Question

Consider the following data set:

	115	191	153	194	236
	184	216	185	183	202

Calculate the 4th number (Q3) of the five-number summary for this data (rounded to the nearest integer).

Answer 1

The minimum is the smallest value in a data set.

Ordering the data from least to greatest, we get:

115   153   183   184   185   191   194   202   216   236   

So, the minimum is 115.

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.

115   153   183   184   185   191   194   202   216   236   

So, the bottom half is

115   153   183   184   185   

The median of these numbers is 183.

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:

115   153   183   184   185   191   194   202   216   236   

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:

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.

115   153   183   184   185   191   194   202   216   236   

So, the upper half is

191   194   202   216   236   

The median of these numbers is 202.

The maximum is the greatest value in a data set.

Ordering the data from least to greatest, we get:

115   153   183   184   185   191   194   202   216   236   

So, the maximum is 236.