Question

Example of cumulative frequency table

Answer 1

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.