Here are two dot plots and two stories. Match each story with a dot plot that could represent it. Explain your reasoning.
(1.) Twenty people—high school students, teachers, and invited guests—attended a rehearsal for a high school musical. The mean age was 38.5 years and the MAD was 16.5 years. Which data set matches and why?
(2.) High school soccer team practice is usually watched by supporters of the players. One evening, twenty people watched the team practice. The mean age was 38.5 years and the MAD was 12.7 years. Which data set matches and why?
Another evening, twenty people watched the soccer team practice. The mean age was similar to that from the first evening, but the MAD was greater (about 20 years).
Here below is data that shows the numbers of siblings of ten students in Tyler’s class
(1.) Without making any calculations, estimate the center of the data based on your dot plot. What is a typical number of siblings for these sixth-grade students? Mark the location of that number on your dot plot.
(2.) Find the mean. Show your reasoning.
(3.) How does the mean compare to the value that you marked on the dot plot as a typical number of siblings? (Is it a little larger, a lot larger, exactly the same, a little smaller, or a lot smaller than your estimate?)
(4.) Do you think the mean summarizes the data set well? Explain your reasoning.
(5.) Invent a data set with a mean that is significantly lower than what you would consider a typical value for the data set.
In one study of wild bears, researchers measured the weights, in pounds, of 143 wild bears that ranged in age from newborn to 15 years old. The data were used to make this histogram.
(1.) What can you say about the heaviest bear in this group?
(2.) What is a typical weight for the bears in this group?
(3.) Do more than half of the bears in this group weigh less than 250 pounds?
(4.) If weight is related to age, with older bears tending to have greater body weights, would you say that there were more old bears or more young bears in the group? Explain your reasoning.
When he sorts the class’s scores on the last test, the teacher notices that exactly 12 students scored better than Clare and exactly 12 students scored worse than Clare.
Does this mean that Clare’s score on the test is the median? Explain your reasoning.
Here below is data that shows a student’s scores for 10 rounds of a video game.
130, 150, 120, 170, 130, 120, 160, 160, 190, 140
Match the dot plot below to the median.