PROBABILITY AND STATISTIC FORMULAS PROJ
The Mean and Median: Measures of Central Tendency
The Mean and the Median
The difference between the mean and median can be illustrated with an example. Suppose we draw a sample of five women and measure their weights. They weigh 100 pounds, 100 pounds, 130 pounds, 140 pounds, and 150 pounds.
To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values. Thus, in the sample of five women, the median value would be 130 pounds; since 130 pounds is the middle weight.
The mean of a sample or a population is computed by adding all of the observations and dividing by the number of observations. Returning to the example of the five women, the mean weight would equal (100 + 100 + 130 + 140 + 150)/5 = 620/5 = 124 pounds. In the general case, the mean can be calculated, using one of the following equations:
Population mean = μ = ΣX / N OR Sample mean = x = Σx / n where ΣX is the sum of all the population observations, N is the number of population observations, Σx is the sum of all the sample observations, and n is the number of sample observations.
When statisticians talk about the mean of a population, they use the Greek letter μ to refer to the mean score. When they talk about the mean of a sample, statisticians use the symbol x to refer to the mean score.
The Mean vs. the Median
As measures of central tendency, the mean and the median each have advantages and disadvantages. Some pros and cons of each measure are summarized below.
The median may be a better indicator of the most typical value if a set of scores has an outlier. An outlier is an extreme value that differs greatly from other values.
However, when the sample size is large and does not include outliers, the mean score usually provides a better measure of central tendency.
To illustrate these points,
The Mean and the Median
The difference between the mean and median can be illustrated with an example. Suppose we draw a sample of five women and measure their weights. They weigh 100 pounds, 100 pounds, 130 pounds, 140 pounds, and 150 pounds.
To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values. Thus, in the sample of five women, the median value would be 130 pounds; since 130 pounds is the middle weight.
The mean of a sample or a population is computed by adding all of the observations and dividing by the number of observations. Returning to the example of the five women, the mean weight would equal (100 + 100 + 130 + 140 + 150)/5 = 620/5 = 124 pounds. In the general case, the mean can be calculated, using one of the following equations:
Population mean = μ = ΣX / N OR Sample mean = x = Σx / n where ΣX is the sum of all the population observations, N is the number of population observations, Σx is the sum of all the sample observations, and n is the number of sample observations.
When statisticians talk about the mean of a population, they use the Greek letter μ to refer to the mean score. When they talk about the mean of a sample, statisticians use the symbol x to refer to the mean score.
The Mean vs. the Median
As measures of central tendency, the mean and the median each have advantages and disadvantages. Some pros and cons of each measure are summarized below.
The median may be a better indicator of the most typical value if a set of scores has an outlier. An outlier is an extreme value that differs greatly from other values.
However, when the sample size is large and does not include outliers, the mean score usually provides a better measure of central tendency.
To illustrate these points,