Question

use the data set listed and technology to create frequency histograms with 5, 10, and 20 classes. which graph 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 classe. choose the correct graph below.

Explanation:

Step1: Determine the range of data

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

Step2: Calculate class - width for 10 classes

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

Step3: Define the classes

The classes will be: 1 - 2, 3 - 4, 5 - 6, 7 - 8, 9 - 10, 11 - 12, 13 - 14, 15 - 16.

Step4: Count the frequencies for each class

For the class 1 - 2: There are 5 values (1, 1, 1, 1, 1).
For the class 3 - 4: There are 6 values (3, 3, 3, 4, 4, 4).
For the class 5 - 6: There is 1 value (6).
For the class 7 - 8: There are 3 values (7, 7, 8).
For the class 9 - 10: There are 5 values (9, 9, 9, 10, 10).
For the class 11 - 12: There are 0 values.
For the class 13 - 14: There are 4 values (13, 13, 14, 14).
For the class 15 - 16: There is 1 value (15).

Step5: Analyze which graph is best

A 10 - class histogram is often a good choice as it provides a good balance between showing the overall distribution of the data and not being too detailed or too coarse. A 5 - class histogram may be too coarse and may not show the details of the data distribution well. A 20 - class histogram may be too detailed and may show a lot of noise in the data.

Since the problem does not provide the actual graphs A and B for the 10 - class histogram, we cannot choose the correct graph from the given options. But the above steps show how to create the 10 - class histogram.

Answer:

The steps to create a 10 - class histogram are shown above. Without the given graphs A and B, we cannot choose the correct graph.