The data below shows the number of hours a week on average a group of students spend volunteering for community service projects. What is a cumulative frequency table that represents the data?
4 5 10 21 6 2 9 8 12 15 8 14 6 4 6 11 3 2 9 16 22 23
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To create a cumulative frequency table, we need to arrange the data in ascending order and then count the number of observations less than or equal to each value. Here is the cumulative frequency table for the given data:
Hours (x) | Cumulative Frequency (cf)
------------------------------------
2 | 2
3 | 3
4 | 5
5 | 6
6 | 9
8 | 11
9 | 13
10 | 14
11 | 15
12 | 16
14 | 17
15 | 18
16 | 19
21 | 20
22 | 21
23 | 22
To create a cumulative frequency table from the given data, follow these steps:
1. Sort the data in ascending order:
2 2 3 4 4 5 6 6 6 8 8 9 9 10 11 12 14 15 16 21 22 23
2. Create two columns in the table: "Values" and "Cumulative Frequency".
3. In the "Values" column, list all unique values from the sorted data.
Values: 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 21, 22, 23
4. Calculate the cumulative frequency for each value by adding up the frequencies of all values equal to or less than the corresponding value.
For example, the first cumulative frequency would be the frequency of 2, which is 2 (since there are two 2's in the data). The second cumulative frequency would be the sum of the frequencies of 2 and 3, which is 3. And so on.
Cumulative Frequency: 2, 3, 5, 6, 9, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22
Here is the cumulative frequency table representing the given data:
Values | Cumulative Frequency
-------------------------------
2 | 2
3 | 3
4 | 5
5 | 6
6 | 9
8 | 11
9 | 13
10 | 14
11 | 15
12 | 16
14 | 17
15 | 18
16 | 19
21 | 20
22 | 21
23 | 22