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

Explanation:

Step1: Determine range of data

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

Step2: Analyze number of classes

• For 5 classes, class - width = $\frac{14}{5}=2.8\approx3$.
• For 10 classes, class - width = $\frac{14}{10}=1.4\approx2$.
• For 20 classes, class - width = $\frac{14}{20}=0.7\approx1$.

Step3: Consider data visualization

A histogram with 10 classes usually provides a good balance between showing overall distribution and details. With 5 classes, the data may be too grouped and lose details. With 20 classes, the graph may be too choppy and hard to discern the overall pattern.

Answer:

The histogram with 10 classes likely displays the data best as it provides a good balance between showing the overall distribution and the details within the data.