1. Lesson 1

1.5. Explore

Mathematics 30-3 Module 4

Module 4: Statistics

 

This photograph shows a man and woman balancing on a rock near a river.

Ingram Publishing/Thinkstock

Explore

 

In Discover you were introduced to the concept of average. The concept of average is connected to the measures of central tendency. Central tendency refers to the “middle” of a set of data and is commonly measured by the arithmetic mean, median, and mode. In this lesson you will explore how each of these measures of central tendency is calculated and how each can be used to describe the average of a set of data.

 

When people think of “average,” they usually think of the measure that is correctly known as the arithmetic mean. To determine the arithmetic mean, find the sum of all the data values and divide the sum by the number of values.

 

For an example of this calculation, view the Arithmetic Mean interactive.

 

 

This is a play button for Arithmetic Mean.

 

For this module, arithmetic mean will be referred to as “mean.”




caution

Calculator Keystrokes Hint: A common mistake made when calculating the mean is to forget to press the equal sign before the divide key. This will result in an incorrect solution, as shown.

 

 

 

The table displays the correct sequence.

 

Steps

Example
  1. Add the numbers of the sequence.

12 + 13 + 17 + 3 + 13 + 15 + 2 + 22
  1. Press the equal key.

= 97
  1. Count the number of numerals in the sequence.

8
  1. Divide the sum of the sequence of numbers by the number of numerals.

97 ÷ 8

= 12.125
Self-Check 1
  1. What is the mean of the data set {9, 16, 10, 32, 7, 16}? Answer
  2. If the mean of a set of numbers is 55, which of the following could be true?
    1. All the numbers in the set could equal 55.
    2. When all the numbers are added and then divided by the number of values, the result is 55.
    3. Some numbers could be over 75.
    4. All of the above.

    Answer
Share 2

 

Refer back to the hockey players’ salary discussion in Discover and answer these questions.

  1. Would you expect half of the players’ salaries to be above the average salary and half of the players’ salaries to be below the average salary?
  2. Given the data {10, 11, 13, 17, 21}, find the middle value.
  3. Given the data {10, 11, 13, 15, 17, 21}, find the middle value.

Consider your findings and share your answers with a partner.

 

course folder If required, place a summary of your discussion in your course folder.