Use this table to complete the tasks that follow it.

Height (in inches) Frequency
50-52 5
53-55 8
56-58 12
59-61 13
62-64 11



Identify the class width.
Identify the midpoint of the first class.
Identify the class boundaries of the first class.
Give the relative frequency for each class.

The first class includes 50, 51 and 52. What do you think its width would be?

The class boundaries include .5 value above and below the indicated class.

Of the 3 numbers above, what would be the midpoint?

The relative frequency is the number of scores in each class divided by the total number of scores.

You can do the calculations.

To complete the tasks, we need to understand some key concepts related to frequency distributions.

1. Class Width: The class width is the difference between the upper and lower class boundaries in a frequency distribution table. To calculate it, we subtract the lower class boundary from the upper class boundary.

In this case, the lower class boundaries are 50, 53, 56, 59, and 62, while the upper class boundaries are 52, 55, 58, 61, and 64. So, the class width is:

Class Width = Upper Class Boundary - Lower Class Boundary

For the first class, the class width is 52 - 50 = 2 inches.

2. Midpoint: The midpoint of a class is the value halfway between the lower and upper class boundaries. To calculate it, we find the average of the lower and upper class boundaries.

For the first class, the lower class boundary is 50 and the upper class boundary is 52. So, the midpoint is:

Midpoint = (Lower Class Boundary + Upper Class Boundary) / 2

For the first class, the midpoint is (50 + 52) / 2 = 51 inches.

3. Class Boundaries: Class boundaries are the values that separate one class from another in a frequency distribution table. They provide the complete range of values covered by each class. The class boundaries are calculated by subtracting 0.5 from the lower class boundary and adding 0.5 to the upper class boundary.

For the first class, the lower class boundary is 50 and the upper class boundary is 52. So the class boundaries are:

Lower Class Boundaries: 50 - 0.5 = 49.5
Upper Class Boundaries: 52 + 0.5 = 52.5

For the first class, the class boundaries are 49.5 - 52.5.

4. Relative Frequency: The relative frequency of a class is calculated by dividing the frequency of that class by the total number of data points. To calculate it, divide the frequency of each class by the sum of all frequencies.

In this case, the total frequency is 5 + 8 + 12 + 13 + 11 = 49.

Relative Frequency for each class = Frequency / Total Frequency

For the first class, the frequency is 5. So the relative frequency is:

Relative Frequency = 5 / 49 = 0.102 (approx.)

Therefore, the answers to the tasks are:

1. The class width is 2 inches.
2. The midpoint of the first class is 51 inches.
3. The class boundaries of the first class are 49.5 (lower) and 52.5 (upper).
4. The relative frequency for the first class is approximately 0.102.