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What are the characteristics, uses, advantages, and disadvantages of each of the measures of location and measures of dispersion? Discuss them with examples

Measures of location and measures of dispersion are two different ways of describing quantitative variables. Measures of location are often known as averages. Measures of dispersion are often known as a variation or spread. Both measures are helpful with describing statistical information. (Lind, Marchal, & Wathen, 2015)

The different measures of location include: the arithmetic mean, the median, the mode, the weighted mean, and the geometric mean. All of these measures of location pinpoint the center of a distribution of data. An advantage of measures of location is that the averages show us the central value of the data. A disadvantage of only using measures of location is that we may not draw an accurate conclusion because an average does not tell the spread of the data. Some examples of using measures of location include: finding the average price of a concert ticket, finding the average age of homeowners in a community, finding the averages shoe size of boys between the ages of 13-19, and finding the average amount of money people spend on food annually. (Lind, Marchal, & Wathen, 2015)

The different measures of dispersion include: the range, the variance, and the standard deviation. All of these measures of dispersion tell us about the spread of the data and it helps us compare the spread in two or more distributions. Advantages of using measures of dispersion are that it gives us a better idea of the range in which an average was calculated, and it is easy to calculate and understand. A disadvantage of using measures of dispersion is that it is a broad measurement because it only shows the maximum and minimum values of data. For example, the salaries of dentists in the state of Georgia might range from \$70,000-\$120,000 (just a made up example – not necessarily accurate data). This information is great for someone to know the range of dentist salaries, but it lacks in showing specific information about dentists’ salaries. (Lind, Marchal, & Wathen, 2015)

Lind, D. A., Marchal, W. G., & Wathen, S. A. (2015). Statistical techniques in business & economics. New York, NY: McGraw-Hill Education.

What are the characteristics, uses, advantages, and disadvantages of each of the measures of location and measures of dispersion? Discuss them with examples.

These are the measures in common use of location and dispersion: arithmetic mean, median, mode, weighted mean, and geometric mean. The arithmetic mean, median, and mode The mean usually refers to the arithmetic mean or average. This is just the sum of the measurements divided by the number of measurements. We make a notational distinction between the mean of a population and the mean of a sample. The general rule is that Greek letters are used for population characteristics and Latin letters are used for sample characteristics. Therefore: “A% * B%” denotes the arithmetic mean of a population of observations and “A * B” denotes the mean of a sample of size selected from a population. The mean can be thought of as a center of gravity of the data values. This property of the mean has advantages and disadvantages. The mean is a natural measure of location for data that have a well-defined middle of high concentration with the frequency decreasing more or less evenly as we move away from the middle in either direction. The mean is not as useful when the data is heavily skewed.

The median is estimated by first ordering the data from smallest to largest, and then counting upwards for half the observations. The estimate of the median is either the observation at the centre of the ordering in the case of an odd number of observations, or the simple average of the middle two observations if the total number of observations is even. The median has the advantage that it is not affected by outliers, so for example the median in the example would be unaffected by replacing ‘2.1’ with ’21’. However, it is not statistically efficient, as it does not make use of all the individual data values.

“The “mode” is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list.” It is not used much in statistical analysis, since its value depends on the accuracy with which the data are measured; although it may be useful for categorical data to describe the most frequent category. In the set of numbers:13, 18, 13, 14, 13, 16, 14, 21, 13. The mode is the number that is repeated more often than any other, so 13 is the mode.

The geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values. A geometric mean is often used when comparing different items finding a single “figure of merit” for these items when each item has multiple properties that have different numeric ranges.

The variance, range, and standard deviation are the measures of dispersion. In statistics, dispersion is the extent to which a distribution is stretched or squeezed. A measure of statistical dispersion is a non-negative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured. In other words, if the measurements are in meters or seconds, so is the measure of dispersion. 