$2025$ - $2026$ 学年 医学科学素养Ⅱ 练习1

基础医学专业课 线下练习题
2025.10.9, 不计分, 不作考勤

一、 Here's where you have to really think about how you can best give a representative age (or ages) for the swimming class. Please see the following table:

Age 1 2 3 31 32 33
Frequency 3 4 2 2 4 3

  1. Why do you think the mean and median both failed for this data? Why are they misleading? (10)

  2. If you had to pick one age to represent this class, what would it be? Why? (10)

  3. What if you could pick two ages instead? Which two ages would you pick, and why? (10)

二、 Find the mode for the following sets of data. (5'*3)

Values 1 2 3 4 5 6 7 8
Frequency 4 6 4 4 3 2 1 1


Category Blue Red Green Pink Yellow
Frequency 4 5 8 1 3


Values 1 2 3 4 5
Frequency 2 3 3 3 3


When do you think the mode is most useful? (5)

When is the mode least useful? (5)

三、Suppose a new drug A can help prolong the survival time of 20 days for every colorectal cancer patient. Drug B increases survival time by 10%. The mean survival time is 100 days, the median is 60 days, and the mode is 90 days.

  1. What happens to the mean, median, and mode if every patient takes drug A? (15)

  2. What happens to the mean, median, and mode if every patient takes drug B instead? (15)

四、A teacher records the following test scores (out of 100) for her class of 20 students:

Scores: 45, 52, 71, 67, 61, 74, 76, 78, 79, 82, 83, 85, 86, 87, 88, 89, 91, 92, 94, 98

Calculate the 25th percentile (first quartile Q1). (6)

五、A sample of 5 individuals with the following weights (in kg):

Weights: 45, 52, 61, 67, 75

Calculate the sample standard deviation. (9)

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