Use the Mean to Describe Data Set

Introduction: 

• In this chapter, we will learn about data set, mean and median. Calculate and use the mean to describe a data set, calculate and use the median to describe a data set.  

Data set: 

A data set is a collection of numbers or values that relate to a particular subject. 

For example, the marks of each student in a particular class is a data set. The number of fish eaten by each penguin at a zoo is a data set. 

Mean: 

The ‘mean” is the average of a set of numbers. It is a measure of center that summarizes a data set with a single value.  

The “mean” is computed by adding all of the values in the data together and dividing by the number of elements contained in the data set. 

Median: 

The “median” is the middle value of a set of ordered numbers. 

8.2.1 Use the mean to describe a data set 

Steps to calculate mean: 

Example 1:  

Find the mean for the data set = 4, 5, 9, 7, 5, 2, 3. 

Solution: 

Number of elements in a data set is 7. 

Mean = ( 4 + 5 + 9 + 7 + 5 + 2 + 3 ) / 7  

= 5 

Let us understand how does mean work. 

6, 11 and 7 added together is the same as 3 lots of 8: 

It is like you are “flattening out” the numbers. 

Example 2: 

Ms. Nancy asked her students in the class the number of hours of TV watched in a week. She collected the data in the following table. What is the mean or average of the number of hours of TV watched in a week?  

Solution: 

To calculate the mean, add the scores in the data set. Then divide the sum by the number of values in the data set. 

8.2.2 Use the median to describe a data set 

Steps to calculate median: 

Example 1: 

8 students were surveyed about the number of hours they spend each week reading for fun. Order their responses from least to greatest values and find the median. 

Hours spent reading for fun each week: 11, 4, 9, 13, 3, 7, 5, 12 

Solution: 

Step 1: 

Order the values from least to greatest, 

2, 4, 5, 7, 9, 11, 12, 13 

Step 2: 

Since there are 8 items, the (8+1)/2th position, which is the 4.5^th median, can be computed by adding the 4th and 5th terms in that group, which is then divided by 2. 

Example 2: 

Louis, the CEO of a manufacturing organization, needs to replace seven robots with new ones. But, he is worried about the cost to be incurred by the company and hence calls Mr. Philip, the purchase manager of the firm, to help him calculate the median cost of the seven new robots. 

Mr. Philip, the purchase manager, suggested that new robots could be purchased only if the median price of the robots is below $84,000. The costs of the new robots are as follows: $75,000, $82,500, $60,000, $57,000, $1,00,000, $70,000, $93,000. Calculate the median cost of the robots. 

Solution: 

Step 1: 

Order the cost of robots from least to greatest, 

$57,000, $60,000, $70,000, $75,000, $82,500, $93,000, $1,00,000 

Step 2: 

Since there are 7 items, the median is (7+1)/2th item. It is 4th item, $75,000. 

Since the median is below $84,000, the new robots can be purchased. 

Exercise

1. Find the mean of the data set 9, 7, 11, 13, 2, 4, 5, 5.
2. Find the mean of the data set 16, 18, 19, 21, 23, 23, 27, 29, 29, 35.
3. Judy scored 5 goals, 6 goals, and 4 goals during her last three soccer games. How can you find the mean or average number of goals Judy scored?
4. The table below shows data about the students in three classes.

What is the mean number of boys in the three classes given in the table?

What is the mean number of girls in the three classes given in the table?

5. Use the table below and find the average low-temperature forecast for the five days.

6. Use the table below and find the average high temperature forecast for the five days

Concept Map: 

What have we learned:

• Understand the terms data set, mean and median.
• Calculate and use the mean to describe a data set.
• Calculate and use the median to describe a data set.