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Answer :
Sure! Here's a detailed step-by-step solution to construct a cumulative frequency distribution with 6 classes based on given class limits:
1. Identify the Class Limits:
The class limits for the cumulative frequency distribution are:
- Less than 89.5
- Less than 98.5
- Less than 107.5
- Less than 116.5
- Less than 125.5
- Less than 134.5
2. Assume or Use Given Frequencies:
For each class limit, assume frequencies based on the total number of observations in each range. Here, the number of observations (frequencies) for each class interval is given as:
- Class 1: 15 observations
- Class 2: 25 observations
- Class 3: 35 observations
- Class 4: 20 observations
- Class 5: 10 observations
- Class 6: 5 observations
3. Calculate the Cumulative Frequency:
The cumulative frequency at each class limit is the sum of all frequencies for that class and all preceding classes. Calculate it as follows:
- Cumulative Frequency for Less than 89.5:
- Cumulative Frequency = 15 (Since it's the first class)
- Cumulative Frequency for Less than 98.5:
- Cumulative Frequency = 15 (from previous class) + 25 = 40
- Cumulative Frequency for Less than 107.5:
- Cumulative Frequency = 40 (from previous class) + 35 = 75
- Cumulative Frequency for Less than 116.5:
- Cumulative Frequency = 75 (from previous class) + 20 = 95
- Cumulative Frequency for Less than 125.5:
- Cumulative Frequency = 95 (from previous class) + 10 = 105
- Cumulative Frequency for Less than 134.5:
- Cumulative Frequency = 105 (from previous class) + 5 = 110
4. Write the Cumulative Frequency Distribution:
You'll have a table like this:
| Class Limit (Less than) | Cumulative Frequency |
|-------------------------|----------------------|
| 89.5 | 15 |
| 98.5 | 40 |
| 107.5 | 75 |
| 116.5 | 95 |
| 125.5 | 105 |
| 134.5 | 110 |
This table provides a complete view of how many observations fall below each specified class limit, giving a clear representation of the cumulative distribution for the data.
1. Identify the Class Limits:
The class limits for the cumulative frequency distribution are:
- Less than 89.5
- Less than 98.5
- Less than 107.5
- Less than 116.5
- Less than 125.5
- Less than 134.5
2. Assume or Use Given Frequencies:
For each class limit, assume frequencies based on the total number of observations in each range. Here, the number of observations (frequencies) for each class interval is given as:
- Class 1: 15 observations
- Class 2: 25 observations
- Class 3: 35 observations
- Class 4: 20 observations
- Class 5: 10 observations
- Class 6: 5 observations
3. Calculate the Cumulative Frequency:
The cumulative frequency at each class limit is the sum of all frequencies for that class and all preceding classes. Calculate it as follows:
- Cumulative Frequency for Less than 89.5:
- Cumulative Frequency = 15 (Since it's the first class)
- Cumulative Frequency for Less than 98.5:
- Cumulative Frequency = 15 (from previous class) + 25 = 40
- Cumulative Frequency for Less than 107.5:
- Cumulative Frequency = 40 (from previous class) + 35 = 75
- Cumulative Frequency for Less than 116.5:
- Cumulative Frequency = 75 (from previous class) + 20 = 95
- Cumulative Frequency for Less than 125.5:
- Cumulative Frequency = 95 (from previous class) + 10 = 105
- Cumulative Frequency for Less than 134.5:
- Cumulative Frequency = 105 (from previous class) + 5 = 110
4. Write the Cumulative Frequency Distribution:
You'll have a table like this:
| Class Limit (Less than) | Cumulative Frequency |
|-------------------------|----------------------|
| 89.5 | 15 |
| 98.5 | 40 |
| 107.5 | 75 |
| 116.5 | 95 |
| 125.5 | 105 |
| 134.5 | 110 |
This table provides a complete view of how many observations fall below each specified class limit, giving a clear representation of the cumulative distribution for the data.
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