Lesson 5: Practice Problems

Problem 1

Three sets of data about ten sixth-grade students were used to make three dot plots. The person who made these dot plots forgot to label them. Match each dot plot with the appropriate label.

  1. A dot plot ranging from 5 to 12 with data as follows: 5(1), 6(1), 7-8(3), 9(2) and no other data.
  2. A dot plot ranging from 5 to 12 with data as follows: 5, 7, 8, 11, 12 one dot, 9 three dots, 10 two dots.
  3. A dot plot ranging from 5 to 12 with one dot at 10, 3 dots at 11, and 6 dots at 12.

  1. Ages in years

  2. Numbers of hours of sleep on nights before school days

  3. Numbers of hours of sleep on nights before non-school days

Problem 2

The dot plots show the time it takes to get to school for ten sixth-grade students from the United States, Canada, Australia, New Zealand, and South Africa.

Five dot plots for "travel time in minutes" labeled “United States”, “Canada”, “Australia”, “New Zealand”, and “South Africa”. Each dot plot has the numbers 0 through 60, in increments of 10. There are also tick marks midway between. The approximate data for "United States" are as follows: 2 minutes, 2 dots; 7 minutes, 2 dots; 8 minutes, 3 dots; 11 minutes, 1 dot; 17 minutes, 1 dot; 20 minutes, 1 dot. The approximate data for "Canada" are as follows: 1 minute, 1 dot; 2 minutes, 1 dot; 5 minutes, 2 dots; 7 minutes, 2 dots; 10 minutes, 1 dot; 15 minutes, 1 dot; 28 minutes, 1 dot; 30 minutes, 1 dot. The approximate data for "Australia" are as follows: 5 minutes, 1 dot; 7 minutes, 1 dot; 9 minutes, 1 dot; 15 minutes, 2 dots; 20 minutes, 3 dots; 25 minutes, 1 dot; 45 minutes, 1 dot. The approximate data for "New Zealand" are as follows: 3 minutes, 1 dot; 6 minutes, 1 dot; 7 minutes, 1 dot; 10 minutes, 2 dots; 15 minutes, 3 dots; 20 minutes, 1 dot; 24 minutes, 1 dot. The approximate data for "South Africa" are as follows: 5 minutes, 2 dots; 10 minutes, 2 dots; 15 minutes, 2 dots; 30 minutes, 1 dot; 40 minutes, 1 dot; 45 minutes, 1 dot; 60 minutes, 1 dot.

  1. List the countries in order of typical travel times, from shortest to longest.

    1. United States

    2. Canada

    3. Australia

    4. New Zealand

    5. South Africa

  2. List the countries in order of variability in travel times, from the least variability to the greatest.

    1. United States

    2. Canada

    3. Australia

    4. New Zealand

    5. South Africa

Problem 3

Twenty-five students were asked to rate—on a scale of 0 to 10—how important it is to reduce pollution. A rating of 0 means “not at all important” and a rating of 10 means “very important.” Here is a dot plot of their responses.

A dot plot for the "importance of reducing pollution" where the numbers 2 through 10 are indicated. The data for the dot plot are as follows: Scale 2, 1 dot Scale 3, 1 dot Scale 4, 1 dot Scale 5, 2 dots Scale 6, 2 dots Scale 7, 2 dots Scale 8, 5 dots Scale 9, 5 dots Scale 10, 6 dots

Explain why a rating of 6 is not a good description of the center of this data set.

Problem 4 From Unit 7 Lesson 10

Tyler wants to buy some cherries at the farmer’s market. He has $10 and cherries cost $4 per pound.

  1. If is the number of pounds of cherries that Tyler can buy, write one or more inequalities or equations describing .

  2. Can 2 be a value of ? Can 3 be a value of ? What about -1? Explain your reasoning.

  3. If is the amount of money, in dollars, Tyler can spend, write one or more inequalities or equations describing .

  4. Can 8 be a value of ? Can 2 be a value of ? What about 10.5? Explain your reasoning.