An indicator of the center of a distribution of observations is a useful summary. This is central tendency.

The three measures of central tendency are the mean, the median, and, to a lesser extent, the mode.

All three are used for numerical data, and the median is used for ordinal data.  

> Next: Mean

 

The mean is the arithmetic average of the observations. It is symbolized by Image not available. (called X-bar).

The mean is sensitive to extreme values.

 

Add the observations to obtain the sum and then divide by the number of observations.

The formula for the mean is written Σ X / n, where Σ (Greek letter sigma) means to add, X represents the individual observations, and n is the number of observations.

 

 

1. Determining if one group or one treatment is different from another.

Example:

If we want to know whether the mean energy intake in 2-year-old children in our practice is different from the mean in a national nutrition study, what evidence is needed to conclude that energy intake is really different in our group and not just a random occurrence? If the mean energy intake is much larger or smaller than the mean in the national nutrition studywe will probably conclude that the difference is real.

 

estimating and testing hypotheses about means and proportions.

 

The median is the middle value of a sample. It is equivalent to the 50th percentile such that half the sample values are above and half are below. It is identified by arranging the values in ascending order, then finding the middle-most number.

If n is odd, the median is the [( n + 1)/2]th largest observation. If n is even, the median is the average of the ( n /2)th and the ( n /2 + 1)th largest observations. In this example, there is an even number of values, so the median is the average of the two middle-most numbers; that is, for 1, 1, 2, 4, 5, 7, 7, 25, the median = (4 + 5)/2 = 4.5.

An advantage of the median is that it is insensitive to extreme values. You may notice that in this sample the mean is greater than the median. This indicates that the distribution has a positive skew.

The most frequently occurring value in a sample.