Math 108 Topics in Mathematics | James Baglama |
5.4 Describing Center: Mean and Median - Video

5.4 Describing Center: Mean and Median - Video

Key Ideas

The mean of a dataset is obtained by adding the values of the observations in the dataset and dividing by the number of data. If the observations are listed as values of a variable x
(namely x_{1} , x_{2} , ... , x_{n}),
then the mean is written as x̄. The formula for the mean is
x̄ = (x_{1} + x_{2} + ... + x_{n})/n , where n represents
the number of pieces of data.

The median, M, of a distribution is a number in the middle of the data, so that half of the data are above the median, and the other half are below it. When determining the median, the data should be placed in order, typically smallest to largest. When there are n pieces of data, then the piece of data
(n+1)/2 observations up from the bottom of the list is the median. This is fairly straightforward when n is
odd. When there are n pieces of data and n is even, then you must find the average of the two center pieces of data (add together and divide by two). The smaller of these two pieces of data is located n/2 observations up from the bottom of the list. The second, larger, of the two pieces of data is the next one in order, or n/2 +1 observations up from the bottom of the list.

The mode of a distribution is the most frequently occurring observation. It is possible that a dataset has more than one observation that ties for being a mode.