A researcher wants to know what people in Melbourne think about football. She asks ten people to rate their attitude towards football on a scale from 0 (don't like football at all) to 10 (like football a lot). The ratings are as follows: 10, 9, 6, 9, 5, 5, 1, 5, 10, 6 What is the interquartile range (IQR) of this data?

Question

A researcher wants to know what people in Melbourne think about football. She asks ten people to rate their attitude towards football on a scale from 0 (don't like football at all) to 10 (like football a lot). The ratings are as follows: 10, 9, 6, 9, 5, 5, 1, 5, 10, 6  What is the interquartile range (IQR) of this data?

BlackTom AI · Accepted Answer

We start by listing the data: 10, 9, 6, 9, 5, 5, 1, 5, 10, 6.
Next, sort the data in ascending order: 1, 5, 5, 5, 6, 6, 9, 9, 10, 10.
There are 10 observations (an even number), so the median is between the 5th and 6th values, but for quartiles we typically divide the data into a lower half and an upper half.
Lower half (first 5 values): 1, 5, 5, 5, 6. The median of this lower half is the third value, which is 5. This gives Q1 = 5.
Upper half (last 5 values): 6, 9, 9, 10, 10. The median of this upper half is the third value, which is 9. This gives Q3 = 9.
The interquartile range (IQR) is Q3 minus Q1, which is 9 − 5 = 4. However, the question seems to present IQR as the interval defined by Q1 and Q3, i.e., (Q1, Q3).
With Q1 = 5 and Q3 = 9, the corresponding option should reflect (5, 9).
Now evaluate the answer choices:
- a. 6, 6: This would imply Q1 = 6 and Q3 = 6, which contradicts the calculated quartiles since the lower half’s median is 5 and the upper half’s median is 9.
- b. 5, 6: This would imply Q3 = 6, but the upper half’s median is 9, not 6.
- c. 6, 9: This would imply Q1 = 6, which is not supported by the lower half’s median of 5.
- d. 5, 9: This matches Q1 = 5 and Q3 = 9 derived from the data.
Thus, the pair that corresponds to the data’s quartiles is (5, 9).

NUT1002 S2 2025 AT2: Midsemester quiz (10%)

查看解析

登录即可查看完整答案

类似问题

位置18的问题 The 题库 1/1[input] range is the difference between the first and third quartiles. (Note: Answer can only be one word or one number, must be lowercase.)

A researcher has collected the following sample data. The mean of the sample is 5. 3 5 12 3 2 The IQR is

An interquartile range describes the spread of the middle 50% of data.

The weights (in kg) carried by the horses in a handicap race are given below. 60 57 57 55 54 53 53 53 52 52 51.5 51 What is the interquartile range? (Write the value only, don't include the units)

The weights (in kg) carried by the horses in a handicap race are given below. 60 57 57 55 54 53 53 53 52 52 51.5 51 What is the interquartile range? (Write the value only, don't include the units)

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单