Question

For the stress data given below with the nearest error of 1:

27-17-11-24-36-13-29-22-18

23-30-12-46-17-32-48-11-18

18-32-26-24-38-24-15-13-13

18-21-27-20-16-15-37-19-19

a) Construct a frequency distribution table.

b) Construct the three types of statistical graphs.

c) Determine the (1) Mean, (2) Median, (3) Mode, (4) Range,

Variance, and (6) Standard Deviation.

Answer 1

Given Data distribution

27	17	11	24	36	13	29	22	18
23	30	12	46	17	32	48	11	18
18	32	26	24	38	24	15	13	13
18	21	27	20	16	15	37	19	19

Max	48
Min	11
range	Max-Min	37
Lets take n	7
Class width = Range / n	5.285714	6

Frequency table

Class limits	Tally	Frequency
11-16	1+1+1+1+1+1+1+1+1	9
17-22	1+1+1+1+1+1+1+1+1+1+1	11
23-28	1+1+1+1+1	5
29-34	1+1+1	3
35-40	1+1	2
41-46	1	1
47-52	1	1

Three types of graphs are

1. Bar graph
2. Pie graph
3. Line graph

Bar graph of given data.

Pie graph

Line graph

Scatter plot of all date

Mean of given data = sum of all values / N = 829 / 36 = 23.0278

Mode is the higest repeated number is 18

Median

l = 29

C = 9+11+5 = 25

f= 3

h=n=6

N =36

29 + ((36/2) -25) / 3 * 6 = 29-14 = 15

Range already calculated

Max - min = 37

Variance (S²) = average squared deviation of values from mean

			(x-mu)^2
		27	15.77855
		17	36.3341
		11	144.6674
		24	0.945216
		36	168.2785
		13	100.5563
		29	35.66744
		22	1.056327
		18	25.27855
		23	0.000772
		30	48.61188
		12	121.6119
		46	527.723
		17	36.3341
		32	80.50077
		48	623.6119
		11	144.6674
		18	25.27855
		18	25.27855
		32	80.50077
		26	8.834105
		24	0.945216
		38	224.1674
		24	0.945216
		15	64.44522
		13	100.5563
		13	100.5563
		18	25.27855
		21	4.111883
		27	15.77855
		20	9.167438
		16	49.38966
		15	64.44522
		37	195.223
		19	16.22299
		19	16.22299
	Mean	23.02777778
	Sum		3138.972
	n-1 = 36-1	35
	Var =	3138.972/35	89.68492
	SD	Sqrt(var)	9.470212

Variance = 89.68

Standard deviation = 9.47

Thanks

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