题目
The back-to-back stem-and-leaf diagram shows the annual salaries of 19 employees at each of two companies, Petral and Ravon.
(a) Find the median and the interquartile range of the salaries of the Petral employees.
The median salary of the Ravon employees is $33 800, the lower quartile is $32 000 and the upper quartile is $34 400.
(b) Represent the data shown in the back-to-back stem-and-leaf diagram by a pair of box-and-whisker plots in a single diagram.
(c) Comment on whether the mean or the median would be a better representation of the data for the employees at Petral.
题目中文翻译
背靠背茎叶图显示了 Petral 和 Ravon 两家公司各 19 名员工的年薪。
(a) 求 Petral 公司员工年薪的中位数和四分位距。
Ravon 公司员工年薪的中位数为 $33 800，下四分位数为 $32 000，上四分位数为 $34 400。
(b) 在同一幅图中画出一对箱线图，表示背靠背茎叶图中的数据。
(c) 评述均值和中位数中哪一个更适合代表 Petral 公司员工的数据。
原卷通用作答要求
Answer all questions. You should use a calculator where appropriate.
You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。
解答
(a)
解法一
思路
展开
19个薪资按大小排列，中位数第10个，下四分位数第5个，上四分位数第15个。图例每一叶代表100元。
答题过程
展开
For the 19 Petral employees, the median is the 10th ordered salary, 32000 dollars.
The lower quartile is the 5th salary, 31200 dollars, and the upper quartile is the 15th salary, 33500 dollars. Hence
(b)
解法一
思路
展开
从茎叶图读最小最大值，与给定或(a)求得的四分位数一起，画同一线性刻度的两条箱线图。
答题过程
展开
Use the five-number summaries
| Company | Minimum | Lower quartile | Median | Upper quartile | Maximum |
|---|---|---|---|---|---|
| Petral | |||||
| Ravon |
Draw the plots on a shared linear salary scale in dollars, labelling each company. Each box runs from its lower to upper quartile, with a median line inside and whiskers to its minimum and maximum.
(c)
解法一
思路
展开
Petral有一笔36800的高端极端值，会把均值向上拉；中位数对其不敏感。
答题过程
展开
The median is a better representation because the unusually high salary of 36800 dollars raises the mean, while the median is resistant to this extreme value.