Question

the data in the table represent the tuition for all 2-year community colleges in a region in 2022-2023
(a) construct a cumulative frequency distribution.
(b) construct a cumulative relative frequency distribution.

tuition (dollars)	number of community colleges
800-824	68
825-849	12
850-874	4
875-899	0
900-924	0
925-949	0
950-974	1

(a) complete the cumulative frequency distribution.

tuition (dollars)	cumulative frequency
800-824
825-849
850-874
875-899
900-924
925-949
950-974

Explanation:

Step1: Start with the first class (775 - 799)

The cumulative frequency for the first class is just its own frequency since there are no previous classes. So for 775 - 799, cumulative frequency = 22.

Step2: For the second class (800 - 824)

We add the frequency of this class to the previous cumulative frequency. Previous cumulative frequency (from 775 - 799) is 22, and the frequency of 800 - 824 is 68. So cumulative frequency = 22 + 68 = 90.

Step3: For the third class (825 - 849)

Add its frequency (12) to the previous cumulative frequency (90). So 90 + 12 = 102.

Step4: For the fourth class (850 - 874)

Add its frequency (4) to the previous cumulative frequency (102). So 102 + 4 = 106.

Step5: For the fifth class (875 - 899)

Add its frequency (0) to the previous cumulative frequency (106). So 106 + 0 = 106.

Step6: For the sixth class (900 - 924)

Add its frequency (0) to the previous cumulative frequency (106). So 106 + 0 = 106.

Step7: For the seventh class (925 - 949)

Add its frequency (0) to the previous cumulative frequency (106). So 106 + 0 = 106.

Step8: For the eighth class (950 - 974)

Add its frequency (1) to the previous cumulative frequency (106). So 106 + 1 = 107.

Now we can fill the cumulative frequency table:

Tuition (dollars)	Cumulative Frequency
800 - 824	90
825 - 849	102
850 - 874	106
875 - 899	106
900 - 924	106
925 - 949	106
950 - 974	107

Answer:

The cumulative frequency distribution is as shown in the table above. For part (a), the cumulative frequencies are 22, 90, 102, 106, 106, 106, 106, 107 for the respective tuition intervals.