Question

) Consider the following values representing the age of group of 31 adults: 75, 90, 60, 95, 85, 84, 76, 74, 92, 62, 83, 80, 90, 65, 72, 79, 36, 78, 65, 98, 70, 88, 99, 60, 82, 65, 79, 76, 80, 52, 75
a) Create a five-number summary for these ages.

b) Create a boxplot using the five-number summary from part (a).

Answer 1

a. The minimum is the smallest value in a data set.

Ordering the data from least to greatest, we get:

36   52   60   60   62   65   65   65   70   72   74   75   75   76   76   78   79   79   80   80   82   83   84   85   88   90   90   92   95   98   99   

So, the minimum is 36.

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

36   52   60   60   62   65   65   65   70   72   74   75   75   76   76   78   79   79   80   80   82   83   84   85   88   90   90   92   95   98   99   

So, the bottom half is

36   52   60   60   62   65   65   65   70   72   74   75   75   76   76   

The median of these numbers is 65.

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

36   52   60   60   62   65   65   65   70   72   74   75   75   76   76   78   79   79   80   80   82   83   84   85   88   90   90   92   95   98   99   

So, the median is 78 .

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

36   52   60   60   62   65   65   65   70   72   74   75   75   76   76   78   79   79   80   80   82   83   84   85   88   90   90   92   95   98   99   

So, the upper half is

79   79   80   80   82   83   84   85   88   90   90   92   95   98   99   

The median of these numbers is 85.

The maximum is the greatest value in a data set.

Ordering the data from least to greatest, we get:

36   52   60   60   62   65   65   65   70   72   74   75   75   76   76   78   79   79   80   80   82   83   84   85   88   90   90   92   95   98   99   

So, the maximum is 99.

Hence 5 number summary is

Min=36, Q1=65, Q2=78, Q3=85, Max=99

b.