Question

Smoothie Consumption (kgs.)
7.7
7.9
5.6
7.5
7.9
6.5
6.7
5.8
7.6
10.1
6.8
6.6
7.9
6
6.4
6.3
6.1
5.3
6
7.5
6.3
7.6
6.8
4.5
6
3.8
5.3
7
6.4
6.9
6.5
6.2
7
6.2
6.3
5.3
5.9
5.3
7.5
6.9
6.1
7.4
8.4
8.3
6.1
8
7.8
7.8
6.3
5.3
6.5
4.7
5.5
8.9
6.5
8.6
7
4.6
7.1
5.9
5
5
5
7.6
7.6
7.2
6.7
7.8
8
5.4
6
5.7
6.3
6.6
4.6
5.7
6.8
6.4
5.7
7.7
6.4
4.7
6.8
7.5
8
6
6.1
6.8
6.3
6.7
7.4
7.5
4.8
5.3
6.1
6.2
5.4
6.4
7.2
6.6
5.4
8.4
6.8
7.6
6.4
7.6
5.6
7.2
6.5
6.6
6
7.1
5.8
7.3
6.7
6.6
7.1
6.5
5
6.8
7.9
6
5.4
8.4
8
6.5
7.2
6.4
6.5
5.2
6.8
8
6.5
3.5
7.4
4.4
6
7
7.2
7.6
5.7
4.8
5.5
6.7

Dunkin’ selects random consumers to analyze smoothie consumption. Use the smoothie consumption data in A1_Excel_Template to answer the following questions:

1. Develop a histogram of the data. Explain what the histogram depicts
2. Construct a relative and a cumulative relative frequency distribution of the data.
3. What percentage of the smoothie drinkers sampled drink 8.0 kg or more annually?

use screenshot of excel solutions.

Answer 1

For the given data, the minimum and the maximum values are

Minimum	3.5
Maximum	10.1

a). We shall therefore have 10 classes with the class inervals of 1.

Class Interval	Bins	Frequency
3.5-4.5	4.5	4
4.5-5.5	5.5	23
5.5-6.5	6.5	48
6.5-7.5	7.5	41
7.5-8.5	8.5	25
8.5-9.5	9.5	2
9.5-10.5	10.5	1

The histogram depicts the frequencies of the various class intervals. The area of each rectange in a calss gives the frequency.

b). Construct a relative and a cumulative relative frequency distribution of the data.

Class Interval	Frequency	Cumulative frequency	Relative Frequency	Cumulative relative frequency
3.5-4.5	4	4	0.0278	0.0278
4.5-5.5	23	27	0.1597	0.1875
5.5-6.5	48	75	0.3333	0.5208
6.5-7.5	41	116	0.2847	0.8056
7.5-8.5	25	141	0.1736	0.9792
8.5-9.5	2	143	0.0139	0.9931
9.5-10.5	1	144	0.0069	1.0000
Total	144

c. What percentage of the smoothie drinkers sampled drink 8.0 kg or more annually?

The class 7.5-8.5 contains teh value 8. Therefore the ferquency that corresponding 8 and above is approximately 25/(8.5-7.5)*0.5=12.5. Therefore, the smoothie drinkers sampled drink 8.0 kg or more annually is 12.5+2+1=15.5 and hence the percentage of  the smoothie drinkers sampled drink 8.0 kg or more annually=15.5/144*100=10.76%