Question

Internet radio: The following table presents the number of hours a sample of 40 subscribers listened to Pandora Radio in a given week. 52 113 4 12 9 16 10 37 15 18 8 23 4 3 17 19 12 20 14 10 37 21 36 17 3 23 28 19 20 29 12 a. Construct a frequency distribution with approximately eleven classes b. Construct a frequency histogram from this frequency distribution. c. Construct a relative frequency distribution for the same classes. d. Construct a relative frequency histogram from this relative frequency distribution e. Are the histograms skewed to the left, skewed to the right, or approximately symmetric? f. Construct a frequency distribution with approximately four classes g. Repeat parts (b)-(d), using the frequency distribution constructed in part (f) h. Do you think that four and eleven classes are both reasonably good choices for these data, or do you think that one choice is much better than the other? Explain your reasoning.

Answer 1

(a)

Minimum value: 2

Maximum value: 52

We need 11 classes so class width will be

Class width = (52-2) /11 = 4.54

That is class width will be 5.

Following table shows the frequency distribution:

Number of hours	Frequency
2-7	7
7-12	8
12-17	6
17-22	11
22-27	2
27-32	2
32-37	1
37-42	2
42-47	0
47-52	0
52-57	1

(c)

Following table shows the relative frequency distribution:

Number of hours	Frequency, f	Relative frequency, f/40
2-7	7	0.175
7-12	8	0.2
12-17	6	0.15
17-22	11	0.275
22-27	2	0.05
27-32	2	0.05
32-37	1	0.025
37-42	2	0.05
42-47	0	0
47-52	0	0
52-57	1	0.025
Total	40	1

(d)

Following is the relative frequency histogram:

0.3 0.25 0.2 - 0.15 5 0.1 0.05 0 2-7 7-12 12-17 17-22 22-27 27-32 32-37 37-42 42-47 47-52 52-57 Number of hours

e)

Histogram is skewed to right.