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## Explore measure of dispersion: range.

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Mr. Campbell teaches an English as Second Language (ESL) class and has just finished grading his students' end of year exam. He has the scores organized in a table, but wants to provide feedback to the class on the range of the scores. How can Mr. Campbell find the range of scores on the English exam?

 Student Test Score (%) AS 89 AS 91 BC 87 CS 77 FR 72 JW 59 ML 76 MY 68 ST 91 SR 83 VS 81 ZS 73

In this concept, you will learn how to calculate the range of a data set.

### Guidance

Data is a set of numerical or non-numerical information. Data can be analyzed in many different ways. In this concept you will analyze numerical data using the range.

The range of a set of data is the difference between the largest and smallest values. The range identifies how far apart the values in the data set are.

Let's look at an example.

Find the range of the data set:  47, 56, 51, 45, and 41.

First, arrange the numbers from smallest to largest.

41, 45, 47, 51, 56

Next, find the difference between the largest and smallest number. The largest value is 56 and the smallest value is 41. To find the difference subtract 41 from 56.

5641=15\begin{align*}56-41=15\end{align*}

The difference between the numbers is the range.

The answer is the range is 15.

### Guided Practice

The chart below shows the daily temperature in San Diego for the first seven days in August. Calculate the range of the temperatures.

San Diego Temperatures in August
Date: Temperature:
Sunday 8/1 88F\begin{align*}88^\circ F\end{align*}
Monday 8/2 83F\begin{align*}83^\circ F\end{align*}
Tuesday 8/3 87F\begin{align*}87^\circ F\end{align*}
Wednesday 8/4 89F\begin{align*}89^\circ F\end{align*}
Thursday 8/5 82F\begin{align*}82^\circ F\end{align*}
Friday 8/6 79F\begin{align*}79^\circ F\end{align*}
Saturday 8/7 87F\begin{align*}87^\circ F\end{align*}

First, arrange the temperatures from smallest to greatest.

79, 82, 83, 87, 87, 88, 89

Next, find the difference between the largest and smallest values. The largest value is 89 and the smallest is 79.

8979=10\begin{align*}89-79=10\end{align*}

The answer is the range of temperatures is 10F\begin{align*}10^\circ F\end{align*}.

### Examples

#### Example 1

Find the range of the following data set.

12,14,15,16,18,20\begin{align*}12, 14, 15, 16, 18, 20\end{align*}

First, arrange the numbers from smallest to largest. In this case, the numbers are already ordered from smallest to largest.

Next, calculate the difference between the largest and smallest numbers, 20 and 12.

2012=8\begin{align*}20-12=8\end{align*}

The answer is the range is 8.

#### Example 2

John wants to find the range of his quiz grades. He has the following quiz scores.

78, 90, 83, 88, 67, 90, 84, 69, 56

First, order the numbers from smallest to largest.

56, 67, 69, 78, 83, 84, 88, 90, 90

Next, subtract the smallest number from the largest number. In this case the smallest number is 56 and the largest is 90.

9056=34\begin{align*}90-56=34\end{align*}

#### Example 3

Miguel measured the height of eight students in his class in inches. Find the range of the heights below.

45, 47, 50, 50, 51, 51, 52, 56

First, sort the data from smallest to largest. In this case, the data is already ordered from smallest to largest.

Next, find the difference between the smallest and largest heights, 45 and 56 inches.

5645=11\begin{align*}56-45=11\end{align*}

The answer is the range of the student heights is 11".

Mr. Campbell has the test results from the final exam and needs to calculate the range of scores.

 Student Test Score (%) AS 89 AS 91 BC 87 CS 77 FR 72 JW 59 ML 76 MY 68 ST 91 SR 83 VS 81 ZS 73

First, organize the data from smallest to greatest.

59, 68, 72, 73, 76, 77, 81, 83, 87, 89, 91, 91

Next, calculate the difference between the greatest and smallest values. The greatest value is 91 and the smallest is 59. To find the difference, subtract 59 from 91.

9159=32\begin{align*}91-59=32\end{align*}

The answer is the range is 32%.

### Explore More

Analyze each data set.

32294035422540\begin{align*}32 \quad 29 \quad 40 \quad 35 \quad 42 \quad 25 \quad 40\end{align*}

1. Mean

2. Median

3. Mode

4. Range –

The weekly paychecks for ten part-time employees are: $140,$132, $200,$150, $175,$200, $180,$95, $145, and$155.

5. Mean –

6. Median

7. Mode –

8. Range –

The data set below depicts the number of points LeBron James scored in the last five NBA games.

2527252922\begin{align*}25 \quad 27 \quad 25 \quad 29 \quad 22\end{align*}

9. Mean –

10. Median

11. Mode –

12. Range –

Here is the number of days that it took the mushers of the Iditarod to finish the race in 2010.

8 days, 9 days, 9 days, 9 days, 9 days, 9 days, 9 days, 9 days, 9 days, 9 days

13. Mean –

14. Median –

15. Mode –

16. Range –

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 11.4.

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Color Highlighted Text Notes

### Vocabulary Language: English

TermDefinition
Data Data is information that has been collected to represent real life situations, usually in number form.
Mean The mean of a data set is the average of the data set. The mean is found by calculating the sum of the values in the data set and then dividing by the number of values in the data set.
measure To measure distance is to determine how far apart two geometric objects are by using a number line or ruler.
Mode The mode of a data set is the value or values with greatest frequency in the data set.
Range The range of a data set is the difference between the smallest value and the greatest value in the data set.