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The focus of Chapter 3 is on the use of statistical techniques to describe data, thereby enabling you to: Distinguish between measures of central tendency, measures of variability, and measures of shape. Understand conceptually the meanings of mean, median, mode, quartile, percentile, and range. Compute mean, median, mode, percentile, quartile, range, variance, standard deviation, and mean absolute deviation on ungrouped data. Differentiate between sample and population variance and standard deviation.

Understand the meaning of standard deviation as it is applied using the empirical rule and Chebyshevs theorem. Compute the mean, median, standard deviation, and variance on grouped data. Understand box and whisker plots, skewness, and kurtosis. Compute a coefficient of correlation and interpret it. Much of the time, statisticians need to describe data by using single numerical measures.

Chapter 3 presents a cadre of statistical measures for describing numerically sets of data. It can be emphasized in this chapter that there are at least two major dimensions along which data can be described.

One is the measure of central tendency with which statisticians attempt to describe the more central portions of the data. Included here are the mean, median, mode, percentiles, and quartiles. It is important to establish that the median is a useful device for reporting some business data, such as income and housing costs, because it tends to ignore the extremes. On the other hand, the mean utilizes every number of a data set in its computation.

This makes the mean an attractive tool in statistical analysis. A second major group of descriptive statistical techniques are the measures of variability. Students can understand that a measure of central tendency is often not enough to fully describe data, often giving information only about the center of the distribution or key milestones of the distribution.

A measure of variability helps the researcher get a handle on the spread of the data. The empirical rule will be referred to quite often throughout the course; and therefore, it is important to emphasize it as a rule of thumb. In this section of chapter 3, z scores are presented mainly to bridge the gap between the discussion of means and standard deviations in chapter 3 and the normal curve of chapter 6. One application of the standard deviation in business is the use of it as a measure of risk in the financial world.

For P a g e 68 example, in tracking the price of a stock over a period of time, a financial analyst might determine that the larger the standard deviation, the greater the risk because of swings in the price. However, because the size of a standard deviation is a function of the mean and a coefficient of variation conveys the size of a standard deviation relative to its mean, other financial researchers prefer the coefficient of variation as a measure of the risk.

That is, it can be argued that a coefficient of variation takes into account the size of the mean in the case of a stock, the investment in determining the amount of risk as measured by a standard deviation. It should be emphasized that the calculation of measures of central tendency and variability for grouped data is different than for ungrouped or raw data.

While the principles are the same for the two types of data, implementation of the formulas is different. Computations of statistics from grouped data are based on class midpoints rather than raw values; and for this reason, students should be cautioned that group statistics are often just approximations. Measures of shape are useful in helping the researcher describe a distribution of data. The Pearsonian coefficient of skewness is a handy tool for ascertaining the degree of skewness in the distribution.

Box and Whisker plots can be used to determine the presence of skewness in a distribution and to locate outliers. The coefficient of correlation is introduced here instead of chapter 14 regression chapter so that the student can begin to think about two-variable relationships and analyses and view a correlation coefficient as a descriptive statistic.

In addition, when the student studies simple regression in chapter 14, there will be a foundation upon which to build. All in all, chapter 3 is quite important because it presents some of the building blocks for many of the later chapters.

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