How to Find the Mean, Median, and Mode

Table of ContentsView AllTable of ContentsCalculate the MeanCalculate the MedianCalculate the ModePros and Cons of EachWhen to Use EachExamples

Table of ContentsView All

View All

Table of Contents

Calculate the Mean

Calculate the Median

Calculate the Mode

Pros and Cons of Each

When to Use Each

Examples

Close

Knowing how to find the mean, median, and mode can help us interpret data collected throughpsychological research. These values provide more insight into what may be considered “normal” or “abnormal” for a specific group of people in terms of cognitive processes or behaviors, for example.

Because they are all measures of central tendency,psychology studentsoften find it easy to confuse the three. Yet, there are differences in what each one is and how it is found. Here are some useful tips to help you distinguish between these measures, as well as how to calculate mean, median, and mode.

Need a Refresher?The meanis the arithmetic average of a set of given numbers. Therefore, the mean in math is often referred to as simply the “average.“The medianis the middle score in a set of given numbers. As the median, half of the scores are above this number and half are below.The modeis the most frequently occurring score in a set of given numbers. In other words, it is the score that appears the greatest number of times.

Need a Refresher?

The meanis the arithmetic average of a set of given numbers. Therefore, the mean in math is often referred to as simply the “average.“The medianis the middle score in a set of given numbers. As the median, half of the scores are above this number and half are below.The modeis the most frequently occurring score in a set of given numbers. In other words, it is the score that appears the greatest number of times.

How Do You Find the Mean?

Take these two steps to calculate the mean:

Recap of How to Find the Mean

How to Find the Median

As an example, consider this set of numbers: 5, 9, 11, 9, 7. First, you arrange them in numerical order (5, 7, 9, 9, 11). Since you have an odd number of scores, the number in the third position of the data set is the median which, in this case, is 9 (5, 7,9, 9, 11).

Recap of How to Find the Median

How Do You Find the Mode?

Of all the measures, finding the mode requires the least amount of mathematical calculation. Instead, since the mode is simply the most frequently occurring score in a distribution, all you do is look at all your scores and select the most common one.

As an example, consider the following number distribution: 2, 3, 6, 3, 7, 5, 1, 2, 3, 9. The mode of these numbers would be 3 since this is the most frequently occurring number (2,3, 6,3, 7, 5, 1, 2,3, 9).

If no number in a set occurs more than once, there is no mode for that set of data. It’s also possible for a data set to have two modes. This is known as bi-modal distribution.

Bi-Modal DistributionBi-modal distribution occurs when there are two numbers that are tied in frequency. For example, consider the following set of numbers: 13, 17, 20, 20, 21, 23, 23, 26, 29, 30. In this set, both 20 and 23 occur twice (13, 17,20,20, 21,23,23, 26, 29, 30). Therefore, they are both modes.

Bi-Modal Distribution

Bi-modal distribution occurs when there are two numbers that are tied in frequency. For example, consider the following set of numbers: 13, 17, 20, 20, 21, 23, 23, 26, 29, 30. In this set, both 20 and 23 occur twice (13, 17,20,20, 21,23,23, 26, 29, 30). Therefore, they are both modes.

Recap of How to Find the ModeTo find the mode, you identify the score that occurs most often within the data set. In cases where you have a large number of scores, creating afrequency distributioncan be helpful in determining the mode.

Recap of How to Find the Mode

To find the mode, you identify the score that occurs most often within the data set. In cases where you have a large number of scores, creating afrequency distributioncan be helpful in determining the mode.

Pros and Cons of Mean, Median, and Mode

Each measure of central tendency has its own strengths and weaknesses. Here are a few to consider.

While the mean in math is theoretically neutral, some contend that the use of the mean in psychology can lead to inappropriate conclusions if care is not taken with its application.This is due, in part, tobehaviorandcognitionbeing both complex and variable in nature.

When to Use Mean, Median, and Mode

How do you determine whether to use the mean, median, or mode when analyzing psychology research? The one you select can depend on the data scores themselves.

If there are no outliers in your data set, the mean may be the best choice in terms of accuracy since it takes into account each individual score and finds the average. Conversely, if outliers exist, the median or mode may be more accurate since the results won’t be skewed.

Also consider what you are trying to measure. Are you looking for the average (the mean), do you want to identify the middle score (the median), or are you looking for the score that appears most often (the mode)? While they are all measures of central tendency, each one looks at this tendency from a slightly different point of view.

An Example of Mean, Median, and Mode in Psychology

Imagine a research study in which psychologists are interested in learning the typical age at which someone might be diagnosed withschizophrenia. To collect this data, they send a questionnaire to mental health providers, asking that they share their patients' ages upon formal diagnosis.

The responses received indicate that the practitioners' patients were the following ages:

Using the calculations above, you would find that the mean, median, and mode for this data set are all around 27 years (27.1 years, 27 years, and 27 years respectively). In this case, any of these measures could be used to help you arrive at the typical age of onset.

In case you are curious, the National Alliance on Mental Health reports that the average age of schizophrenia onset for men is late teens to early 20s, while women tend to be diagnosed with this condition in their late 20s to early 30s.

2 SourcesVerywell Mind uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read oureditorial processto learn more about how we fact-check and keep our content accurate, reliable, and trustworthy.Speelman CP, McGann M.How mean is the mean?Front Psychol. 2013;4:451. doi:10.3389/fpsyg.2013.00451National Alliance on Mental Illness.Schizophrenia.Additional ReadingHogg RV, McKean JW, Craig AT.Introduction to Mathematical Statistics.Boston: Pearson; 2013.Laerd Statistics.Measures of Central Tendency.

2 Sources

Verywell Mind uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read oureditorial processto learn more about how we fact-check and keep our content accurate, reliable, and trustworthy.Speelman CP, McGann M.How mean is the mean?Front Psychol. 2013;4:451. doi:10.3389/fpsyg.2013.00451National Alliance on Mental Illness.Schizophrenia.Additional ReadingHogg RV, McKean JW, Craig AT.Introduction to Mathematical Statistics.Boston: Pearson; 2013.Laerd Statistics.Measures of Central Tendency.

Verywell Mind uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read oureditorial processto learn more about how we fact-check and keep our content accurate, reliable, and trustworthy.

Speelman CP, McGann M.How mean is the mean?Front Psychol. 2013;4:451. doi:10.3389/fpsyg.2013.00451National Alliance on Mental Illness.Schizophrenia.

Speelman CP, McGann M.How mean is the mean?Front Psychol. 2013;4:451. doi:10.3389/fpsyg.2013.00451

National Alliance on Mental Illness.Schizophrenia.

Hogg RV, McKean JW, Craig AT.Introduction to Mathematical Statistics.Boston: Pearson; 2013.Laerd Statistics.Measures of Central Tendency.

Hogg RV, McKean JW, Craig AT.Introduction to Mathematical Statistics.Boston: Pearson; 2013.

Laerd Statistics.Measures of Central Tendency.

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