# Statistics 101: Mean, Median and Mode

An introduction to statistical averages and finding the mean, median and mode.

Mean, median and mode are three statistical ways of talking about the average of a set of numbers or a data set. Although the mean, median and mode are all measures of averages, they are calculated in completely different ways. Each one has its own advantages and disadvantages, while accurately and inaccurately representing the averages in different situations.

#### Mean

The mean is the statistical average that most people think of when someone mentions an average. The mean is determined by adding up every value in the number set and dividing by the total amount of value points.

Example: Number Set = 3, 5, 2, 8, 2

In order to find the mean for the example number set above you first must add up all the values in the number set (3+5+2+8+2=20) then you must divide by the total number of values in the number set, which in the example is equal to 5 because there are 5 numbers in the data set. Therefore the mean of this data set equal to (20/5=4). If each of the numbers in the data set is equal to the number of years of schooling people have, out of the group of 5 people the mean number of years of schooling is 4 years.

The mean is advantageous because it takes into account the magnitude of every single value point in the data set.

The mean is disadvantageous because it is easily affected by extreme values in the data set.

#### Median

The median is determined by a ordering the the numbers in the data set in ascending order and then determining what value is in the middle of the data set (in place not value).

Example: Number Set = 3, 5, 2, 8, 2

Example reordered in ascending order = 2, 2, 3, 5, 8

Once the number set is ordered you can see the the third number in the data set is in the exact middle of the five numbers in the data set. In the example it just so happens that the third number in the data set is 3 and therefore the median value of the number set is 3. If there are an even number of numbers in the data set then the two middle values are added together then divided by two to determine the median.

The median is advantageous because it is not affected by any extreme values in the data set

The mean is disadvantageous because it is easily affected by extreme values in the data set.

#### Mode

The mode is the easiest measure of average to find. The mode is simply the value in the data set that occurs the most often.

Example: Number Set = 3, 5, 2, 8, 2

In the example above the mode is 2 because the number 2 shows up the most often in the data set.

The mode is advantageous because it is very easy to find.

The mode is disadvantageous because it does not take into account any of the other values in the data set.

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