Organize Data: First, we need to organize the data into a frequency distribution table. We'll create intervals (also known as classes) for the scores and then count how many scores fall into each interval.
Choose Intervals: Let's choose intervals of size 10, starting from 50 and ending at 90, since the lowest score is 48 and the highest is 90. The intervals will be: 50−59, 60−69, 70−79, 80−89, 90−99.
Count Scores: Now, we count how many scores fall into each interval. For 50−59, we have 2 scores (57,57). For 60−69, we have 6 scores (64,68,62,68,65,68). For 70−79, we have 15 scores (71,75,75,71,75,71,72,74,79,75,75,75,75,75,75). For 80−89, we have 20 scores (21). For 22, we have 2 scores (24).
Frequency Distribution: The frequency distribution table will look like this:| Interval | Frequency ||----------|-----------|| 50−59 | 2 || 60−69 | 6 || 70−79 | 15 || 80−89 | 9 || 90−99 | 2 |
Create Cumulative Frequency: Next, we'll create the cumulative frequency distribution table by adding the frequencies of each interval to the sum of the frequencies of all previous intervals.
Create Cumulative Frequency: Next, we'll create the cumulative frequency distribution table by adding the frequencies of each interval to the sum of the frequencies of all previous intervals. Starting with the first interval, the cumulative frequency for 50−59 is 2. For 60−69, it's 2 (previous) +6=8. For 70−79, it's 8 (previous) +15=23. For 80−89, it's 23 (previous) 20. For 21, it's 22 (previous) 23.
Create Cumulative Frequency: Next, we'll create the cumulative frequency distribution table by adding the frequencies of each interval to the sum of the frequencies of all previous intervals. Starting with the first interval, the cumulative frequency for 50−59 is 2. For 60−69, it's 2 (previous) +6=8. For 70−79, it's 8 (previous) +15=23. For 80−89, it's 23 (previous) 20. For 21, it's 22 (previous) 23. The cumulative frequency distribution table will look like this:| Interval | Cumulative Frequency ||----------|----------------------|| 50−59 | 2 || 60−69 | 8 || 70−79 | 23 || 80−89 | 22 || 21 | 60−693 |
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