Averages and Probability

Averages and Probability

Learning Objectives

By the end of this section, you will be able to:

Calculate the mean of a set of numbers.

Find the median of a set of numbers

Find the mode of a set of numbers

Apply the basic definition of probability

Calculate the Mean of a Set of Numbers

The mean is often called the arithmetic average. It is computed by dividing the sum of the values by the number of values.

Suppose Ethan’s first three test scores were 85,88,and94.

To find the mean score, he would add them and divide by 3.

(85+88+94)/3= 267/3= 89

Calculate the mean of a set of numbers.

8,12,15,9,and 6

8,9,7,12,10,5

9,13,11,7,5

The ages of the members of a family who got together for a birthday celebration were 16,26,53,56,65,70,93,and 97 years. Find the mean age.

Find the Median of a Set of Numbers

The median of a set of data values is the middle value.

Half the data values are less than or equal to the median.

Half the data values are greater than or equal to the median.

Find the median

Step 1. List the numbers from smallest to largest.

Step 2. Count how many numbers are in the set. Call this n.

Step 3. Is n odd or even?

If n is an odd number, the median is the middle value.

If n is an even number, the median is the mean of the two middle values.

Problem

What if Carmen, the pianist, joins the singing group on stage? Carmen is 62 inches tall, so she fits in the height order between Bianca and Dora. Now the data set looks like this:

59,60,62,65,68,70

There is no single middle value. The heights of the six girls can be divided into two equal parts.

Find the median of a set of numbers.

12,13,19,9,11,15,and 18

43,38,51,40,46

15,35,20,45,50,25,30

83,79,85,86,92,100,76,90,88,and 64

Mode

The mode of a set of numbers is the number with the highest frequency.

How to Identify the mode of a set of numbers

Step 1. List the data values in numerical order.

Step 2. Count the number of times each value appears.

Step 3. The mode is the value with the highest frequency.

Examples

The number of sick days employees used last year: 3,6,2,3,7,5,6,2,4,2. Identify the mode.

5,6,3,1,5,8,1,5,8,5. Identify the mode.

Use the Basic Definition of Probability

The probability of an event tells us how likely that event is to occur. We usually write probabilities as fractions or decimals.

Example 1

The ski club is holding a raffle to raise money. They sold 100

tickets. All of the tickets are placed in a jar. One ticket will be pulled out of the jar at random, and the winner will receive a prize. Cherie bought one raffle ticket.

ⓐ Find the probability she will win the prize.

ⓑ Convert the fraction to a decimal.

Example 2

Hoang is among 20people available to sit on a jury. One person will be chosen at random from the 20.

ⓐ Find the probability Hoang will be chosen.

ⓑ Convert the fraction to a decimal.

Example 3

Three women and five men interviewed for a job. One of the candidates will be offered the job.

ⓐ Find the probability the job is offered to a woman.

ⓑ Convert the fraction to a decimal.

Example 4

A bowl of Halloween candy contains 5

chocolate candies and 3

lemon candies. Tanya will choose one piece of candy at random.

ⓐ Find the probability Tanya will choose a chocolate candy.

ⓑ Convert the fraction to a decimal.

Multiple Choice

A store sells shirts that are either small, medium, or large. The colors are either red, blue, green, or white. What is the probability someone will select a large green shirt?

• 1/3
• 1/7
• 1/9
• 1/12

Multiple Choice

What is the probability of spinning an even number?

• 16 2/3%

• 33 1/3%

• 50%

• 75%

Multiple Choice

What is the probability of spinning green?

• 0
• 1/4
• 1/2
• 3/4

Multiple Choice

Define: Outcome

• A possible result

• A probability that is determined by analyzing a situation

• A probability that is determined through testing

• One round of an experiment

Multiple Choice

Convert the fraction to a percent:

• 62.5% or 63%

• 55.5% or 56%

• 44.2% or 44%

Multiple Choice

What is the mode?

• # happening the most
• the average
• biggest - smallest
• the middle #

Multiple Choice

Roger bowled 7 games last weekend. His scores are: 155, 165, 138, 172, 127, 193, 142. What is the range of Roger's scores?

• 193
• 127
• 60
• 66

Multiple Choice

At Donald's Donuts the number of donut holes in a bag can vary. Help Donald find the mode.
12,10,10,10,13,12,11,13,10

• 13
• 12
• 11
• 10