Range and Scales: Homework

The range tells you how spread out the data is. The scale has to cover it, with equal steps all the way across.

Part A — Plot, Range and Scale / 11

For 1 and 2, put a dot on the number line for each data value, then find the range. For 3 to 11, write the answer.

1.
Plot the data 22, 47, 31 and 18. Then find the range.
Answer
2.
Plot the data 2.3, 3.8 and 4.6. Then find the range.
Answer
3.
Find the range: 12, 7, 19, 4, 15Answer
4.
Find the range: 3.6, 8.2, 5.9, 1.4Answer
5.
Find the range: 45, 45, 45Answer
6.
Find the range: 102, 88, 95, 120, 77Answer
7.
Find the range: $4.50, $9.25, $6.75Answer
8.
Find the range: 0.52, 0.8, 0.35Answer
9.
A scale runs from 0 to 60 in 6 equal steps. How big is each step?Answer
10.
A scale runs from 20 to 50 counting by 5s. How many marks are there, counting both ends?Answer
11.
A data value is 38. What is the smallest end for a scale that starts at 0 and counts by 5s?Answer

Each of these has a trap. Check that the scale covers the data, and that the steps are equal.

1.
A scale runs from 10 to 30 for the data 8, 14 and 29. What is wrong?Answer
2.
Find the range of 5.5, 0.5 and 9. Be careful with the 0.5.Answer
3.
A scale is marked 0, 5, 10, 20, 25. What is wrong with it?Answer
4.
Set A is 80, 82, 84. Set B is 10, 50, 90. Which has the greater range, and what is it?Answer
5.
The data are 20, 50 and 80. A student says the range is 80 because it is the greatest number. What is the real range?Answer

Real numbers. Heights are in meters, and coin widths are in millimeters.

Think it through, then write your answer and one sentence about how you knew.

1.
The data are 12, 30, 18 and 25. Maya picks a scale from 0 to 40 counting by 10. Ben picks one from 10 to 35 counting by 5. Do both work? How many ranges does this data have, and what does that show about scales?Answer
2.
Two scales both run from 0 to 100. One counts by 25 and one counts by 10. Which would you use for the data 33, 47 and 52, and why?Answer

Write your own, then solve it yourself.

1.
Write a data set of five numbers whose range is exactly 20. Then pick a scale and a step that fit it, and say why they work.Answer

Total / 25

Graded by

Notes

Part A — the answers.

Part B — the answer.

8 is below 10, so one data value has nowhere to go. The scale must start lower, at 5 or 0.
8.5
The step from 10 to 20 is 10, but every other step is 5. The mark between them, 15, is missing, so the steps are not equal.
80 is the range of Set B, and Set A's is only 4. Set B is more spread out.
60. The range is the greatest minus the least, 80 - 20.

Part C — the answers.

a. 363.86 meters b. From 8,400 to 8,900 counting by 100 works, because 8,485 and 8,848.86 both fit, and it has 6 marks. c. 237.86 meters
a. 6.35 millimeters b. 6 marks. Yes, 17.91 and 24.26 both fall between 16 and 26. c. Yes, it holds them, but it is a poor choice. All four widths crowd between the 10 and 30 marks, so the differences are hard to see.

Part D — one correct answer, and what a good explanation says.

18. Both scales hold all the data. The data has only one range, 30 - 12 = 18, but there can be many good scales and intervals, as long as they cover the data in equal steps.
Counting by 10. The three values are close together, and steps of 25 would put all three between two marks. Steps of 10 show how they differ.

Part E — what a good problem looks like.

Answers vary. A good one checks the range and the scale, such as 14, 22, 9, 29, 17: the range is 29 - 9 = 20, and a scale from 5 to 35 counting by 5 holds every value in equal steps.