Data About Us Investigation 2.2 Name: Comparing Distributions with the Same Mean In Problem 2.1, you represented data using dot plots. Another way to represent data is by using a balance. The picture below shows the frequency of the data from Household Size Table 1. When the fulcrum is located at the mean of the distribution, the ruler is level, as the purple ruler shows. The distribution in Household Size Table 1 balances around 4. Notice that the green ruler tips to the left. When the fulcrum is not located at the mean of the distribution, the ruler is not level. A. Household Size Table 1 and Household Size Table 2 in Problem 2.1 each show six households with a mean of four people. 1. Make up a different data set of six households that has a mean of four people per household. 2. Make an ordered –value bar graph and a line or dot plot to represent your set of data. 3. Describe how to use your bar graph to verify the mean is four people. 4. Explain how you can find the following on your graphs: a. each person’s household size b. the total number of households c. the total number of people in the combined households d. How can you use the information in parts (a) – (c) to find the mean? B. A group of seven students has a mean of three people per household. 1. Make up a data set that fits this description. 2. Make an ordered-valued bar graph and a line or dot plot to represent your set of data. 3. Describe how to use your bar graph to verify the mean is three people. 4. Suppose you found another data set with seven households and a mean of three people per household, but with a greater range. How would this change the appearance of your line or dot plot? 5. Explain how you can find the following on your graphs: a. each person’s household size b. the total number of households c. the total number of people in the combined households d. How can you use the information in parts (a) – (c) to find the mean? C. A group of six students has a mean of 3 ½ people. 1. Make up a data set that fits this description. 2. Make an ordered-value bar graph and a line or dot plot to represent your set of data. 3. How can the mean be 3 ½ people when “half” a person does not exist? D. The dot plot below show the household sizes for a group of eight students. 1. Identify the median, mode, and range of the distribution. 2. Think about viewing the distribution on a balance. Make an estimate or guess about where the mean is located. 3. Identify the mean of the distribution. How does this compare with your estimate or guess? Explain. 4. a. Compare the three measures of center ---mean, median, and mode. How are they the same or different? Explain? b. Is it possible to have the three measures of center of a distribution all be the same? Explain. All be different? Explain. c. Which measure would you choose to describe the typical household size for the eight households? Explain. E. Look back at the work you did in Questions A-D and in Problem 2.1. Describe a method to compute the mean in any situation.