Chapter 3, Problem 1CRE

Listed below are measured weights (in pounds) of the contents in samples of cans of regular Pepsi and Diet Pepsi. Use these data for Exercises 1–3

1.

1. a. Construct a frequency table for the weights of regular Pepsi. Use these bins:

   0.8130–0.8179

   0.8180–0.8229

   0.8230–0.8279

   0.8280–0.8329

   0.8330–0.8379

   0.8380–0.8429

2. b. Construct a frequency table for the weights of Diet Pepsi. Use these bins:

   0.7740–0.7779

   0.7780–0.7819

   0.7820–0.7859

   0.7860–0.7899

   0.7900–0.7939

3. c. Compare the frequency tables from parts (a) and (b). What notable differences are there? How can those notable differences be explained?

To determine

Create a frequency table for the weights of regular Pepsi using the given bins.

Answer to Problem 1CRE

The relative frequency table for the weights of regular Pepsi using the given bins is as follows,

Weights	Frequency
0.8130–0.8179	5
0.8180–0.8229	12
0.8230–0.8279	12
0.8280–0.8329	5
0.8330–0.8379	0
0.8380-0.8429	2
Total	36

Explanation of Solution

Calculation

The given information is that,the data represents the weights (in pounds) of the contents in samples of cans of Regular Pepsi and Diet Pepsi.

From the data it is observed that, the values are ranging from 0.8139 to 0.8401. One-way to arrange the data in a group with these bins are classify the weights into different groups. Those are, 0.8130-0.8179, 0.8180-0.8229, 0.8230-0.8279, 0.8280-0.8329, 0.8330-0.8379 and 0.8380-0.8429.

Now, count the frequency for each bin. That is, 5 for bin 0.8130-0.8176 because in that range there are 5 cans and for bin 0.8180-0.8229, 12. Similarly the remaining frequencies are obtained and tabulated below.

The frequency table is as follows,

Weights	Frequency
0.8130–0.8179	5
0.8180–0.8229	12
0.8230–0.8279	12
0.8280–0.8329	5
0.8330–0.8379	0
0.8380–0.8429	2
Total	36

To determine

Create a frequency table for the weights of Diet Pepsi.

Answer to Problem 1CRE

The frequency table for the weights of Diet Pepsi is as follows,

Weights	Frequency
0.7740–0.7779	5
0.7780–0.7819	5
0.7820–0.7859	16
0.7860–0.7899	8
0.7900–0.7939	2
Total	36

Explanation of Solution

Calculation

From the data it is observed that, the values are ranging from 0.7742 to 0.7938. The groups for the weights of different bins are 0.7740-0.7779, 0.7780-0.7819, 0.7820-0.7859, 0.7860-0.7899 and 0.7900-0.7939.

Now, count the frequency for each bin. That is, 5 for bin 0.7740-0.7779 because in that range there are 5 cans and for bin 0.7780-0.7819, 5. Similarly the frequencies for remaining bins are obtained and tabulated below.

The frequency table is as follows,

Weights	Frequency
0.7740–0.7779	5
0.7780–0.7819	5
0.7820–0.7859	16
0.7860–0.7899	8
0.7900–0.7939	2
Total	36

To determine

Explain whether there are any notable differences by comparing the frequency tables from parts (a) and (b).

Explanation of Solution

From the frequencies tables of parts (a) and (b) it can be observed that, the regular Pepsi weights are more than the diet Pepsi weights because of the sugar levels in the regular Pepsi. But the volumes of both type cans are approximately same.