Question

A telemarketing firm is monitoring the performance of its employees based on the number of sales per hour. One employee had the following sales for the last 19 hours

9,5,2,6,5,6,4,4,4,7,4,4,7,8,4,4,5,5,4

What is the mode, median and mean for the distribution of number of sales per hour?

What is the first and third quartile for the distribution of number of sales per hour?

For the distribution of sales per hour, what is the interquartile range?

Draw a dot plot for the data

Answer 1

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

2   4   4   4   4   4   4   4   4   5   5   5   5   6   6   7   7   8   9   

We see that the mode is 4 .

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:

2   4   4   4   4   4   4   4   4   5   5   5   5   6   6   7   7   8   9   

So, the median is 5 .

Mean=

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.

2   4   4   4   4   4   4   4   4   5   5   5   5   6   6   7   7   8   9   

So, the bottom half is

2   4   4   4   4   4   4   4   4   

The median of these numbers is 4.

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.

2   4   4   4   4   4   4   4   4   5   5   5   5   6   6   7   7   8   9   

So, the upper half is

5   5   5   6   6   7   7   8   9   

The median of these numbers is 6.

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

The third quartile is 6.

The first quartile is 4.

The interquartile range = 6 - 4 = 2.