Page

# Lesson 28 โ Activity 1: Measures of Central Tendency

Completion requirements

# Lesson 28 โ Activity 1:

#
Measures of Central Tendency

#### Getting Ready

####
Statistics are a part of everyday life โ especially in sports! Sports recruiters use statistics to check out potential athletes. Sports teams also use statistics to prepare for upcoming opponents. They look to see which players on the opposing teams are doing well at that time. They also use statistics to see which of their own players are doing well and decide who will bring the best results for the game. In this activity, you will learn more about statistics and the measures of central tendency.

Courtesy of ADLC

#### Statistics are a part of sports. There isn't a sport out there that at some level doesn't use statistics. The rule book for Major League Baseball even has a section that is dedicated to statistics and how to keep them.

The result of every play of every game that Northern Alberta Volleyball Club (NAVC) played in was recorded. After every game, you knew how each player did, how many serves each player made and if they were in or out, who scored the points,
who substituted in and out of the game, and what the final score was, along with many other things. This information can be used to find trends to be used in the future.

####
Three measures that can be calculated with the information gathered are what are called the **measures of central tendency**.

#### They are the mean, median, and mode.

#### For example, if Ian serves 5 times per game, Leighton serves 8 times per game and Jay serves 10 times per game, I can calculate the mean of the number of serves like this:

####
1. Add up all of the numbers:

5 + 8 + 10 = 23

2. Divide the sum by the number of values you have. In this case, there are three numbers.

23 รท 3 = 7.7

The mean number of serves for the three players is 7.7 serves per game.

#### The median is the middle number of a set of values arranged in order from lowest to highest.

####
For example, in various tournaments, NAVC played the following number of games: 10, 15, 11, 12, 14, 13, and 10. You could calculate the median number of games like this:

1. Arrange the numbers in order from lowest to highest.

10, 10, 11, 12, 13, 14, 15

2. Count the number of terms. In this case there are seven. If there are an odd number of terms, divide the number by 2 and round up.

7 รท 2 = 3.5 rounds up to 4

The fourth term is 12. Therefore the median is 12.

####
But what if there is an even number of terms? Let's say that I forgot one tournament when I wrote down the list and they actually played 11 games in that tournament. My corrected list is now:

10, 10, 11, 11, 12, 13, 14, 15

I now have eight terms.

####
8 รท 2 = 4

####
If you have an even number of terms, you must take the middle two terms, add them up, and divide by 2 in order to get the median. In this case, I would count four terms in from each end. That gives me the numbers 11 and 12.

11 + 12 = 23

23 รท 2 = 13.5

My median is now 13.5.

#### The mode is the number that occurs most often in a set of values.

####
For example, if Brendan sets the ball 12 times, Jordan sets the ball 14 times, Boston sets the ball 12 times, and Mike sets the ball 11 times, we could find the mode like this:

1. Put the numbers from lowest to highest.

11, 12, 12, 14

2. Look for repeating numbers. In this case, the number 12 is the only repeating number. There are two 12s. It is our mode.

It is important to note that while you can only have one mean and one median in a set of numbers, you can have more than one mode.

####
For example, if our list changed to:

11, 11, 12, 12, 14

We would have two modes because both 11 and 12 occur twice.

That's a lot of information! Now it's your turn to work with these concepts. It really does become a bit easier after you practise a bit.

####
Exploring Measures of Central Tendency Game

To learn more about the concept of measures of central tendency, it might be fun for you to play a game! The game will provide you with hints if you don't understand the questions or get some answers wrong.

Click here to play LearnAlberta.ca's Exploring Measures of Central Tendency. To move around the museum, use your left/right and up/down arrows. Collect items to answer questions on measures of central tendency. Press your spacebar to select
an artifact. When you have collected enough artifacts, you will be given a question to earn points.

#### Have fun learning about measures of central tendency while playing this interactive online game!

## Self-check!

## Try this!

Complete this Self Check on measures of central tendency. For the following questions, find the required measure of central tendency. Use your notes and information from this lesson if you need help. Show all of your work on a seperate piece of paper.

During a volleyball game, Stephen blocked 7 hits, John blocked 9 hits, Lucus blocked 3 hits and Joe blocked 5 hits.

What is the **mean number** of hits blocked during the game?

Hint: **The mean is the sum of a set of value divided by the number of values.**

7+9+3+5 = 24 /4 = 6 is the mean

What is the

**medium**number of passes made at the basketbal practice?

Hint:

**The median is the middle number of a set of values arranged in order from lowest to highest.**

The median is 11.5

What is the

**mode**for the number of substitutions at the game?

Hint:

**The mode is the number that occurs most often in a set of values.**

5, 5, 5, 10, 10 The mode is 5