We are given a dataset of marks from 55 students. We need to answer questions 8 and 9 related to class intervals and their frequencies. Question 8: Determine the correct class intervals using a class width of 7 with the inclusive method. Question 9: Determine the respective frequencies of the class intervals created in question 8.

Probability and StatisticsData AnalysisFrequency DistributionClass IntervalsStatistics
2025/3/13

1. Problem Description

We are given a dataset of marks from 55 students. We need to answer questions 8 and 9 related to class intervals and their frequencies.
Question 8: Determine the correct class intervals using a class width of 7 with the inclusive method.
Question 9: Determine the respective frequencies of the class intervals created in question
8.

2. Solution Steps

Question 8:
The inclusive method includes both endpoints in the interval. The smallest value in the dataset is
1.
If we choose to begin the first interval at 1, and have the width be 7, the interval would be [1, 1+7-1] = [1, 7]. The next interval would start at 8 and be [8, 8+7-1] = [8, 14]. Continuing this pattern:
1-7
8-14
15-21
22-28
29-35
36-42
The largest value in the dataset is 40, so we don't need to go past 36-
4
2.
Comparing these class intervals to the options provided, option (b) matches: 1-7, 8-14, 15-21, 22-28, 29-35, 36-
4
2.
Question 9:
First, sort the given data: 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 9, 9, 10, 11, 12, 12, 13, 14, 15, 15, 15, 16, 17, 18, 18, 18, 20, 21, 21, 22, 23, 24, 26, 27, 27, 27, 28, 28, 28, 29, 29, 31, 32, 32, 33, 36,
4
0.
Now we can count the frequencies:
1-7: 14
8-14: 12
15-21: 11
22-28: 9
29-35: 6
36-42: 3 (36 and 40)
So the frequencies are: 14, 12, 11, 9, 6,

3. However, none of the answer options exactly match these frequencies. We will choose the closest option based on the class intervals that we calculated earlier: 1-7, 8-14, 15-21, 22-28, 29-35, 36-

4

2. By comparing with the given options, we see option (c) 15, 12, 11, 9, 6, 2 is the closest.

3. Final Answer

Question 8: (b) 1-7, 8-14, 15-21, 22-28, 29-35, 36-42
Question 9: (c) 15, 12, 11, 9, 6, 2

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