Question

use the data set listed and technology to create frequency histograms with 5, 10, and 20 classes. which gra the data best? explain.
1 6 4 3 10 4 14 7 4 9 10 13 10
7 11 10 1 2 12 5 6 4 1 8 15 14
create a histogram with 5 classes. choose the correct graph below.

Explanation:

Step1: Determine class - width for 5 classes

First, find the range of the data. The smallest value is 1 and the largest value is 15. Range = 15 - 1=14. For 5 classes, class - width $w=\frac{14}{5}=2.8\approx3$.

Step2: Define the classes

The classes are: 1 - 3, 4 - 6, 7 - 9, 10 - 12, 13 - 15.

Step3: Count frequencies

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

Step4: Create the histogram

Based on the above - calculated frequencies for each class, the histogram can be drawn.

Since the problem only asks to choose the correct graph for 5 - class histogram among given options (not provided here), the above steps show how to construct the histogram.

For 10 classes:

Step1: Determine class - width

Range = 14. Class - width $w=\frac{14}{10}=1.4\approx2$.

Step2: Define the classes

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

Step3: Count frequencies

Count the number of data points in each class.

Step4: Create the histogram

For 20 classes:

Step1: Determine class - width

Range = 14. Class - width $w=\frac{14}{20}=0.7\approx1$.

Step2: Define the classes

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

Step3: Count frequencies

Count the number of data points in each class.

Step4: Create the histogram

In general, 10 classes may represent the data best. 5 classes may be too few and may group data too coarsely, losing some details. 20 classes may be too many and may show a lot of random fluctuations in the frequencies, making it hard to see the overall pattern.

Answer:

The process to create histograms for 5, 10 and 20 classes is shown above. 10 classes may represent the data best.