Question

The following data represent the length of shaft life of machine, in years of 36 machines

19	21	12	11	23	14	12	19	18
13	15	7	20	11	14	18	17	12
12	19	15	6	15	6	10	6	25
20	16	9	8	11	6	14	14	10

a. Construct a cumulative and relative frequency distribution using 6 classes.

b. Find the mean, median and mode for the life span of shaft.

c. Find 4th deciles and 41th percentile

d. Also construct the histogram and comment the shape of the data

Answer 1

a)

Class Interval	Frequency	Class Boundaries	Relative Frequency	Cumulative Frequency
6-9	7	5.5-9.5	7/36=0.1944	7
10-13	10	9.5-13.5	10/36=0.2778	17
14-17	9	13.5-17.5	9/36=0.25	26
18-21	8	17.5-21.5	8/36=0.2222	34
22-25	2	21.5-25.5	2/36=0.0556	36
Total	36

b)

Class Boundaries	f	x,Midpoint	fx	fx^2	Cumulative frequency
5.5-9.5	7	7.5	52.5	393.75	7
9.5-13.5	10	11.5	115	1322.5	17
13.5-17.5	9	15.5	139.5	2162.25	26
17.5-21.5	8	19.5	156	3042	34
21.5-25.5	2	23.5	47	1104.5	36
Total	36	77.5	510	8025

Mean=∑fx/∑f

14.1667

Median=N/2 the term

14

Mode=6

c)

Decile=i*(n+1)/10th date=14.8 that is 14 and 15 term

=12+0.8(12-12)=12

41 percentile=12

d)

The shape of the distribution is positive that is right-skewed distribution.

...........................................................................................................................................

The Given data is:

6
6
6
6
7
8
9
10
10
11
11
11
12
12
12
12
13
14
14
14
14
15
15
15
16
17
18
18
19
19
19
20
20
21
23
25