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Chapter 4

# Chapter 4 - Chapte r4 Describing Data Displaying and...

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Chapte r4: Describing Data: Displaying and Exploring Data Chapter Opener GOALS When you have completed this chapter, you will be able to: 1. Develop and interpret a dot plot. 2. Develop and interpret a stem-and-leaf display. 3. Compute and understand quartiles, deciles, and percentiles. 4. Construct and interpret box plots . 5. Compute and understand the coefficient of skewness. 6. Draw and interpret a scatter diagram. 7. Construct and interpret a contingency table.

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McGivern Jewelers recently ran an advertisement in the local newspaper reporting the shape, size, price, and cut grade for 33 of its diamonds in stock. Using the data provided in Exercise 37, develop a box plot of the variable price and comment on the result. (Goal 4) Chapter4: Describing Data: Displaying and Exploring Data Introduction p. 100 Chapter 2 began our study of descriptive statistics. In order to transform raw or ungrouped data into a meaningful form, we organize the data into a frequency distribution. We present the frequency distribution in graphic form as a histogram or a frequency polygon. This allows us to visualize where the data tends to cluster, the largest and the smallest values, and the general shape of the data. In Chapter 3 we first computed several measures of location, such as the mean and the median. These measures of location allow us to report a typical value in the set of observations. We also
computed several measures of dispersion, such as the range and the standard deviation. These measures of dispersion allow us to describe the variation or the spread in a set of observations. We continue our study of descriptive statistics in this chapter. We study (1) dot plots, (2) stem-and- leaf displays, (3) percentiles, and (4) box plots. These charts and statistics give us additional insight into where the values are concentrated as well as the general shape of the data. Then we consider bivariate data. In bivariate data we observe two variables for each individual or observation selected. Examples include: the number of hours a student studied and the points earned on an examination; whether a sampled product is acceptable or not and the shift on which it is manufactured; and the amount of electricity used in a month by a homeowner and the mean daily high temperature in the region for the month. Chapter 4: Describing Data: Displaying and Exploring Data Dot Plots A histogram groups data into classes. Recall in the Whitner Autoplex data from Table 2-4 that 80 observations were condensed into seven classes. When we organized the data into the seven classes we lost the exact value of the observations. A dot plot A dot plot summarizes the distribution of one variable by stacking dots at points on a number line that shows the values of the variable. A dot plot shows all values. , on the other hand, groups the data as little as possible and we do not lose the identity of an individual observation. To develop a dot plot we simply display a dot for each observation along a horizontal number line indicating the possible values of the data. If there are

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