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Construct a cumulative frequency distrib...

Construct a cumulative frequency distribution table from the frequency table given below :
`{:("Calss Interval","Frequency"),(1-10,12),(11-20,18),(21-30,23),(31-40,15),(41-50,10):}`

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To construct a cumulative frequency distribution table from the given frequency table, we will follow these steps: ### Step 1: Set Up the Table We will create a table with three columns: Class Interval, Frequency, and Cumulative Frequency. | Class Interval | Frequency (f) | Cumulative Frequency (cf) | |----------------|----------------|---------------------------| | 1 - 10 | 12 | | | 11 - 20 | 18 | | | 21 - 30 | 23 | | | 31 - 40 | 15 | | | 41 - 50 | 10 | | ### Step 2: Fill in the Cumulative Frequency The cumulative frequency is calculated by adding the frequency of the current class interval to the cumulative frequency of the previous class interval. 1. **First Class Interval (1 - 10)**: - Cumulative Frequency (cf) = Frequency (f) = 12 2. **Second Class Interval (11 - 20)**: - Cumulative Frequency (cf) = Previous cf + Current f = 12 + 18 = 30 3. **Third Class Interval (21 - 30)**: - Cumulative Frequency (cf) = Previous cf + Current f = 30 + 23 = 53 4. **Fourth Class Interval (31 - 40)**: - Cumulative Frequency (cf) = Previous cf + Current f = 53 + 15 = 68 5. **Fifth Class Interval (41 - 50)**: - Cumulative Frequency (cf) = Previous cf + Current f = 68 + 10 = 78 ### Step 3: Complete the Table Now we can fill in the cumulative frequencies in the table. | Class Interval | Frequency (f) | Cumulative Frequency (cf) | |----------------|----------------|---------------------------| | 1 - 10 | 12 | 12 | | 11 - 20 | 18 | 30 | | 21 - 30 | 23 | 53 | | 31 - 40 | 15 | 68 | | 41 - 50 | 10 | 78 | ### Final Cumulative Frequency Distribution Table The final cumulative frequency distribution table is as follows: | Class Interval | Frequency (f) | Cumulative Frequency (cf) | |----------------|----------------|---------------------------| | 1 - 10 | 12 | 12 | | 11 - 20 | 18 | 30 | | 21 - 30 | 23 | 53 | | 31 - 40 | 15 | 68 | | 41 - 50 | 10 | 78 |
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