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Construct a cumulative, frequency distri...

Construct a cumulative, frequency distribution table from the frequency table given below :
`{:("Calss Interval","Frequency"),(0-8,9),(8-16,13),(16-24,12),(24-32,7),(32-40,15):}`

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To construct a cumulative frequency distribution table from the given frequency table, we will follow these steps: ### Step 1: Write down the class intervals and their corresponding frequencies. | Class Interval | Frequency (F) | |----------------|----------------| | 0 - 8 | 9 | | 8 - 16 | 13 | | 16 - 24 | 12 | | 24 - 32 | 7 | | 32 - 40 | 15 | ### Step 2: Create a new column for cumulative frequency (Cn). The cumulative frequency is calculated by adding the frequency of the current class interval to the cumulative frequency of the previous class interval. ### Step 3: Calculate the cumulative frequency for each class interval. 1. **For the first class interval (0 - 8)**: - Cumulative Frequency (Cn) = Frequency = 9 2. **For the second class interval (8 - 16)**: - Cn = Previous Cn + Current Frequency = 9 + 13 = 22 3. **For the third class interval (16 - 24)**: - Cn = Previous Cn + Current Frequency = 22 + 12 = 34 4. **For the fourth class interval (24 - 32)**: - Cn = Previous Cn + Current Frequency = 34 + 7 = 41 5. **For the fifth class interval (32 - 40)**: - Cn = Previous Cn + Current Frequency = 41 + 15 = 56 ### Step 4: Compile the cumulative frequency into a table. | Class Interval | Frequency (F) | Cumulative Frequency (Cn) | |----------------|----------------|----------------------------| | 0 - 8 | 9 | 9 | | 8 - 16 | 13 | 22 | | 16 - 24 | 12 | 34 | | 24 - 32 | 7 | 41 | | 32 - 40 | 15 | 56 | ### Step 5: Verify the cumulative frequency. To ensure our cumulative frequency is correct, we can check if the last cumulative frequency equals the sum of all frequencies. - Sum of Frequencies = 9 + 13 + 12 + 7 + 15 = 56 - Last Cumulative Frequency = 56 Since both values are equal, our cumulative frequency table is correct. ### Final Cumulative Frequency Distribution Table: | Class Interval | Frequency (F) | Cumulative Frequency (Cn) | |----------------|----------------|----------------------------| | 0 - 8 | 9 | 9 | | 8 - 16 | 13 | 22 | | 16 - 24 | 12 | 34 | | 24 - 32 | 7 | 41 | | 32 - 40 | 15 | 56 |
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