Question

A marketing study was conducted to assess the new bottle design of a popular soft drink. Sixty randomly selected shoppers participated and rated the new design. The data are given below:

34 33 33 29 26 33 28 25 32 33
32 25 27 33 22 27 32 33 32 29
24 30 20 34 31 32 30 35 33 31
32 28 30 31 31 33 29 27 34 31
31 28 33 31 32 28 26 29 32 34
32 30 34 32 30 30 32 31 29 33

a. Explain why we need to construct a frequency distribution and histogram for this data set.
b. Construct a relative frequency distribution and a percent frequency distribution for the bottle design ratings.
c. Construct a cumulative frequency distribution and cumulative percent frequency distribution.

Answer 1

1. We need to draw frequency distribution and histogram for the given data in manner to read the data easily and quickly . If the data remains in the same type than it would not be easy to know the observations. So by frequency distribution and histogram we can easily find out the number of observations belonging to a particular value.

2. S. No.	X	f	relative frequency	%relative frequency
   1.	20	1	0.017	1.7%
   2.	22	1	0.017	1.7%
   3.	24	1	0.017	1.7%
   4.	25	2	0.034	3.4%
   5.	26	2	0.034	3.4%
   6.	27	3	0.05	5%
   7.	28	4	0.067	6.7%
   8.	29	5	0.083	8.3%
   9.	30	6	0.1	10%
   10.	31	8	0.134	13.4%
   11.	32	11	0.184	18.4%
   12.	33	10	0.167	16.7%
   13.	34	5	0.084	8.4%
   14.	35	1	0.017	1.7%

Relative frequency = frequency of the class/total frequency

Percentage relative frequency = relative frequency *100

3. comulative frequency = sum of frequency with preceding frequency

% comulative frequency=( comulative frequency / total frequency )*100

S. No.	Comulative frequency	% comulative frequency
1.	1	1.7%
2.	2	3.3%
3.	3	5%
4.	5	8.3%
5.	7	11.6%
6.	10	16.7%
7.	14	23.4%
8.	19	31.7%
9.	25	41.6%
10.	33	55%
11.	44	73.4%
12.	54	90%
13.	59	98.4%
14	60	100%
Total	60	100%