Lesson 4Dot Plots

Let's investigate what dot plots and bar graphs can tell us.

Learning Targets:

  • I can describe the center and spread of data from a dot plot.

4.1 Pizza Toppings (Part 1)

Fifteen customers in a pizza shop were asked, “How many toppings did you add to your cheese pizza?” Their responses are shown in the table.

1 2 1 3 0 1 1 2 0 3 0 0 1 2 2
  1. Could you use a dot plot to represent the data? Explain your reasoning.
  2. Complete the table.

    number of toppings frequency (number)
    0
    1
    2
    3

4.2 Pizza Toppings (Part 2)

  1. Use the tables from the warm-up to display the number of toppings as a dot plot. Label your drawing clearly.

    A dot plot with the numbers 0 through 6 indicated.

  2. Use your dot plot to study the distribution for number of toppings. What do you notice about the number of toppings that this group of customers ordered? Write 2–3 sentences summarizing your observations.

Are you ready for more?

Think of a statistical question that can be answered with the data about the number of toppings ordered, as displayed on the dot plot. Then answer this question.

4.3 Homework Time

Twenty-five sixth-grade students answered the question: “How many hours do you generally spend on homework each week?”

  1. Why is this question a statistical question?
“studying” by English106 via Flickr. CC BY 2.0.
  1. This dot plot shows the number of hours per week that these 25 students reported spending on homework.
    Dots showing the following distribution of "hours spent on homework per week": 0: 1, 1: 5, 2: 4, 3: 3, 4: 4, 5: 2, 6: 3, 7: 0, 8: 2, 9: 1, 10: 0

    Use the dot plot to answer the following questions. For each, show or explain your reasoning.

    1. What percentage of the students reported spending 1 hour on homework each week?
    2. What percentage of the students reported spending 4 or fewer hours on homework each week?
  2. Would 6 hours per week be a good description of the number of hours this group of students spends on homework per week? What about 1 hour per week? Explain your reasoning.
  3. What value do you think would be a good description of the homework time of the students in this group? Explain your reasoning.
  4. Someone said, “In general, these students spend roughly the same number of hours doing homework.” Do you agree? Explain your reasoning.

Lesson 4 Summary

We often collect and analyze data because we are interested in learning what is “typical,” or what is common and can be expected in a group.

Sometimes it is easy to tell what a typical member of the group is. For example, we can say that a typical shape in this set is a large circle.

A set that consists of 17 shapes. There are 10 large circles, 1 medium circle, 3 small circles, 1 large square, and 2 small squares.

Just looking at the members of a group doesn’t always tell us what is typical, however. For example, if we are interested in the side length typical of squares in this set, it isn’t easy to do so just by studying the set visually.

A set that consists of 18 squares of varying side lengths.

In a situation like this, it is helpful to gather the side lengths of the squares in the set and look at their distribution, as shown in this dot plot.

A dot plot for "side lengths in centimeters". The numbers 1 through 8 are indicated. The data are as follows: 2 centimeters, 4 dots. 3 centimeters, 5 dots. 4 centimeters, 3 dots. 5 centimeters, 3 dots. 6 centimeters, 2 dots. 7 centimeters, 1 dot.

We can see that many of the data points are between 2 and 4, so we could say that side lengths between 2 and 4 centimeters or close to these lengths are typical of squares in this set.

Lesson 4 Practice Problems

  1. Clare recorded the amounts of time spent doing homework, in hours per week, by students in sixth, eighth, and tenth grades. She made a dot plot of the data for each grade and provided the following summary.

    • Students in sixth grade tend to spend less time on homework than students in eighth and tenth grades.
    • The homework times for the tenth-grade students are more alike than the homework times for the eighth-grade students.

    Use Clare's summary to match each dot plot to the correct grade (sixth, eighth, or tenth).

    Three dot plots are labeled A, B, and C. Each dot plot has the numbers 10 through 22 indicated.  Dot plot A has the following data:  10 through 13 hours, 0 dots; 14 hours, 1 dot; 15 hours, 1 dot; 16 hours, 2 dots; 17 hours, 3 dots; 18 hours, 3 dots; 19 hours, 4 dots; 20 hours, 3 dots; 21 hours, 3 dots; 22 hours, 0 dots.  Dot plot B has the following data:  10 hours, 0 dots; 11 hours, 1 dot; 12 hours, 0 dots; 13 hours, 3 dots; 14 hours, 2 dots; 15 hours, 2 dots; 16 hours, 4 dots; 17 hours, 3 dots; 18 hours, 3 dots; 19 hours, 1 dot; 20 hours, 1 dot; 21 hours, 0 dots; 22 hours, 0 dots.  Dot plot C has the following data:  10 through 15 hours, 0 dots; 16 hours, 2 dots; 17 hours, 6 dots; 18 hours, 9 dots; 19 hours, 2 dot; 20 hours, 1 dot; 21 hours, 0 dots; 22 hours, 0 dots.
  2. Mai played 10 basketball games. She recorded the number of points she scored and made a dot plot. Mai said that she scored between 8 and 14 points in most of the 10 games, but one game was exceptional. During that game she scored more than double her typical score of 9 points. Use the number line to make a dot plot that fits the description Mai gave.

    A blank dot plot for "points" with the numbers 8 through 22, in increments of 2, indicated.
  3. A movie theater is showing three different movies. The dot plots represent the ages of the people who were at the Saturday afternoon showing of each of these movies.

    Three dotplots for age are labeled "movie A", "movie B", and "movie C" each with the numbers 0 through 55, increments of 5, indicated.  Movie A has the following data: age 31, 1 dot; age 32, 1 dot; age 35, 1 dot; age 37, 2 dots; age 38, 3 dots; age 39, 4 dots; age 40, 3 dots; age 41, 1 dot; age 42, 2 dots; age 43, 4 dots; age 44, 2 dots; age 45, 1 dot; age 46, 2 dots; age 48, 1 dot; age 53, 1 dot; age 54, 1 dot. Movie B has the following data: age 3, 1 dot; age 4, 8 dots; age 5, 4 dots; age 6, 4 dots; age 7, 3 dots; age 8, 5 dots; age 9, 4 dots; age 10, 1 dot; age 26, 1 dot; age 27, 1 dot; age 28, 3 dots; age 30, 3 dots; age 31, 3 dots; age 32, 1 dot; age 38, 1 dot;  age 40, 1 dot; age 41, 1 dot; age 43, 1 dot; age 45, 1 dot; age 46, 1 dot; age 49, 1 dot; age 50, 1 dot. Movie C has the following data: age 21, 2 dots age 22, 2 dots; age 25, 2 dots; age 26, 2 dots; age 27, 2 dots; age 28, 3 dots; age 30, 1 dot; age 31, 1 dot; age 32, 1 dot; age 33, 4 dots; age 35, 3 dots; age 36, 2 dots; age 37, 1 dot; age 38, 3 dots; age 39, 1 dot.
    1. One of these movies was an animated movie rated G for general audiences. Do you think it was Movie A, B, or C? Explain your reasoning.
    2. Which movie has a dot plot with ages that that center at about 30 years?
    3. What is a typical age for the people who were at Movie A?
  4. Find the value of each expression.

    1. 3.727 + 1.384
    2. 3.727 - 1.384
    3. 5.01 \boldcdot 4.8
    4. 5.01 \div 4.8