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