Measures of Dispersion Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

A quality control inspector records the weight variations, in ounces, of five identical manufactured parts. The recorded weights are: $8.5$ , $4.0$ , $10.5$ , $6.0$ , and $7.5$ . What is the range of these recorded weights?

1.0

10.1

6.5

7.5

Show answer & explanation

Answer: 6.5

Answer

6.5

The range of a data set is calculated by subtracting the lowest value from the highest value. In this list, the highest weight is

10.5

and the lowest weight is

4.0

. Subtracting

4.0

from

10.5

yields a range of

6.5

.

Step-by-Step Solution

1

Identify the maximum and minimum values in the given data set.

The maximum weight is

10.5

and the minimum weight is

4.0

.

The range is defined as the difference between the highest and lowest values in a set of data.

2

Subtract the minimum value from the maximum value.

10.5 - 4.0 = 6.5

Performing the subtraction gives the statistical range of the data.

Key Concept

Measures of Dispersion

Question 2Question →

A scientist records the temperature changes, in degrees Celsius, of a chemical solution during five different phases of an experiment. The recorded changes are: $-2.5$ , $3.0$ , $-5.5$ , $4.5$ , and $-1.0$ . What is the range of these temperature changes?

10.0

1.5

1.0

-1.0

Show answer & explanation

Answer: $10.0$

Answer

10.0

The correct answer is found by taking the highest value in the dataset (

4.5

) and subtracting the lowest value (

-5.5

). Using the rules for subtracting negative numbers,

4.5 - (-5.5)

becomes

4.5 + 5.5

, which equals

10.0

.

Step-by-Step Solution

1

Order the dataset from least to greatest.

-5.5, -2.5, -1.0, 3.0, 4.5

Sorting the data is necessary to correctly identify the minimum and maximum values in the set.

2

Identify the maximum and minimum values.

Maximum =

4.5

, Minimum =

-5.5

The range formula requires the absolute highest and lowest numbers in the dataset.

3

Subtract the minimum value from the maximum value.

4.5 - (-5.5) = 4.5 + 5.5 = 10.0

Range is defined as the difference between the highest and lowest values, measuring the total spread of the data.

Key Concept

Range is calculated by finding the difference between the maximum and minimum values in a dataset.

Question 3Question →

Match each data set to its corresponding statistical range.

Click a left item, then click its matching right item

Show answer & explanation

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

1

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.

2

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.

3

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.

4

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.

Measures of Dispersion

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes