数据比较 - 掌握多组数据对比分析的方法
位置度量：比较数据的中心位置（均值、中位数）。
离散度量：比较数据的分散程度（标准差、四分位距）。
一致性原则：确保比较的统计量类型一致。
| 数据特征 | 位置度量 | 离散度量 | 适用场景 |
|---|---|---|---|
| 有极端值 | 中位数 | 四分位距 | 收入、房价等 |
| 无极端值 | 均值 | 标准差 | 身高、体重等 |
| 对称分布 | 均值 = 中位数 | 标准差 ≈ IQR/1.35 | 正态分布数据 |
The daily mean temperature (°C) during August is recorded at London Heathrow Airport and Dubai International Airport.
For London Heathrow, \( \Sigma x = 562.0 \) and \( \Sigma x^2 = 10301.2 \)
a) Calculate the mean and standard deviation for London Heathrow.
For Dubai International, the mean temperature was 31 °C with a standard deviation of 1.35 °C.
b) Compare the data for the two airports using the information given.
a) 伦敦希思罗机场统计量计算：
八月有31天，故\( n = 31 \)
b) 两机场数据对比：
The box plots show the distribution of speeds of cars on two motorways.
Compare the distributions of the speeds on the two motorways.
箱线图比较分析：
Two classes of primary school children complete a puzzle. Summary statistics for the times the children took, in minutes, are shown in the table.
| \( n \) | \( \Sigma x \) | \( \Sigma x^2 \) | |
|---|---|---|---|
| Class 2B | 20 | 650 | 22000 |
| Class 2F | 22 | 598 | 19100 |
Calculate the mean and standard deviation of the times and compare the distributions.
答题区域：
The stem and leaf diagram shows the age, in years, of the members of a sports club.
| Male | Stem | Female |
|---|---|---|
| 8 8 7 6 | 1 | 6 6 6 7 7 8 8 9 |
| 7 6 5 5 3 3 2 1 | 2 | 1 3 3 4 5 7 8 8 9 9 |
| 9 8 4 4 3 | 3 | 2 3 3 4 7 |
| 5 2 1 | 4 | 0 1 8 |
| 9 0 | 5 | 0 |
Key: 1|4|0 represents a male aged 41 and a female aged 40
a) Find the median and interquartile range for the males.
b) The median and interquartile ranges for the females are 27 and 15 respectively. Make two comparisons between the ages of the males and females.
答题区域：
In the box plots here, the marks for a group of students taking their Mathematics exam for the first time are shown on the top. The marks for a group of students who are retaking their Mathematics exam are shown on the bottom.
Compare and contrast the marks between the two groups taking the exam. (3 marks)
答题区域：
The heights of students in two different schools are measured. The summary statistics are:
School A: Mean = 165 cm, Standard deviation = 8 cm, n = 30
School B: Mean = 170 cm, Standard deviation = 6 cm, n = 25
a) Compare the average heights of students in the two schools.
b) Compare the variability in heights between the two schools.
c) Which school has more consistent heights? Explain your answer.
答题区域：
解答过程：
Class 2B统计量计算：
Class 2F统计量计算：
对比分析：
解答过程：
a) 男性年龄统计量：
男性年龄升序：16,17,18,18,21,22,23,23,25,25,26,27,33,34,34,38,39,41,42,45,50,59（共22人）
b) 男女年龄对比：
解答过程：
解答过程：
a) 平均身高对比：
b) 身高变异性对比：
c) 一致性分析：