To analyze the ages of the students in both classes, we will calculate the mean and the median for each class.
Class I Ages: 14, 15, 15, 16, 16, 16, 17, 17, 18
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Calculate the mean of Class I:
- Sum of ages = 14 + 15 + 15 + 16 + 16 + 16 + 17 + 17 + 18 = 14 + 2(15) + 3(16) + 2(17) + 18 = 14 + 30 + 48 + 34 + 18 = 144
- Number of students = 9
- Mean = Total sum / Number of students = 144 / 9 = 16
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Calculate the median of Class I:
- To find the median, we need to find the middle value.
- Since there are 9 values (an odd number), the median is the 5th value when arranged in order:
- The ages in order: 14, 15, 15, 16, 16, 16, 17, 17, 18
- Median = 16
Class II Ages: 13, 14, 15, 16, 16, 17, 18, 18, 19
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Calculate the mean of Class II:
- Sum of ages = 13 + 14 + 15 + 16 + 16 + 17 + 18 + 18 + 19 = 13 + 14 + 15 + 2(16) + 17 + 2(18) + 19 = 13 + 14 + 15 + 32 + 17 + 36 + 19 = 146
- Number of students = 9
- Mean = Total sum / Number of students = 146 / 9 ≈ 16.222 (approximately)
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Calculate the median of Class II:
- To find the median, we need to find the middle value.
- Since there are 9 values (an odd number), the median is the 5th value when arranged in order:
- The ages in order: 13, 14, 15, 16, 16, 17, 18, 18, 19
- Median = 16
Now we can summarize the findings:
- Class I: Mean = 16, Median = 16
- Class II: Mean ≈ 16.222, Median = 16
Comparison:
- Mean of Class II (≈ 16.222) is larger than Mean of Class I (16).
- Median of Class II (16) is the same as Median of Class I (16).
Thus, the correct statement about Class II is: D. The mean of Class II is larger than Class I, and the median is the same.
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