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STAT 212

# STAT 212 - Variables Examining Distributions Displaying...

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8/22/08 1 Examining Distributions - Displaying Distributions with Graphs Section 1.1 Variables In a study, we collect information—data—from individuals . Individuals can be people, animals, plants, or any object of interest. A variable is any characteristic of an individual. A variable varies among individuals. Examples: height, blood pressure, ethnicity, dividend rate, annual spending The distribution of a variable tells us what values the variable takes and how often it takes these values. Two types of variables Variables can be either quantitative… Something that takes numerical values for which arithmetic operations such as adding and averaging make sense Example: How tall you are, your age, your blood cholesterol level, the number of credit cards you own … or categorical. Something that falls into one of several categories. What can be counted is the count or proportion of individuals in each category. Example: Your blood type (A, B, AB, O), your hair color, your ethnicity, whether you paid income tax last tax year or not Ways to chart categorical data Because the variable is categorical, the data in the graph can be ordered any way we want (alphabetical, by increasing value, by year, by personal preference, etc.) Bar graphs Each category is represented by a bar. Pie charts The slices must represent the parts of one whole. Child poverty before and after government intervention—UNICEF, 1996 What does this chart tell you? •The United States has the highest rate of child poverty among developed nations (22% of under 18). •Its government does the least—through taxes and subsidies—to remedy the problem (size of orange bars and percent difference between orange/blue bars). Could you transform this bar graph to fit in 1 pie chart? In two pie charts? Why? The poverty line is defined as 50% of national median income. Ways to chart quantitative data Histograms and stemplots These are summary graphs for a single variable. They are very useful to understand the pattern of variability in the data. Line graphs: time plots Use when there is a meaningful sequence, like time. The line connecting the points helps emphasize any change over time.

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8/22/08 2 Histograms The range of values that a variable can take is divided into equal size intervals. The histogram shows the number of individual data points that fall in each interval. Example: Histogram of the December 2004 unemployment rates in the 50 states and Puerto Rico. Interpreting histograms When describing the distribution of a quantitative variable, we look for the overall pattern and for striking deviations from that pattern. We can describe the overall pattern of a histogram by its shape, center, and spread. Histogram with a line connecting each column too detailed Histogram with a smoothed curve highlighting the overall pattern of the distribution Most common distribution shapes A distribution is symmetric if the right and left sides of the histogram are approximately mirror images of each other.
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