Difference Between Mean & Mode
In statistics, the "mean" and the "mode" are ways to understand how a list of values or numbers are distributed around a central number. The mean involves finding the central value using an arithmetic calculation, whereas the mode focuses on how often the same values may occur. Mean and mode give different perspectives for understanding patterns within distributions.
Other People Are Reading
-
Definitions
-
The mean is the arithmetic "balance point" of a distribution of values. Another word for the mean that is more commonly used is "average." The mode is the most frequently occurring value in a distribution or in a data set.
How to Calculate
-
To calculate the mean of a data set, add all the numbers and divide the sum by the number of occurrences. For example, in the data set ( 3, 1, 11, 5, 10 ), the sum of the numbers is 30. The mean will be the result of dividing 30 by 5, which is the number of occurrences. The mean of this data set is 6.
To find the mode of the data set ( 4, 11, 6, 14, 6, 7, 18, 6, 9, 13 ), put the numbers is order from low to high. The reordered data set is now ( 4, 7, 6, 6, 6, 9, 11, 13, 14, 18 ). The number that occurs most frequently in this data set is 6, therefore the mode is 6.
-
Practical Use for the Mean
-
An example of mean might be a person's average bowling score over the course of a year. An avid bowler could bowl 500 games in a year's time. During this time the scores could range from 185 to 290. The mean bowling score would be found by adding all the scores and dividing by 500, or the total number of games bowled.
Practical Use for the Mode
-
The results of a survey can be used as an example to find the mode of political preference in an election. If 100 people were surveyed and the results were Republican 30, Democrat 42, Independent 10 and those that declined to respond 8, the mode would be Democrat. This is because the variable Democrat occurs more frequently in the survey--42 times.
Considerations
-
The mean, or average, value can be influenced or skewed by just one or two extremely low or high values. For example, the average income for individuals in the United States is higher than most people's income. High income individuals skew the mean calculation to be on the high side. In this example, "average" and "most people" are not the same thing.
It is possible for there to be no mode of a data set. In the data set ( 4, 7, 11, 19 ), there is no number that occurs more than once. It is also possible to have two modes in a data set, which is called "bimodal." "Multimodal" is when there are more than two modes in a data set.
-
