Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92

Determine the interquartile range of the age of senior citizens.

Question

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92

Determine the interquartile range of the age of senior citizens.

BlackTom AI · Accepted Answer

We start by listing the ages in nondecreasing order, which the data already provide: 
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92.
There are 25 observations, so the overall median is the 13th value (since (25 + 1) / 2 = 13). The 13th value is 73, so the median is 73.
To find the quartiles, we need to decide how to split the data into halves. One common approach (which matches the given answer) uses inclusive halves, meaning the median is included in both the lower and upper halves:
- Lower half (including the median): the first 13 values: 60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73.
- Upper half (including the median): the last 13 values: 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92.
Now, compute Q1 as the median of the lower half. With 13 values in the lower half, the middle value is the 7th value: that is 66. 
Similarly, compute Q3 as the median of the upper half. With 13 values in the upper half, the middle value is the 7th value: that is 81. 
Finally, the interquartile range (IQR) is Q3 minus Q1: 81 − 66 = 15. 
Note: if a different convention is used (e.g., excluding the median from one or both halves), you would obtain a different IQR, such as 16, which corresponds to the method where the lower and upper halves each contain 12 values after removing the median. The chosen convention affects the quartile values and hence the IQR. In this dataset, using inclusive halves yields an IQR of 15.

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

智能学习助手

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