Use this table to answer the questions.

Height (in inches)
Frequency

50-52
5

53-55
8

56-58
12

59-61
13

62-64
11


1. Identify the class width.
2. Identify the midpoint of the first class.
3. Identify the class boundaries of the first class.
4. Give the relative frequency for each class.

1. How many values included in the class?

2. The midpoint of 56-58 is 57, but that isn't the first class.

3. Class boundaries of 56-58 = 55.5-58.5.

4. Divide n of class scores by total n of scores.

To answer these questions, we need to understand the concepts of class width, midpoint, class boundaries, and relative frequency.

1. Class width: To find the class width, we need to subtract the lower bound of one class from the lower bound of the next class. From the given table, we can see that the lower bounds for the classes are: 50, 53, 56, 59, and 62.

Class width between the first and second class: 53 - 50 = 3
Class width between the second and third class: 56 - 53 = 3
Class width between the third and fourth class: 59 - 56 = 3
Class width between the fourth and fifth class: 62 - 59 = 3

Therefore, the class width is 3 inches.

2. Midpoint of the first class: To find the midpoint of a class, we need to calculate the average of the lower and upper bounds of the class.

For the first class, the lower bound is 50 and the upper bound is 52.

Midpoint of the first class: (50 + 52) / 2 = 51 inches.

So, the midpoint of the first class is 51 inches.

3. Class boundaries of the first class: Class boundaries are the ranges that include the lower and upper bounds of a class, with a small overlap to the adjacent classes.

For the first class, the lower bound is 50 and the upper bound is 52.

The class boundaries can be calculated as follows:

Lower class boundary: Lower bound - 0.5 = 50 - 0.5 = 49.5 inches
Upper class boundary: Upper bound + 0.5 = 52 + 0.5 = 52.5 inches

Therefore, the class boundaries of the first class are 49.5 inches (lower boundary) and 52.5 inches (upper boundary).

4. Relative frequency: Relative frequency is the ratio of the frequency of each class to the total frequency.

To calculate the relative frequency for each class, we need to divide the frequency of each class by the sum of all the frequencies.

Total frequency: 5 + 8 + 12 + 13 + 11 = 49

Relative frequency for the first class: 5 / 49 = 0.102
Relative frequency for the second class: 8 / 49 = 0.163
Relative frequency for the third class: 12 / 49 = 0.245
Relative frequency for the fourth class: 13 / 49 = 0.265
Relative frequency for the fifth class: 11 / 49 = 0.224

Therefore, the relative frequencies for each class are approximately:
- First class: 0.102
- Second class: 0.163
- Third class: 0.245
- Fourth class: 0.265
- Fifth class: 0.224