1. 1: Analyzing Categorical Data
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- Caution: Even a strong association between two categorical variables can be influenced by other variables lurking in the background.
| Ex: Examine the relationship between gender and opinion. Based on the survey, can we conclude that young men and women differ in their opinions about the likelihood of future wealth?
We say that there is an association between two variables if knowing the value of one variable helps predict the value of the other. If knowing the value of one variable does not help you predict the value of the other, then there is no association between the variables. Can we say there is an association between gender and opinion in the population of young adults? Making this determination requires formal inference, which will have to wait a few chapters. Caution: Even a strong association between two categorical variables can be influenced by other variables lurking in the background. 1.2: Displaying Quantitative Data with Graphs Activity: Distribution Shapes You will each receive one piece of a graph. You will have to find other people in the class whose graph pieces align with yours. Once you’ve completed the graph, form a group at one of the tables and discuss which of the following you think your group’s graph describes: People born each month of the year Student GPAs at South Miami Student heights at South Miami House prices in Miami Describing distributions of quantitative data Ex: Brian and Jessica have decided to move and are considering seven different cities. The dotplots below show the daily high temperatures in June, July, and August for each of these cities. 
What is the most important difference between cities A, B, and C? What is the most important difference between cities C and D? What is the most important difference between cities D and E? What is the most important difference between cities C, F, and G? Describing Shape When you describe a distribution’s shape, concentrate on the main features. Look for rough symmetry or clear skewness. A distribution is roughly symmetric if the right and left sides of the graph are approximately mirror images of each other. A distribution is skewed to the right (right-skewed) if the right side of the graph (containing the half of the observations with larger values) is much longer than the left side. Ex: right foot with big toe on left and pinkie toe on right It is skewed to the left (left-skewed) if the left side of the graph is much longer than the right side. Ex: left foot with pinkie on left and big toe on right 
Although both of the dotplots on the right have different shapes, they share something in common. Both are unimodal, that is, they have a single peak. 
We would describe the distribution’s shape on the right as roughly symmetric and bimodal (or multimodal) because it has two clear peaks: one near 2 minutes and the other near 4.5 minutes. 
The distribution’s shape on the right is called uniform. This happens when the observations in a set of data are 
equally spread across the range of the distribution (no clear peaks). Making and interpreting dotplots Ex: How do the numbers of people living in households in the United Kingdom (U.K.) and South Africa compare? To help answer this question, we used Census At School’s “Random Data Selector” to choose 50 students from each country. Here is a comparative dotplot of the household sizes reported by the survey respondents. Problem: Compare the distributions of household size for these two countries. 
Making and interpreting stem-and-leaf plots Ex: To become president of the United States, a candidate does not have to receive a majority of the popular vote. The candidate does have to win a majority of the 538 electoral votes that are cast in the Electoral College. Data on the number of electoral votes for each of the 50 states and the District of Columbia in 2015 are shown in the table below. AL 9 AK 3 AZ 11 AR 6 CA 55 CO 9 CT 7 DE 3 DC 3 FL 29 GA 16 HI 4 ID 4 IL 20 IN 11 IA 6 KS 6 KY 8 LA 8 ME 4 MD 10 MA 11 MI 16 MN 10 MS 6 MO 10 MT 3 NE 5 NV 6 NH 4 NJ 14 NM 5 NY 29 NC 15 ND 3 OH 18 OK 7 OR 7 PA 20 RI 4 SC 9 SD 3 TN 11 TX 38 UT 6 VT 3 VA 13 WA 12 WV 5 WI 10 WY 3 Make a stemplot. Describe what you see. When data values are “bunched up”, we can get a better picture of the distribution by splitting stems. Two distributions of the same quantitative variable can be compared using a back-to-back stemplot with common stems.  Directory: ourpages -> auto -> 2017 2017 -> Senior Division Solutions 2017 -> Avant garde adademy of broward 2017 -> Have you always wanted to go to space camp? Dreamt of becoming an astronaut here’s your chance! 2017 -> Atlanta, georgia-april 2017-a total solar eclipse occurs when the moon lines up between the earth and the sun-an extremely rare and beautiful event 2017 -> United states history and geography unit 1: The Rise of Industrial America 1877-1914 2017 -> Out-of-Field Notification to Parents/Guardians English 2017 -> Modern History Notes 9-21-2017 Entertainment 2017 -> The secret of change is to focus all of your energy, not on fighting the old, but on building the new 2017 -> The Berlin Conference 1884 Simulation Historical Context 2017 -> Island Biogeography and Biodiversity Part I: Background Reading Download 10.83 Mb. Share with your friends:
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