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2.1: Descriptive Statistics and Distributions
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To get a firm grasp on a set of data generally requires several descriptive statistics and a method of visualization. Two very different data sets may have the same values for certain descriptive statistics while differing for others. A good place to start is to see how the data is distributed. Frequency and relative frequency distributions are quite common and informative.
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2.2: Using and Understanding Graphs
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Graphs and charts are excellent ways to quickly share information with a larger audience. In this section, we will look at several different types of graphs. However, our goal in this class is not just to identify or create a certain type of graph but rather to become informed consumers of information and critical thinkers who are actively engaged in the world around them.
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2.3: Histograms
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A histogram is a graphical representation without gaps between the bars to represent a continuous quantitative variable. When the bars have gaps, we have a bar graph representing either a qualitative or discrete quantitative variable.
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2.4: Box Plots, Quartiles, and Percentiles
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Box plots allow us to visualize the data by grouping it by position in four comparably sized classes. Using the five-number summary and a box plot, we can easily make comparisons between data sets. Additionally, we study the development of quartiles and percentiles to measure relative position.
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2.5: Measures of Central Tendency
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In this section, we motivate and discuss the most common descriptive statistics that provide information about where the data falls; we call such descriptive statistics measures of central tendency. The three most common measures of central tendency are the mode, the median, and the mean.
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2.6: Measures of Dispersion
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In this section, we motivate and discuss the most common descriptive statistics that provide information about how spread out data are; we call such descriptive statistics measures of dispersion. We shall discuss some of the most common measures: range, interquartile range, mean absolute deviation, variance, and standard deviation.
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2.7: Distributions- Using Centrality and Variability Together
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The coupling of measures of centrality and dispersion tells us a lot about the distribution of our data. We can set lower bounds on the percentage of observations that fall in certain ranges regardless of the distribution; this result is called Chebyshev's Inequality. If we restrict our interest to a class of distributions called normal distributions, we can specify precisely the percentage of observations that fall in certain ranges; this result is called the Empirical Rule.
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2.8: Measures of Median and Mean on Grouped Data
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Sometimes data is given in summarized format of a frequency or relative frequency distribution instead of as a list of individual values/characteristics. As such, can one find our measures of center from such summarized format of the data? This section investigates that possibility in regard to the median and the arithmetic mean measures. Then, a short extension to the concept of "weighted" means is also discussed.
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2.9: Measures of Variance and Standard Deviation on Grouped Data
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In an expansion of the ideas from Section \(2.8\) Measures of Median and Mean on Grouped Data, we know examine how one can find our measures of variance and standard deviation from discrete data presented in a frequency or relative frequency table.
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