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Range of Spread/Dispersion

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Remember Tania and the carrots in the Mode Concept? Well, now let's think about range.

Here is Tania’s data about the number of carrots picked each week over nine weeks of harvest.

2, 8, 8, 14, 9, 12, 14, 20, 19, 14

What is the range of carrots picked?

This Concept will teach you all about range. Then we will revisit this problem at the end of the Concept.

Guidance

The range of a set of data simply tells where the numbers fall, so that we know if they are close together or spread far apart. A set of data with a small range tells us something different than a set of data with a large range. We’ll discuss this more, but first let’s learn how to find the range.

Here are the steps for finding the range of a set of data.

  1. What we need to do is put the values in the data set in numerical order. Then we know which is the greatest number in the set (the maximum), and which is the smallest number (the minimum).
  2. To find the range, we simply subtract the minimum from the maximum.

Take a minute to copy these steps into your notebook.

Take a look at the data set below.

11, 9, 8, 12, 11, 11, 14, 8, 10

First, we arrange the data in numerical order.

8, 8, 9, 10, 11, 11, 11, 12, 14

Now we can see that the minimum is 8 and the maximum is 14. We subtract to find the range.

14 - 8 = 6

The range of the data is 6. That means that all of the numbers in the data set fall within six places of each other. All of the data results are fairly close together.

How can we use a range to help us answer a question? Suppose we wanted to know the effect of a special soil on plant growth. The numbers in this data set might represent the height in inches of 9 plants grown in the special soil. We know that the range is 6, so all of the plants heights are within 6 inches of each other.

What if the 9 plants had these heights instead?

6, 11, 4, 12, 18, 9, 25, 16, 22

Let’s reorder the data and find the range.

4, 6, 9, 11, 12, 16, 18, 22, 25

Now we can see that the minimum is 4 and the maximum is 25. Let’s subtract to find the range.

25 - 4 = 21

The range of this data is 21. That means the numbers in the data set can be much farther apart.

What does this mean about plants grown in special soil?

If the first group of plants had a range of only 6, their heights ended up being fairly close together. So they grew about the same in the special soil. In contrast, the second group of plants had a much greater range of heights. We might not be so quick to assume that the special soil had any effect on the plants, since their heights are so much more varied.

The range has helped us understand the results of the experiment.

Here are a few for you to try on your own. Find the range of the following data sets.

Example A

4, 5, 6, 9, 12, 19, 20

Solution: 16

Example B

5, 2, 1, 6, 8, 20, 25

Solution: 24

Example C

65, 23, 22, 45, 11, 88, 99, 123, 125

Solution: 114

Now let's go back to Tania and the carrots.

Here is Tania’s data about the number of carrots picked each week over nine weeks of harvest.

2, 8, 8, 14, 9, 12, 14, 20, 19, 14

What is the range of carrots picked?

To find this out, we need to figure out the difference between the greatest number of carrots picked and the least number of carrots picked.

The greatest number picked was 20.

The least number picked was 2.

20 - 2 = 18

The range is 18 carrots.

Vocabulary

Maximum
the greatest score in a data set
Minimum
the smallest score in a data set
Range
the difference between the smallest value in a data set and the greatest number in a data set

Guided Practice

Here is one for you to try on your own.

The following is the number of patrons at a local movie theater.

26, 22, 40, 45, 46, 18, 30, 80, 60, 75

What is the range of the data?

Answer

To figure this out, we need to find the difference between the highest number of patrons and the lowest number of patrons.

The highest number of patrons was 80.

The lowest number of patrons was 22.

80 - 22 = 58

The range for the data set is 58.

Video Review

Khan Academy: Range and Mid-range

Practice

Directions: Find the range for each set of data.

1. 4, 5, 4, 5, 3, 3

2. 6, 7, 8, 3, 2, 4

3. 11, 10, 9, 13, 14, 16

4. 21, 23, 25, 22, 22, 27

5. 27, 29, 29, 32, 30, 32, 31

6. 34, 35, 34, 37, 38, 39, 39

7. 43, 44, 43, 46, 39, 50

8. 122, 100, 134, 156, 144, 110

9. 224, 222, 220, 222, 224, 224

10. 540, 542, 544, 550, 548, 547

11. 2, 3, 3, 3, 2, 2, 2, 5, 6, 7

12. 4, 5, 6, 6, 6, 7, 3, 2

13. 23, 22, 22, 24, 25, 25, 25

14. 123, 120, 121, 120, 121, 125, 121

15. 678, 600, 655, 655, 600, 678, 600, 600

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