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Measures of Central Tendency

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Measures of Central Tendency

Central tendency is commonly known as the ‘average’. In more technical terms, it is the ‘most central or representative number in a data set’.

There are various measures of central tendency in psychology that are used in descriptive statistics.

Imagine that you are a first-year university student, and a friend asks you about the ages of people in your psychology course. You'll say: ‘Well, most people are 18, there are a few in their 20’s and two or three over 40.’ You gave the average age or central tendency of 25.

In descriptive statistics, there are three ways to measure central tendency, mean, median, and mode.

The measures of central tendency

Let's take a look at measures of central tendency the mean, median, and mode with examples.

Mean

The mean in everyday terms is ‘average’. It is what you get if you add up all the values in a data set, and then divide by the total number of values.

A data set has the values 2, 4, 6, 8, 10. The mean would be (2+4+6+8+10) ÷ 5 = 6.

Advantages and disadvantages of the mean

Advantages

The mean is a powerful statistic used in population parameters.

Population parameter: When we conduct psychological studies, we use a limited number of participants as it would be impossible to test a whole population. The measures from these participants are measures of a sample (sample statistics) and we use these sample statistics as an estimate and reflection of the general population (population parameter).

These population parameters we derive from the mean can be used in inferential statistics.

The mean is the most sensitive and precise of the three measures of central tendency. This is because it is used on interval data (data measured in fixed units with equal distances between each point on the scale. E.g., the temperature measured in degrees, IQ test). The mean takes into account the exact distances between values in a data set.

Disadvantages

As the mean is so sensitive it can easily be distorted by unrepresentative values (outliers).

A sports coach is measuring how long it takes for pupils to swim 100m. There are 10 pupils, all of the pupils take around 2 minutes except for one who takes 5 minutes. Due to this outlier of 5 minutes, the value we get for the mean would actually be unrepresentative of the group.

Additionally, as the mean is very precise, sometimes the values calculated do not make sense.

A headteacher would like to calculate what is the average number of siblings children have at their school. After getting data of all sibling numbers and dividing by the number of pupils, it turns out the mean number of siblings is 2.4.

Median

The median is the central number in a data set when it is ordered from lowest to highest.

Out of the numbers 2, 3, 6, 11, 14, the median is 6.

If there are an even number of values in a data set, the median is between the two central values.

Out of the numbers 2, 3, 6, 11, 14, 61, the median is between 6 and 11. We calculate the mean of these two numbers, (6+11) ÷ 2, which is 8.5; thus the median of this data set is 8.5.

Advantages and disadvantages of the median

Advantages

  • Unaffected by extreme values unrepresentative of the data set.

  • The median is easier to calculate than the mean.

Disadvantages

  • The median does not take into account the exact distances between values like the mean does.

  • The median cannot be used in estimates of population parameters.

Mode

The mode is a measure of the category with the highest frequency count.

For a data set of 3, 4, 5, 6, 6, 6, 7, 8, 8, the mode is 6.

It is normally used for nominal data (named data that can be separated into categories such as gender, ethnicity, eye colour, hair colour). However, the mode can be used for any level of data. E.g., say for eye colour we have the categories ‘brown’, ‘blue’, ‘green’, ‘grey’, the mode can measure which category has the highest eye colour count.

Advantages and disadvantages of the mode

Advantages

  • Can show which category is the most frequently occurring.

  • Unaffected by extreme values unrepresentative of the data set.

Disadvantages

  • The mode does not take into account the exact distances between values.

  • The mode cannot be used in estimates of population parameters.

  • Not useful for small data sets which have values that occur equally frequently. E.g., 5, 6, 7, 8.

  • Not useful for categories with grouped data, e.g., 1-4, 5-7, 8-10.

Measures of Central Tendency - Key takeaways

  • In descriptive statistics, there are three ways to measure central tendency, mean, median, and mode.

  • The mean in everyday terms is ‘average’. It is what you get if you add up all the values in a data set and then divide by the total number of values.

  • The median is the central number in a data set.

  • The mode is a measure of the category with the highest frequency count.

Frequently Asked Questions about Measures of Central Tendency

The measures of central tendency are mean, median, and mode.

While each measure of central tendency has its advantages and disadvantages, the mean is the most sensitive and precise of the three measures of central tendency. This is because it is used on interval data and takes into account the exact distances between values in a data set.

To calculate the mean, add up all the values in a data set, and then divide by the total number of values. To find the median, it is the central number in a data set. The mode is a measure of the category with the highest frequency count.

The most common measure of central tendency is the mean.

The best way depends on your data. There is not a measure of central tendency that is the ‘best’. The mean is good to use when the data has no outliers. If the data is skewed the median would be better to use. The median is also preferred for ordinal data (data that is on a scale but with no fixed equal distances between each point. For example, a rating of happiness on a scale of 0-10. Depending on the participant, the difference between happiness 1-2, and 7-8 cannot be said to be exactly the same.  A rating of 4 might be very unhappy for one participant, but fairly cheerful for another participant). The mode is used when the data is nominal (named data that can be separated into categories).

Final Measures of Central Tendency Quiz

Question

What are the three measures of central tendency?

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Answer

The three measures of central tendency are mean, median, and mode.

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Question

How do you calculate the mean?

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Answer

Add up all the values in a data set, and then divide by the total number of values. For example, a data set has the values 2, 4, 6, 8, 10. The mean would be (2+4+6+8+10) ÷ 5 = 6.

Show question

Question

What are the advantages of the mean?


Show answer

Answer

  • The mean is a powerful statistic used in population parameters. These population parameters we derive from the mean can be used in inferential statistics.

  • The mean is the most sensitive and precise of the three measures of central tendency. 

Show question

Question

What are the disadvantages of the mean?


Show answer

Answer

  • As the mean is so sensitive it can easily be distorted by unrepresentative values (outliers).

  • As the mean is very precise, sometimes the values calculated do not make sense. For example, at a school, the mean number of siblings someone has is 2.4.

Show question

Question

What is the median?


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Answer

The median is the central number in a data set.

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Question

How do you calculate the median if there is an even number in the data set?


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Answer

The median is between the two central values. For example, if the central values are 6 and 11, the mean of these two numbers is (6+11) ÷ 2 = 8.5.

Show question

Question

What are the advantages of the median?


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Answer

  • The median is unaffected by extreme values unrepresentative of the data set.

  • The median is easier to calculate than the mean.

Show question

Question

What are the disadvantages of the median?


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Answer

  • The median does not take into account the exact distances between values.

  • The median cannot be used in estimates of population parameters.

Show question

Question

How do you find out the mode?


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Answer

The mode is the category with the highest frequency count. For example, for a data set of 3, 4, 5, 6, 6, 6, 7, 8, 8, the mode is 6.

Show question

Question

What are the advantages of the mode?


Show answer

Answer

  • Can show which category is the most frequently occurring.

  • Unaffected by extreme values unrepresentative of the data set.

Show question

Question

What are the disadvantages of the mode?


Show answer

Answer

  • The mode does not take into account the exact distances between values.

  • The mode cannot be used in estimates of population parameters.

  • Not useful for small data sets which have values that occur equally frequently. 

  • Not useful for categories with grouped data.

Show question

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