#### Averages

An average is a number used to describe a set of data. Averages give a measure of the “middle” of a set.

The most common averages are the arithmetic mean, the median and the mode. The mean is often thought of as the average, but the terms are not interchangeable. The GMAT uses the term arithmetic mean instead of average to be more precise.

#### Arithmetic Mean and Median

The arithmetic mean is the sum of a set of numbers divided by the number of elements in the set.

mean = sum of the values/number of values

The median is the “middle” number of a list of data. To find the median, arrange the numbers in numerical order. If the number of values is odd, the median is the middle number. If the number of values is even, the median is the mean of the two middle numbers.

The median can differ greatly from the arithmetic mean.

Using the median, half of the people in a neighborhood pay more than the median rent, and half pay less. For example, if 5 people have monthly rent of $1100, $900, $1000, $10,000 and $3000, the median is $1100.

The mean does not split the people into a top half and bottom half. For example, for the monthly rents given above, the mean rent is $3200.

Compare this median of $1100 and the mean of $3200. If a large number of people pay very little rent and a few pay a huge amount, the mean would be quite high, but the median would be surprisingly low.