Entertainment is big business. According to pcmag. com, Americans spend more than $2.6 billion dollars on digital music each year. Video games are popular, too. Americans spend more than $24.7 billion dollars on video games and related accessories each year. Today you will investigate music downloads and usage of video games. You will make graphs, read and interpret graphs, and analyze entertainment data. You will review and apply the statistics terms and concepts you learned in this unit.
As you complete the task, you will use measures of center and measures of spread to draw conclusions about a data set. As you do, you will be answering the question, “Does one’s gender or age tell us anything about their entertainment choices?”
Directions:
Complete each of the following tasks, reading the directions carefully as you go.
You will be graded on the work you show, or your solution process, in addition to your answers. Show all of your work and answer each question as you complete the task. Type all of your work into this document so you can submit it to your teacher for a grade. You will be given partial credit based on the work you show and the completeness and accuracy of your explanations.
Your teacher will give you further directions on submitting your work. You may be asked to upload the document, e-mail it to your teacher, or hand in a hard copy.

Now let’s get started!
Step 1: Describing and analyzing the data
Sixth-grade students completed a random survey to determine how many songs each student has downloaded to his/her media player in the past two months. The data gathered is represented in the table below.

a) Compute the measures of center for both the boys and girls data. Describe their differences. Use the terms mean and median to justify your answer. (3 points)

b) Compute the measures of spread for the data collected for boys and girls. Describe their differences in detail using specific terms of spread. (4 points)

c) Is it possible to make valid conclusions based on the data collected? (2 points)

Step 2: Displaying numerical data in histograms, and describing and analyzing the data

A recent study was conducted to determine the percentage of children who spend at least one hour per week playing video games. The results of the study are displayed in the histogram below.

a) Analyze the shape of the data and describe it in detail. Use mathematical reasoning to justify your response. (2 points)

b) Determine if the following statement is true or false: Children are typically introduced to video games between the ages of six and eight. Explain your answer using data from the graph. (2 points)

c) If we knew that 500 families living in various cities were surveyed randomly to gather this data, is it possible to make a valid conclusion? (2 points)

Step 3: Displaying numerical data in dot plots, and describing and analyzing
the data

A survey was conducted to determine how many movies were seen in one month among the 26 students in Mrs. Hampton’s sixth-grade class. The results are shown in the dot plot below.

a) Calculate the measures of center for the data in the dot plot, rounding your answers to the nearest tenths place. Show how you determined your answer. (2 points)

b) Are there any overall patterns in the data set? Striking deviations? Use mathematical reasoning to justify your answer. (2 points)

c) Calculate the measures of spread for Mrs. Hampton’s class data. Justify your response by describing the process used to find each measure. (2 points)

d) Which is a better measure of spread: range or interquartile range? Why? (2 points)

e) What does the value of the mean absolute deviation tell you about the spread of the data? (2 points)