Mean, Median & Mode

The GRE frequently tests the three different mathematical averages, known as the mean, median, and mode.

Rules

The “mean” is the sum of all elements divided by the number of elements in the set.

The “median” is the middle number in a series. If there are two middle numbers, the median is halfway between them.

The “mode” is the number that appears the most frequently.

“Average” is a term used for various data measures to determine what is “normal” in a series of numbers. For example, suppose in four quarters of a basketball game, the basketball team scores 14, 15, 14, and 13 points. The median number of points scored is 14 - the middle number. The mode is also 14.

As mentioned above, "mean" is calculated by adding all the numbers together and dividing by the number of elements in the set. For example the numbers 6, 10, and 20, would have a mean value of 12. (6 + 10 + 20 = 36, divided by 3 = 12)

“Mean” as used on the GRE refers to “arithmetic mean.” There is also a concept called “geometric mean” which the appropriate root of the product of all the numbers. It is not tested on the GRE.

Practice

1. Four friends each spend money at a shoe store. Andy spends $145, Becky spends $122, Carla spends $140, and Donald spends $182. What is the median expenditure on shoes?

2. H&T Holdings' stock portfolio had a value of $1.1 million in February, $1.5 million in March, and $1.6 million in April. What was the average (arithmetic mean) value of H&T's stock portfolio over these months?

3. Erin works 14 overtime hours during week 1, 16 overtime hours during week 2, and 17 overtime hours during weeks 3 and 4. Which is greater - the median overtime hours Erin worked, or the arithmetic mean of overtime hours that Erin worked?

Comments

The GRE likes to ask questions which test the nuances of the rules, such as what the median is in an even-numbered set. The test will also commonly scramble numbers and ask the test taker to pick out the median or mode - in which case sorting the numbers numerically can be useful.

A commonly asked question is what the "mode" is in a series where two numbers both show up an equal number of times. The answer from a statistical perspective is that both of these numbers are modes (this is known as a multimodular dataset). However, the answer from a GRE preparation perspective is that this is not tested on the GRE.

Answers to Practice Questions

1. $142.50

The median is the middle number, or halfway between two middle numbers.

The numbers are $122, $140, $145, and $182; thus, the median is $142.50 - halfway between $140 and $145.

2. $1.4 million

Mean is the sum of all values divided by how many values there were.

= $1.4 million

3. The median is greater.

The median is the middle number, or halfway between two middle numbers. The three numbers in this case are 14, 16, and 17; thus, the median is 16.

Mean is the sum of all values divided by how many values there were. The mean in this case is thus: