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# Statistics and Probability Word Problems Study Guide

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Updated on Aug 24, 2011

Find practice problems and solutions for these concepts at Statistics and Probability Word Problems Practice Problems.

When working with a data set, such as a group of test scores or a series of measurements, we can calculate various statistics that help us describe that data set. This data is often presented in a graph, but you may have to calculate statistics based on information in a wordproblem. In this chapter, we'll look at statistics word problems and probability word problems. As always, we'll use the eight-step process to help us identify the type of problem and the operation or operations needed to solve it.

### Statistics: Subject Review

A mean is an average of a set of values. The mean is found by adding all of the values together and then dividing by the number of values.

A median is the middle value of a set after the values in the set are put in order from least to greatest. If there is an even number of values in a set, the median is the average of the two middle values.

A mode is the value in a set that occurs the most often. If there are two or more unique values that occur most often, then the set will have more than one mode.

A range is the difference between the smallest value and the greatest value in a set.

Given a set of numbers, such as 10, 6, 4, 10, and 30, we can find the mean, median, mode, and range of the set.

The mean of this set is 12, because 10 + 6 + 4 + 10 + 30 = 60, and = 12.

The median of this set is 10, because after the set is ordered, it becomes 4, 6, 10, 10, 30, and the middle value is 10. 10 + 10 = = 10.

The mode of this set is 10, because it is the value that occurs the most often. There are two 10s in the set, and no other value occurs more than once.

The range of this set is 26, because the lowest value in the set is 4 and the highest value in the set is 30: 30 – 26 = 4.

Now that we know how to find mean, median, mode, and range, let's look at how to recognize and solve statistics word problems.

### Mean

Some word problems may ask you for the mean of a set, but more often, you'll be asked to find the average. The word average is just another word for mean, so if a question asks you for an average, it's asking you for a mean.

#### Example

Nancy plays nine holes of golf. Her scores are 7, 4, 6, 5, 3, 6, 5, 4, and 5. What was her average score for a hole?

We are given the number of holes of golf Nancy plays and her score on each hole.

We are looking for her average score for a hole.

Underline the keywords and words that indicate formulas.

The word average means that we are looking for the mean of the set.

Cross out extra information and translate words into numbers.

There is no extra information in this problem.

List the possible operations.

The mean is found by adding all of the scores and dividing by the number of scores, so we must use addition and division.

Write number sentences for each operation.

First, find the sum of all the scores. We will need the sum before we can divide:

7 + 4 + 6 + 5 + 3 + 6 + 5 + 4 + 5

Solve the number sentences and decide which answer is reasonable.

7 + 4 + 6 + 5 + 3 + 6 + 5 + 4 + 5 = 45

Write number sentences for each operation.

Now that we have the total of all the scores, divide by the number of scores, 9:

Solve the number sentences and decide which answer is reasonable.

= 5

The mean multiplied by the number of values should equal the sum of the values: 5 × 9 = 45 and 7 + 4 + 6 + 5 + 3 + 6 + 5 + 4 + 5 = 45, so our answer is correct.

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