216.51
67	69.71429	4860.082
80	82.71429	6841.653
93	95.71429	9161.224
-27	-24.2857	589.7959
-40	-37.2857	1390.224
-53	-50.2857	2528.653
-66	-63.2857	4005.082
-79	-76.2857	5819.51
-92	-89.2857	7971.939
-105	-102.286	10462.37
14.5	17.21429	296.3316
27.5	30.21429	912.9031
40.5	43.21429	1867.474
53.5	56.21429	3160.046
66.5	69.21429	4790.617
79.5	82.21429	6759.189
92.5	95.21429	9065.76
-27.5	-24.7857	614.3316
-40.5	-37.7857	1427.76
-53.5	-50.7857	2579.189
-66.5	-63.7857	4068.617
-79.5	-76.7857	5896.046
-92.5	-89.7857	8061.474
-105.5	-102.786	10564.9
7	9.714286	94.36735
13	15.71429	246.9388
16	18.71429	350.2245
21	23.71429	562.3673
15	17.71429	313.7959
6	8.714286	75.93878
2	4.714286	22.22449
-95		121745.6429

= -95/35

= -2.7143

= 59.8394

Tailedness is measured using skewness. let us use Karl Pearson's coefficient of Skewness.

Karl Pearson's coefficient of Skewness = (Mean-Mode)/Standard Devation

We have already calculated mean and Standard deviation. We have mean= 2.7143 and SD = 59.8394. Mode of the given data is 15

Therefore, Karl Pearson's coefficient of Skewness = (-2.7143-15)/59.8394 = -2.9650