Question

use the data set listed and technology to create frequency histograms with 5, 10, and 20 classes. which number of classes represents the data best? explain.
3 6 3 1 10 3 14 7 4 9 9 13 8
7 10 10 1 1 13 4 7 4 1 9 15 14
create a histogram with 10 classes. choose the correct graph below.
a.
b.

Explanation:

Step1: Find the range of the data

The smallest value in the data - set is 1 and the largest is 15. So the range $R=15 - 1=14$.

Step2: Calculate the class - width for 10 classes

The class - width $w=\frac{R}{n}$, where $n = 10$ (number of classes). So $w=\frac{14}{10}=1.4$. We can round it up to 2 for convenience.

Step3: Tally the data into classes

The classes will be: 1 - 2, 3 - 4, 5 - 6, 7 - 8, 9 - 10, 11 - 12, 13 - 14, 15 - 16.
Count the number of data points in each class:

• Class 1 - 2: 4
• Class 3 - 4: 6
• Class 5 - 6: 2
• Class 7 - 8: 4
• Class 9 - 10: 5
• Class 11 - 12: 0
• Class 13 - 14: 4
• Class 15 - 16: 1

Step4: Match with the given histograms

By comparing the frequencies of each class with the heights of the bars in the histograms, we can determine the correct one.

Answer:

(Without seeing all the options C and D, we assume based on the above - calculated frequencies that if we had to choose between A and B, we need to match the frequencies of the classes. If the frequencies in the histogram match the ones we calculated above, we can choose the appropriate option. Since we don't have full options, we can't give a definite letter - based answer. But the process to create the histogram is as above.)