Organize the data into a class interval frequency distribution using 10 intervals with frequency (f) and relative frequency (rf).
Data Set: 100, 97, 99, 70, 72, 75, 82, 68, 85, 88, 71, 77, 93, 94, 54, 59, 83, 87, 98, 84, 72, 96, 98, 89, 74, 98, 77, 82, 83, 98, 90, 95, 85, 76, 62, 72, 36, 21, 42, 86, 75, 42, 91, 90, 81, 78, 79, 74, 82, and 98
To organize the data into a class interval frequency distribution, we need to follow these steps:
Step 1: Find the range of the data.
The range is the difference between the maximum and minimum values in the dataset. In this case, the maximum value is 100 and the minimum value is 21, so the range is 100 - 21 = 79.
Step 2: Determine the width of each interval.
To determine the width of each interval, we divide the range by the desired number of intervals. In this case, we want to use 10 intervals, so the width of each interval is 79 / 10 = 7.9. Since we can't have a fraction as the width, we can round it up to 8.
Step 3: Determine the lower and upper limits of each interval.
The lower limit of the first interval can be set as the minimum value (21). The upper limit of each interval is found by adding the width to the lower limit. For the subsequent intervals, the lower limit will be the upper limit of the previous interval, and the upper limit will be calculated accordingly.
Step 4: Count the frequency of each interval.
To find the frequency of each interval, we count the number of data points that fall within each interval. We will use brackets to denote the intervals.
Step 5: Calculate the relative frequency of each interval.
The relative frequency of each interval is the ratio of the frequency of that interval to the total number of data points (in this case, 50).
Now, let's go through each step:
Step 1: Range: 100 - 21 = 79
Step 2: Width of each interval: 8
Step 3: Lower and upper limits of each interval:
- Interval 1: 21 - 28
- Interval 2: 29 - 36
- Interval 3: 37 - 44
- Interval 4: 45 - 52
- Interval 5: 53 - 60
- Interval 6: 61 - 68
- Interval 7: 69 - 76
- Interval 8: 77 - 84
- Interval 9: 85 - 92
- Interval 10: 93 - 100
Step 4: Frequency of each interval:
- Interval 1: 1
- Interval 2: 2
- Interval 3: 3
- Interval 4: 3
- Interval 5: 2
- Interval 6: 4
- Interval 7: 6
- Interval 8: 9
- Interval 9: 5
- Interval 10: 5
Step 5: Relative frequency of each interval (rounded to 2 decimal places):
- Interval 1: 0.02
- Interval 2: 0.04
- Interval 3: 0.06
- Interval 4: 0.06
- Interval 5: 0.04
- Interval 6: 0.08
- Interval 7: 0.12
- Interval 8: 0.18
- Interval 9: 0.10
- Interval 10: 0.10
Therefore, the class interval frequency distribution with 10 intervals, frequency, and relative frequency for the given data set is as follows:
Interval Frequency Relative Frequency
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21 - 28 1 0.02
29 - 36 2 0.04
37 - 44 3 0.06
45 - 52 3 0.06
53 - 60 2 0.04
61 - 68 4 0.08
69 - 76 6 0.12
77 - 84 9 0.18
85 - 92 5 0.10
93 - 100 5 0.10