Question

Find the five-number summary, and (b) draw a box-and-whisker plot of the data 3 8 8 6 2 9 8 7 9 6 9 5 1 6 2 9 8 7 7 9

Answer 1

The minimum value of the data set is 1.

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.

1   2   2   3   5   6   6   6   7   7   7   8   8   8   8   9   9   9   9   9   

So, the bottom half is

1   2   2   3   5   6   6   6   7   7   

The median of these numbers is 5.5.

The first quartile of the data set is 5.5.

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:

1   2   2   3   5   6   6   6   7   7   7   8   8   8   8   9   9   9   9   9   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median=(7+7) / 2=7

The median of the data set is 7.

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.

1   2   2   3   5   6   6   6   7   7   7   8   8   8   8   9   9   9   9   9   

So, the upper half is

7   8   8   8   8   9   9   9   9   9   

The median of these numbers is 8.5.

The third quartile of the data set is 8.5.

The maximum value of the data set is 9.