Comparing Data Sets Using Range

1) The range of a data set is found by:

Adding the highest and lowest values

Subtracting the lowest value from the highest value

Finding the middle value

Adding all values and dividing by the number of values

Range measures spread. You take the maximum and subtract the minimum (max − min) to see how far apart the data values are.

Explanation

Range measures spread. You take the maximum and subtract the minimum (max − min) to see how far apart the data values are.

2) Data Set A has a range of 15 and Data Set B has a range of 8. Which statement is true?

Data Set B shows more variability

Data Set A shows more variability

Both data sets have the same variability

The ranges are too close to compare

A larger range means values are more spread out. Since 15 > 8, Data Set A is more variable.

Explanation

A larger range means values are more spread out. Since 15 > 8, Data Set A is more variable.

3) The daily high temperatures for one week were: 72°F, 75°F, 68°F, 71°F, 73°F, 70°F, 74°F. What is the range?

5°F

6°F

7°F

8°F

Max = 75°F, Min = 68°F ⇒ Range = 75 − 68 = 7°F.

Explanation

Max = 75°F, Min = 68°F ⇒ Range = 75 − 68 = 7°F.

4) A smaller range in a data set indicates:

The data values are spread far apart

The data values are closer together

There are more data points

The data set has larger numbers

Smaller range = less spread. Values cluster more closely around each other.

Explanation

Smaller range = less spread. Values cluster more closely around each other.

5) What is the range of Class A's test scores?

5

6

7

8

Max = 92, Min = 85 ⇒ Range = 92 − 85 = 7.

Explanation

Max = 92, Min = 85 ⇒ Range = 92 − 85 = 7.

6) What is the range of Class B's test scores?

20

22

24

25

Max = 95, Min = 70 ⇒ Range = 95 − 70 = 25.

Explanation

Max = 95, Min = 70 ⇒ Range = 95 − 70 = 25.

7) Which class has more consistent test scores?

Both Class A and Class B

Class B

Class A

Cannot be determined

Consistency ↔ smaller range. Class A’s range 7 is smaller than Class B’s 25, so Class A is more consistent.

Explanation

Consistency ↔ smaller range. Class A’s range 7 is smaller than Class B’s 25, so Class A is more consistent.

8) What does the difference in ranges tell you about the two classes?

Class A has higher scores overall

Class B has more variability in performance

Class B has more students

Class A has lower scores overall

Class B’s larger range (25) shows more spread in scores—i.e., greater variability.

Explanation

Class B’s larger range (25) shows more spread in scores—i.e., greater variability.

9) The ages of players on Team 1 range from 12 to 15 years old. The ages of players on Team 2 range from 10 to 18 years old. Which team has a greater range?

Team 1 with a range of 3

Team 2 with a range of 8

Both teams have the same range

Team 1 with a range of 4

Team 1: 15 − 12 = 3; Team 2: 18 − 10 = 8 ⇒ Team 2 has the greater range.

Explanation

Team 1: 15 − 12 = 3; Team 2: 18 − 10 = 8 ⇒ Team 2 has the greater range.

10) If a data set has a range of 0, what does this mean?

There is no data

The data has one value only

All values in the data set are the same

The data set is invalid

Range 0 occurs when max = min, meaning every value is identical (could be one repeated value or multiple identical values).

Explanation

Range 0 occurs when max = min, meaning every value is identical (could be one repeated value or multiple identical values).

11) What is the range for Coffee Shop X?

5

6

7

8

Max = 32, Min = 25 ⇒ Range = 32 − 25 = 7.

Explanation

Max = 32, Min = 25 ⇒ Range = 32 − 25 = 7.

12) What is the range for Coffee Shop Y?

25

23

20

28

Max = 40, Min = 15 ⇒ Range = 40 − 15 = 25.

Explanation

Max = 40, Min = 15 ⇒ Range = 40 − 15 = 25.

13) Which coffee shop had more consistent customer traffic?

Coffee Shop X

Coffee Shop Y

Both had equal consistency

Neither shop was consistent

Consistency ↔ smaller range. X has 7 vs Y’s 25, so X’s traffic is more consistent.

Explanation

Consistency ↔ smaller range. X has 7 vs Y’s 25, so X’s traffic is more consistent.

14) If Coffee Shop Y wants to have more predictable customer flow, what should happen to its range?

The range should increase

The range should decrease

The range should stay the same

The range does not affect predictability

Lower range = less variability = more predictability in daily counts.

Explanation

Lower range = less variability = more predictability in daily counts.

15) Two students recorded their quiz scores. Student M’s scores have a range of 12 points, and Student N’s scores have a range of 4 points. Which student’s performance is more consistent?

Student M

Student N

Both students are equally consistent

Cannot determine from range alone

Smaller range indicates steadier scores. 4 (Student N)

Explanation

Smaller range indicates steadier scores. 4 (Student N)

16) The heights of plants in Garden A range from 8 inches to 20 inches. The heights of plants in Garden B range from 12 inches to 16 inches. What is the difference between the two ranges?

4 inches

6 inches

8 inches

12 inches

Range A = 20 − 8 = 12; Range B = 16 − 12 = 4; Difference = 12 − 4 = 8 inches.

Explanation

Range A = 20 − 8 = 12; Range B = 16 − 12 = 4; Difference = 12 − 4 = 8 inches.

17) What is the range for Group 1?

3

4

5

6

Max = 9, Min = 5 ⇒ Range = 9 − 5 = 4.

Explanation

Max = 9, Min = 5 ⇒ Range = 9 − 5 = 4.

18) What is the range for Group 2?

7

8

9

10

Max = 12, Min = 3 ⇒ Range = 12 − 3 = 9.

Explanation

Max = 12, Min = 3 ⇒ Range = 12 − 3 = 9.

19) Which group shows greater variability in the number of books read?

Group 1

Group 2

Both groups show equal variability

Neither group shows variability

Group 1 range = 4; Group 2 range = 9. Larger range (9) ⇒ greater variability (Group 2).

Explanation

Group 1 range = 4; Group 2 range = 9. Larger range (9) ⇒ greater variability (Group 2).

20) A coach wants to select a team with players who have similar skill levels. Team P has a range of 18 points in their scoring averages, and Team Q has a range of 6 points. Which team likely has more similar skill levels?

Team P

Team Q

Both teams have similar skill levels

Cannot be determined from range

Smaller range suggests players’ performances are closer together. Team Q’s range (6) is smaller than Team P’s (18), indicating more similar skill levels.

Explanation

Smaller range suggests players’ performances are closer together. Team Q’s range (6) is smaller than Team P’s (18), indicating more similar skill levels.