Question

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

Explanation:

Step1: Determine range of data

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

Step2: Calculate class - width for 20 classes

The class - width $w=\frac{R}{20}=\frac{14}{20}=0.7$. We can round it up to 1.

Step3: Create frequency distribution

We create 20 classes starting from 1 - 2, 2 - 3, 3 - 4, etc. and count the number of data points falling into each class.

Step4: Analyze which graph displays data best

A histogram with 10 classes often provides a good balance. With 5 classes, the data may be too grouped and lose details. With 20 classes, the graph may be too fragmented and it may be difficult to see the overall pattern. A 10 - class histogram will show the distribution well while still providing a clear overview.

However, since the question only asks for the 20 - class histogram creation, we focus on that. But in general for best display, 10 classes is often better.

Since no graphs are provided to choose from for the 20 - class histogram part, we can't actually choose a correct graph as asked in the "Choose the correct graph below" part. But the process to create the 20 - class histogram is as above.

Answer:

No graph can be chosen as no graphs are provided. For best display of data in general, 10 - class histogram is often better.