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. 3
2. 51
3. 50 and 52
4. Relative to what? The frequencies listed are already relative.
To answer these questions, we need to understand the information provided in the table. The table shows the height (in inches) and frequency of individuals falling into different height ranges.
1. To identify the class width, we need to determine the range of values in each height class. The class width is the difference between the upper and lower limits of a class. In this case, we can see that each class has a range of 3 inches. Therefore, the class width is 3 inches.
2. To identify the midpoint of the first class, we need to determine the average or midpoint value of the lower and upper limits of the class. The first class is from 50-52 inches. The midpoint can be calculated by adding the lower and upper limits and dividing by 2. So, (50 + 52) / 2 = 51. Therefore, the midpoint of the first class is 51 inches.
3. To identify the class boundaries of the first class, we need to determine the upper and lower boundaries of the class. The lower boundary is the lower limit subtracted by 0.5, and the upper boundary is the upper limit added by 0.5. So, for the first class, the lower boundary would be 50 - 0.5 = 49.5 inches and the upper boundary would be 52 + 0.5 = 52.5 inches. Therefore, the class boundaries of the first class are 49.5-52.5 inches.
4. To calculate the relative frequency for each class, we need to divide the frequency of each class by the total number of observations. In this case, the total number of observations is the sum of the frequencies, which is 5 + 8 + 12 + 13 + 11 = 49. The relative frequency for each class can be calculated by dividing the frequency of the class by 49.
For the first class (50-52 inches), the frequency is 5. So, the relative frequency is 5/49.
For the second class (53-55 inches), the frequency is 8. So, the relative frequency is 8/49.
For the third class (56-58 inches), the frequency is 12. So, the relative frequency is 12/49.
For the fourth class (59-61 inches), the frequency is 13. So, the relative frequency is 13/49.
For the fifth class (62-64 inches), the frequency is 11. So, the relative frequency is 11/49.
Therefore, the relative frequency for each class is as follows:
First class: 5/49
Second class: 8/49
Third class: 12/49
Fourth class: 13/49
Fifth class: 11/49