QMB Chp 3 - 2

The simplest measure of dispersion is the?

Range. It is the difference between the largest and the smallest values in a data set.

Mean deviation is defined as.

The arithmetic mean of the absolute values of the deviations from the arithmetic mean.

As an example of the geometric mean, suppose you receive a 5 percent increase in salary this year and a 15 percent increase next year.

The average annual percent increase is 9.886, not 10.0. Why is this so? We begin by calculating the geometric mean. Recall, for example, that a 5 percent increase in salary is 105 percent. We will write it as 1.05.

What is commonly used as a measure to compare the spread in two or more sets of observations?

The standard deviation.

Why study Dispersion?

A measure of location, such as the mean or the median, only describes the center of the data. It is valuable from that standpoint, but it does not tell us anything about the spread of the data. Also, to compare the spread in two or more distributions.

Explain Chebyshev's Theorem and the Empirical Rule.

For any set of observations -sample or population-, the proportion of the values that lie within k standard deviations of the mean is at least 1-1/k2 , where k is any constant greater than 1.

Continuing Chebyshev's Theorem and the Empirical Rule. Pt. 2

Further, at least eight of nine values, or 88.9 percent, will lie between plus three standard deviations and minus three standard deviations of the mean. At least 24 of 25 values, or 96 percent, will lie between plus and minus five standard deviations of the mean.

Why do we ignore the signs of the deviations from the mean?

If we didn't, the positive and negative deviations from the mean would exactly offset each other, and the mean deviation would always be zero. Such a measure (zero) would be a useless statistic.

A defect of the range is that it is based on only two values, the highest and the lowest; it does not take into consideration all of the values. The mean deviation does. The arithmetic mean of the absolute values of the deviations from the arithmetic mean.

It measures the mean amount by which the values in a population, or sample, vary from their mean.

A geometric mean is?

Never greater than the arithmetic mean and all data values must be positive.

The three types of measures of Dispersion are?

Range, Mean deviation, and variance and standard deviation.

Continuing Chebyshev's Theorem and the Empirical Rule.

at least three of four values, or 75 percent, must lie between the mean plus two standard deviations and the mean minus two standard deviations. This relationship applies regardless of the shape of the distribution.