Chapter 5

# Chapter 5 - MSIT 3000 Chapter 5 Displaying and Describing...

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MSIT 3000 Chapter 5 Displaying and Describing Quantitative Data The Distribution of a Variable To describe a variable, include all of the following: Shape Center Spread or variation MSIT 3000 Section 5.1 Displaying Distributions SHAPE: To determine the shape, look at a graph of the data. Graphs used most often are: Histogram Boxplots Histograms A histogram is similar to a bar chart with the bin counts used as the heights of the bars. Note: there are no gaps between bars unless there are actual gaps in the data. Insurance companies take risks. When they insure a property or a life, they must price the policy in such a way that they bring in more money than they pay out over the long term. A manager wanted to see how well one sales representative was doing, so she selected 30 matured policies that had been sold by the sales rep and computed the (net) profit (premiums charged minus claims paid). Notice each bar, or bin, has a width of \$1000. The histogram displays how many of the price change values fall into each these bins. For example, we see that there were about 6 profits monthly that were between \$1500 and \$2500. We may also choose to create a relative frequency histogram by displaying the percentage of cases in each bin instead of the count. 45

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Note: The shape is exactly the same; only the vertical label has changed. MSIT 3000 Section 5.2 Shape Identify the overall pattern and deviations from that pattern by describing modes, symmetry, and whether gaps or outlying values exist. 1. Most data are approximately symmetric, skewed to the right, or skewed to the left. (Some data are uniform or bimodal). 2. Are there any extreme observations? (These are usually called outliers, and will be defined more specifically shortly) Shapes of Histograms Unimodal and Symmetric (aka bell-shaped, mound shaper, or Normal) The sides of the first distribution below the middle are mirror images, but real data are NEVER PERFECTLY SYMMETRIC . 46
Also, unimodal and approximately symmetric The graph of quantitative variables can be skewed right or skewed left Skewed left – left tail is stretched out longer than the right tail. 47

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The goal with shape is to look at a histogram of data and see which smooth curve fits the data best – approximately symmetric, skewed left or skewed. Note all of these shown are unimodal. Modes Peaks or humps seen in a histogram are called the modes of a distribution. A distribution whose histogram has one main peak is called unimodal , two peaks – bimodal (see figure), three or more – multimodal . Outliers Always be careful to point out the outliers in a distribution. An Outlier is a data value that is much smaller or much larger than the rest of the data values, atypical or unusual. Outliers …
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Chapter 5 - MSIT 3000 Chapter 5 Displaying and Describing...

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