Question

Given the following data set 11 20 33 45 52 30 27 21 38 42 28 25 79 60 14 35 100 23 88 58

A. Find the quartiles

B. Determine if there are any outliers

C. Draw a box plot (exclude outliers but plot them as well).

Answer 1

A. 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.

11   14   20   21   23   25   27   28   30   33   35   38   42   45   52   58   60   79   88   100   

So, the bottom half is

11   14   20   21   23   25   27   28   30   33   

The median of these numbers is 24.

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:

11   14   20   21   23   25   27   28   30   33   35   38   42   45   52   58   60   79   88   100   

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=

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.

11   14   20   21   23   25   27   28   30   33   35   38   42   45   52   58   60   79   88   100   

So, the upper half is

35   38   42   45   52   58   60   79   88   100   

The median of these numbers is 55.

B. First we need to find IQR

The interquartile range is the difference between the third and first quartiles.

The third quartile is 55.

The first quartile is 24.

The interquartile range = 55 - 24 = 31.

So 1.5*IQR=1.5*31=46.5

So Q1-IQR*1.5=24-46.5=-22.5

And Q3+1.5*IQR=55+46.5=101.5

As all the points lie within the fences, no outliers

C.