88 CHAPTER 3 Describing, Exploring, and Comparing Data 3-2 Measures of Variation • Develop the ability to measure variation in a set of sample data by finding values of the range, variance, and standard deviation. • Develop the ability to interpret values of the standard deviation by applying the range rule of thumb to determine whether a particular value is significantly low or significantly high. 3-3 Measures of Relative Standing and Boxplots • Develop the ability to compute a z score and use the result to determine whether a given value x is significantly low or significantly high. • Identify percentile values and quartile values from a set of data. • Develop the ability to construct a boxplot from a set of data. w x significantly loww significantly high. Key Concept The focus of this section is to obtain a value that measures the center of a data set. In particular, we present measures of center, including mean and median. Our objective here is not only to find the value of each measure of center, but also to interpret those values. Part 1 of this section includes core concepts that should be understood before considering Part 2. PART 1 Basic Concepts of Measures of Center In Part 1 of this section, we introduce the mean, median, mode, and midrange as different measures of center. Measures of center are widely used to provide representative values that “summarize” data sets. 3-1 Measures of Center DEFINITION A measure of center is a value at the center or middle of a data set. There are different approaches for measuring the center, so we have different definitions for those different approaches. We begin with the mean. Mean The mean (or arithmetic mean) is generally the most important of all numerical measurements used to describe data, and it is what many people call an average. v Go Figure $3.70: Mean amount left by the tooth fairy, based on a survey by Visa. An unlucky 10% of kids get nothing. CAUTION Never use the term average when referring to a measure of center. The word average is often used for the mean, but it is sometimes used for other measures of center. The term average is not used by statisticians and it will not be used throughout the remainder of this book when referring to a specific measure of center. The term average is not used by the statistics community or professional journals. From this point forward, it would be wise to abandon use of the term average when referring to a measure of center.
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