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

Explanation:

Step1: Determine data range

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

Step2: Calculate class width for 10 classes

The class width $w=\frac{R}{n}$, where $n = 10$. So $w=\frac{14}{10}=1.4$. We can round it up to 2 for convenience.

Step3: Define class intervals

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

Step4: Count frequencies

For the class $1 - 2$: There are 4 values (1, 1, 1, 2). For the class $3 - 4$: There are 6 values (3, 4, 4, 4, 4, 4). For the class $5 - 6$: There are 3 values (5, 6, 6). For the class $7 - 8$: There are 3 values (7, 7, 8). For the class $9 - 10$: There are 5 values (9, 10, 10, 10, 10). For the class $11 - 12$: There are 2 values (11, 12). For the class $13 - 14$: There are 3 values (13, 14, 14). For the class $15 - 16$: There is 1 value (15). However, since we don't have the actual graphs A and B provided, we can't choose the correct graph. But in general, a good - looking histogram should have a clear pattern and not be too sparse or too crowded. Usually, 10 classes can be a good balance for a data - set of this size to show the distribution pattern. If 5 classes are used, the data may be over - grouped and important details may be lost. If 20 classes are used, the data may be too fragmented and the overall pattern may not be clear.

Answer:

Since the graphs A and B are not shown, we cannot determine which is the correct graph for the 10 - class histogram. But in terms of which number of classes displays the data best, 10 classes is often a good choice as it balances showing details and the overall distribution pattern compared to 5 (which may over - group) and 20 (which may under - group).