use the data set listed and technology to create frequency histograms with 5, 10, and 20 classes. which…

use the data set listed and technology to create frequency histograms with 5, 10, and 20 classes. which graph displays the data best? explain.\n3 6 3 1 10 3 14 7 4 9 9 13 8\n7 10 10 1 1 13 4 7 4 1 9 15 14

use the data set listed and technology to create frequency histograms with 5, 10, and 20 classes. which graph displays the data best? explain.\n3 6 3 1 10 3 14 7 4 9 9 13 8\n7 10 10 1 1 13 4 7 4 1 9 15 14

Answer

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.