Question

The data below represent the number of people seen at a walk-in clinic on 30 randomly selected Mondays.

105   141   172   9   70   64   141    19   152    144

174   30     102     97    149   52      189     18    37    167

57    92    69   90   20    3     3    181     10    31

1) Compute the 5 number summary for the data.

a) Create a box and whisker plot using the 5 number summary. Please include the location of outliers, if any.

b) Compute the IQR of the data.

c) If you had to choose one combination of center/spread (choose from: mean/standard deviation, median/IQR, mode/range) to best summarize this set of data, which would you select? Please describe the rationale for your choice.

Answer 1

The five-number summary of a data set consists of the five numbers determined by computing the minimum, Q1, median, Q3, and maximum of the data set.

1. First, we write the data in increasing order: 3   3   9 10 18 19 20 30 31 37 52 57 64 69 70 90 92 97 102 105 141 141 144 149 152 167 172 174 181 189

five number summary

Min.	1st Qu.	Median	3rd Qu	Max
3	30.25	80	143.25	189

2. Box and whisker plot using the 5 number summary.

$wM5RR0bAKRb6gAAAABJRU5ErkJggg==$

3. The interquartile range of a data set is the distance between the two quartiles.
   Interquartile range = Q3 – Q1.

IQR = 143.25 – 30.25 = 113

4. The shape of a given distribution of a quantitative variable determines which numerical measures of center and spread are appropriate to use. In our case, the data is left skewed hence the median should be used to describe the center of the distribution because it is resistant to outliers and the IRQ to describe the spread of the distribution.