Chapter 8 Analyzing Data Sets For One Variable

My Favorite Breakfast

Which is your favorite breakfast?

Academic Learning Goals

• Students will be able to:• 1. Represent and interpret data displayed on dot plots.• 2. Represent and interpret data displayed on histograms.• 3. Represent and interpret data displayed on box-and-whisker plots.

Lesson 1 : Start Your Day Right

Look at the two Cereal Boxes

Box A Box B

1. Think about the amount of sugar in the each cereal box.

2. What can you conclude about the amount sugar in the cereal boxes?

3. How did you compare the amount of sugar in the cereal boxes?

Talk to your partner. Write a conclusion of what you think of the amount sugar in the cereal.

Was it easy for you to make a conclusion? Explain how you came to a conclusion.

Dot PlotLook at the graph below. Tell your partner what you notice.

What is dot plot?

• A dot plot, also called a dot chart, is a type of simple histogram-like chart used in statistics for relatively small data sets where values fall into a number of discrete bins. To draw a dot plot, count the number of data points falling in each bin and draw a stack of dots that number high for each bin. The illustration above shows such a plot for a random sample of 100 integers chosen between 1 and 25 inclusively.

How much sugar is too much?

Ms. Romano is a health coach and nutritionist. Recently, she encouraged Matthew to eat a healthier breakfast and recommended a cereal with less sugar. There are many different cereals and it seems like the amount of sugar in each type varies widely. Matthew took a trip to the grocery store and recorded the sugar amount that each cereal has in one serving.

Based on the information given in the table, create a dot plot. • Sample of Dot Plot

Sugar Amount in Cereal Bars

1. Construct a dot plot to represent the sugar amount in oneserving of each breakfast cereal. Label the number line usingintervals that will include all the data values. Place an “x”above the number that represents each data value. Makesure you name your dot plot.

2. Analyze the dot plot . Make a conclusion. Compare with your partner.

Your graph should have a similar shape. Otherwise check your plotting. Use a different color to make the correction,

Jordan states that those numbers on the number line that do not contain any datavalues should be eliminated. Toni disagrees and says that all the numbers on thenumber line must be included even if there are no data values for that particularnumber. Who is correct? Explain your reasoning

Toni is correct.All of the numbers between the least and greatest data value must be included.Without this information the dot plot is not a true representation of the data.

1. Describe the distribution of the sugar amount in one serving of breakfast cereal. Explainwhat this means in terms of the problem situation.

Making conclusion on the Sugar Content in the Breakfast Cereal

2. Do you think your conclusion is true for all breakfast cereal? Why or why not?

BOX- AND WHISKER PLOT

How to Construct a Box-And-Whisker Plot

BOX- AND WHISKER PLOT

There are four sections of the graphical display:minimum to Q1 Q1 to median, median to Q3, Q3 to maximum. Each section of the box-and-whiskerplot represents 25 percent of the data set.

Another way to display quantitative data is to create a histogram. A histogram is a graphicalway to display quantitative data using vertical bars. The width of a bar in a histogramrepresents an interval of data and is often referred to as a bin. A bin is represented byintervals of data instead of showing individual data values. The value shown on the leftside of the bin is the least data value in the interval.The height of each bar indicates the frequency, which is the number of data values includedin any given bin.Histograms are effective in displaying large amounts of continuous data. Continuous datais data which can take any numerical value within a range.The histogram shown represents the data distribution for the number of hours studentsspend playing video games on the weekends. The data is gathered to the nearest half-hour.

Representing Data Using Histogram