Question

Consider the following table of data that was generated from randomly surveying 100 people and recording how much change (from coins) was in their pockets:

0.33	0.01	0.69	0.04	0.46
0.16	1.67	0.12	0.03	0.17
0.09	0.17	0.57	0.04	0.29
0.85	0.46	1.17	0.02	0.12
0.74	1.72	0.28	0.12	1.37
0.61	0.06	1.46	0.42	0.03
0.39	0.10	0.02	0.20	1.08
1.27	0.30	1.13	0.06	0.27
3.76	0.43	0.04	0.37	0.09
0.09	0.22	1.06	0.09	0.01
0.17	1.23	0.12	1.51	0.13
0.18	0.50	0.73	0.03	0.63
0.05	0.36	0.11	0.74	0.12
0.90	0.91	0.12	0.38	0.02
0.17	0.20	0.40	0.47	0.36
0.99	0.35	1.27	1.64	1.67
0.74	0.04	0.62	0.08	0.09
0.15	0.01	0.05	1.03	0.15
0.09	0.49	0.89	0.18	0.10
0.15	1.27	1.23	0.34	0.42

1. Construct a histogram of the empirical data. Use ten "bins".Hint: It may be helpful to construct ten "bins" over the interval [0,4]

2. Construct a histogram of the empirical data. Use 20 bins.

3. Describe the shape of each graph.

Answer 1

1:

Assuming number of classes 10 so class width of each will be

Class width = (4-0) / 10= 0.40

That is classes are

0- 0.4, 0.4 - 0.8, 0.8-0.12,.....

Following is the frequency distribution:

Following is the histogram

(b)

Assuming number of classes 20 so class width of each will be

Class width = (4-0) / 20 = 0.20

That is classes are

0- 0.2, 0.2 -0.4, 0.4 - 0.6, 0.6- 0.8, 0.8-0.10,.....

Following is the frequency distribution:

Following is the histogram:

3:

Histogram of part a shows that distribution is skewed to right It is unimodal. It seems that distribution has high outlier namely 3.76.

Histogram of part b shows that distribution is skewed to right It is unimodal. It seems that distribution has high outlier namely 3.76.