What does it measure of central tendency mean?
Measure of central tendency is a single value that attempts to describe a set of data by identifying the central value of that set of data.
Mean
When NOT to use mean?
Mean is susceptible to outliers. Which means it is effected by extremely high and extremely low values in the data. In such situations median is preferred over mean.
Another case is when the distribution is skewed. As the data becomes skewed the mean loses its ability to provide the best central location for the data as the skewed data is dragging it away from the typical value in the direction of the skew. In this case also median is preferred measure of central tendency.
Median
Median is a value that splits the data in two equal halves.
To calculate median arrange the data in ascending order then:
1. If the number of data (n) is odd then median is (n+1)/2th value.
2. If the number of data (n) is even, median is the average of n/2 and (n/2 + 1)th value.
Median is more resistant to outliers and skewed data than mean.
If data is non-normal then it is customary to use median instead of mean.
Mode
Mode is the most frequently occurring value in the data. Normally mode is used for categorical data.
The problem with mode is that it is not unique. In case of multi-modal data which mode represents the central tendency of data set becomes a difficult question.
Mode is also not suitable measure of central tendency in case of a continuous data, especially if the data set is not large. In such cases getting a clear mode becomes a problem.
Another case may arise when the most frequent data is far away from the rest of the data. In such case mode does not give a good measure of central tendency.
Summary of when to use mean, median , mode
PS1: Source: Laerd Statistics: Mean, Mode, Median - Measures of Central Tendency
PS2: Corrections/Improvements/Comments are welcome.
Measure of central tendency is a single value that attempts to describe a set of data by identifying the central value of that set of data.
Mean
When NOT to use mean?
Mean is susceptible to outliers. Which means it is effected by extremely high and extremely low values in the data. In such situations median is preferred over mean.
Another case is when the distribution is skewed. As the data becomes skewed the mean loses its ability to provide the best central location for the data as the skewed data is dragging it away from the typical value in the direction of the skew. In this case also median is preferred measure of central tendency.
Median
Median is a value that splits the data in two equal halves.
To calculate median arrange the data in ascending order then:
1. If the number of data (n) is odd then median is (n+1)/2th value.
2. If the number of data (n) is even, median is the average of n/2 and (n/2 + 1)th value.
Median is more resistant to outliers and skewed data than mean.
If data is non-normal then it is customary to use median instead of mean.
Mode
Mode is the most frequently occurring value in the data. Normally mode is used for categorical data.
The problem with mode is that it is not unique. In case of multi-modal data which mode represents the central tendency of data set becomes a difficult question.
Mode is also not suitable measure of central tendency in case of a continuous data, especially if the data set is not large. In such cases getting a clear mode becomes a problem.
Another case may arise when the most frequent data is far away from the rest of the data. In such case mode does not give a good measure of central tendency.
Summary of when to use mean, median , mode
| Type of Variable | Best measure of central tendency |
| Nominal | Mode |
| Ordinal | Median |
| Interval/Ratio (not skewed) | Mean |
| Interval/Ratio (skewed) | Median |
PS1: Source: Laerd Statistics: Mean, Mode, Median - Measures of Central Tendency
PS2: Corrections/Improvements/Comments are welcome.
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