A cumulative frequency table is a useful way to depict the frequency of data points as they accumulate up to a certain point. Here’s an example based on a dataset of test scores for a group of students:
Example Data: Test Scores
Let's say we have the following scores out of 100 for a class of 20 students:
45, 55, 70, 75, 80, 85, 90, 92, 78, 66,
88, 50, 60, 73, 83, 95, 80, 67, 72, 100
Step 1: Organize the Data
First, we organize the scores into groups (bins) and count the frequency of scores within each group. Here’s how you might group them:
| Score Range | Frequency | |-------------|-----------| | 0 - 49 | 2 | | 50 - 59 | 3 | | 60 - 69 | 4 | | 70 - 79 | 6 | | 80 - 89 | 4 | | 90 - 100 | 1 |
Step 2: Create Cumulative Frequencies
Next, we calculate the cumulative frequency by adding the frequency from the previous bin to the current bin.
| Score Range | Frequency | Cumulative Frequency | |-------------|-----------|----------------------| | 0 - 49 | 2 | 2 | | 50 - 59 | 3 | 5 | | 60 - 69 | 4 | 9 | | 70 - 79 | 6 | 15 | | 80 - 89 | 4 | 19 | | 90 - 100 | 1 | 20 |
Interpretation
From the cumulative frequency table, you can interpret the data as follows:
- 2 students scored 49 or below.
- 5 students scored 59 or below.
- 9 students scored 69 or below.
- 15 students scored 79 or below.
- 19 students scored 89 or below.
- All 20 students scored 100 or below.
Cumulative frequency tables provide a clear visual representation of the data distribution, helping in analyzing how many observations fall below certain values.
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