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Bot GPT 3.5 A. To construct a frequency distribution, first, we need to find the range of the data. The difference between the highest and lowest values in the data set is:
29.23 - 8.22 = 21.01
Next, we need to decide on the number of intervals (or classes) for the frequency distribution. A general guideline is to use 5-20 intervals. Here, we will use 10 intervals.
The width of each interval can be calculated by dividing the range by the number of intervals:
21.01 / 10 = 2.101 (approximately)
Now, we can start creating the frequency distribution table:
Interval Frequency
8.22 - 10.32 | 3
10.32 - 12.42 | 7
12.42 - 14.52 | 5
14.52 - 16.62 | 2
16.62 - 18.72 | 2
18.72 - 20.82 | 2
20.82 - 22.92 | 1
22.92 - 25.02 | 0
25.02 - 27.12 | 2
27.12 - 29.23 | 1
The intervals are determined by adding the width to the lower limit of each interval.
B. To plot the ogive curve and frequency polygon, we need to calculate the cumulative frequency. We add up the frequencies starting from the first interval.
Interval Frequency Cumulative Frequency
8.22 - 10.32 | 3 | 3
10.32 - 12.42 | 7 | 10
12.42 - 14.52 | 5 | 15
14.52 - 16.62 | 2 | 17
16.62 - 18.72 | 2 | 19
18.72 - 20.82 | 2 | 21
20.82 - 22.92 | 1 | 22
22.92 - 25.02 | 0 | 22
25.02 - 27.12 | 2 | 24
27.12 - 29.23 | 1 | 25
Using this information, we can plot the ogive curve and frequency polygon. The x-axis represents the intervals, and the y-axis represents the cumulative frequency.
The ogive curve connects the points representing the upper limits of each interval with the cumulative frequency.
The frequency polygon connects consecutive points with the midpoints of each interval and the frequency.
Note: Please note that the graph cannot be visualized accurately as I cannot draw it.