Match each data set to its corresponding statistical range.

Data Set: $\{15, 8, 22, 14, 9\}$ $14$
Data Set: $\{-3, 5, 12, -7, 4\}$ $19$
Data Set: $\{4.5, 7.2, 3.1, 8.9, 6.0\}$ $5.8$
Data Set: $\{100, 100, 100, 100, 100\}$ $0$

Answer

Match the first data set to

14

, the second to

19

, the third to

5.8

, and the fourth to

0

Each data set is correctly matched to its range by finding the maximum and minimum values in the set, and then subtracting the minimum from the maximum.

Step-by-Step Solution

Calculate the range for the first data set:

\{15, 8, 22, 14, 9\}

Maximum =

22

, Minimum =

8

. Range =

22 - 8 = 14

The range is the difference between the largest and smallest values in the set.

Calculate the range for the second data set:

\{-3, 5, 12, -7, 4\}

Maximum =

12

, Minimum =

-7

. Range =

12 - (-7) = 19

When subtracting a negative number, it is equivalent to adding its absolute value.

Calculate the range for the third data set:

\{4.5, 7.2, 3.1, 8.9, 6.0\}

Maximum =

8.9

, Minimum =

3.1

. Range =

8.9 - 3.1 = 5.8

Identify the extreme decimal values to find the overall spread of the data.

Calculate the range for the fourth data set:

\{100, 100, 100, 100, 100\}

Maximum =

100

, Minimum =

100

. Range =

100 - 100 = 0

If all values in a data set are identical, there is no dispersion, resulting in a range of

0

Key Concept

The range is a measure of dispersion calculated as the difference between the highest (maximum) and lowest (minimum) values in a given data set.

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