ABSTRACT
This chapter continues our understanding of concepts learned in Chapter 6. An initial data set is entered and modified in one of three ways: (1) adding a constant to each data value, (2) multiplying each data value by a constant, or (3) replacing the last value by a different number. The purpose of this chapter, however, is to observe the effect of these modifications on three measures of dispersion: range, variance, and standard deviation. The sample range is the difference between the largest and smallest data value. The sample variance is the average squared deviation of the data values from their sample mean. The sample standard deviation is the square root of the sample variance. The formula for the sample variance is:
The numerator (top of equation) indicates that the mean of all the data values is subtracted from each data value, squared, and summed. The summing of the squared values is denoted by the symbol, Σ. This is referred to as the sum of squared deviations from the mean or simply sum of squared deviations (SS). The sum of squared deviations (SS) divided by the number of data values is referred to as the variance.
