Question

Use the accompanying data set to complete the following actions.

a. Find the quartiles
b. Find the Interquartile Range
c. Identify the outliers

40 50 36 44 41 37 39 48 44 37 34 54 43 34 15 51 38 51 30 30

In order:

15 30 30 34 34 36 37 38 39 40 41 43 44 44 47 48 50 51 51 54

a. Find the quartiles.

The first quartile, Q1, is

The second quartile, Q2, is

The third quartile, Q3, is

b. Find the Interquartile range.

The interquartile range (IQR) is.

c. Identify the Outliers

Answer 1

Solution:- Given values 15 30 30 34 34 36 37 38 39 40 41 43 44 44 47 48 50 51 51 54

a.

The first quartile, Q1, is 35

Explanation

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.

15 30 30 34 34 36 37 38 39 40 41 43 44 44 47 48 50 51 51 54

So, the bottom half is

15 30 30 34 34 36 37 38 39 40

The median of these numbers is 35.

=> The second quartile,Q2 is 40.5

Explanation

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:

15 30 30 34 34 36 37 38 39 40 41 43 44 44 47 48 50 51 51 54

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 = (40+41)/2 = 40.5

=> The third quartile,Q3, is 47.5

Explanation

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.

15   30   30   34   34   36   37   38   39   40   41   43   44   44   47   48   50   51   51   54   

So, the upper half is

41   43   44   44   47   48   50   51   51   54   

The median of these numbers is 47.5.

b. The interquartile range (IQR) is 12.5

Explanation

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

The third quartile is 47.5.

The first quartile is 35.

The interquartile range = 47.5 - 35 = 12.5.

c.

The outliers : 15