When you have completed this chapter, you will be able to: Calculate the arithmetic mean, the weighted mean, the median, the mode, and the geometric mean of a given data set; identify the relative positions of the arithmetic mean, median and mode for both symmetric and skewed distributions; point out the proper uses and common misuses of each measure; explain your choice of the measure of central tendency of data; explain your choice of the measure of central tendency of data. | Describing Data: Numerical Measures Chapter 3 GOALS Calculate the arithmetic mean, weighted mean, median, mode, and geometric mean. Explain the characteristics, uses, advantages, and disadvantages of each measure of location. Identify the position of the mean, median, and mode for both symmetric and skewed distributions. Compute and interpret the range, mean deviation, variance, and standard deviation. Understand the characteristics, uses, advantages, and disadvantages of each measure of dispersion. Understand Chebyshev’s theorem and the Empirical Rule as they relate to a set of observations. Parameter Versus Statistics PARAMETER A measurable characteristic of a population. STATISTIC A measurable characteristic of a sample. Population Mean For ungrouped data, the population mean is the sum of all the population values divided by the total number of population values. The sample mean is the sum of all the sample values divided by the total number of sample values. EXAMPLE: | Describing Data: Numerical Measures Chapter 3 GOALS Calculate the arithmetic mean, weighted mean, median, mode, and geometric mean. Explain the characteristics, uses, advantages, and disadvantages of each measure of location. Identify the position of the mean, median, and mode for both symmetric and skewed distributions. Compute and interpret the range, mean deviation, variance, and standard deviation. Understand the characteristics, uses, advantages, and disadvantages of each measure of dispersion. Understand Chebyshev’s theorem and the Empirical Rule as they relate to a set of observations. Parameter Versus Statistics PARAMETER A measurable characteristic of a population. STATISTIC A measurable characteristic of a sample. Population Mean For ungrouped data, the population mean is the sum of all the population values divided by the total number of population values. The sample mean is the sum of all the sample values divided by the total number of sample values. EXAMPLE: The Median PROPERTIES OF THE MEDIAN There is a unique median for each data set. It is not affected by extremely large or small values and is therefore a valuable measure of central tendency when such values occur. It can be computed for ratio-level, interval-level, and ordinal-level data. It can be computed for an open-ended frequency distribution if the median does not lie in an open-ended class. EXAMPLES: MEDIAN The midpoint of the values after they have been ordered from the smallest to the largest, or the largest to the smallest. The ages for a sample of five college students are: 21, 25, 19, 20, 22 Arranging the data in ascending order gives: 19, 20, 21, 22, 25. Thus the median is 21. The heights of four basketball players, in inches, are: 76, 73, 80, 75 Arranging the data in ascending order gives: 73, 75, 76, 80. Thus the median is The Mode MODE The value of the observation that appears most frequently. The Relative Positions of the Mean, Median and the Mode
