Measuring Central Tendency — Mean, Median, Mode

Central tendency is a statistical term that refers to the middle or central value of a data set. It provides us with an idea about the concentration of values in a data set. There are three measures of central tendency — mean, median, and mode. Each of these measures has its own strengths and limitations.

Mean:

Mean is the most commonly used measure of central tendency. It is calculated by adding all the values in a data set and dividing by the number of values.

For example, suppose we have a data set that consists of the following values: 10, 20, 30, 40, and 50.

The mean of this data set is (10+20+30+40+50)/5 = 30.

Mean has the following strengths:

• It takes into account all the values in a data set.
• It is a reliable measure of central tendency when the data set has a normal distribution.

However, mean has the following limitations:

• It is affected by outliers or extreme values in a data set.
• It may not be a representative measure of central tendency when the data set is skewed.

Median:

Median is the middle value of a data set when the values are arranged in ascending or descending order. If the number of values is odd, then the median is the middle value.

If the number of values is even, then the median is the average of the two middle values.

For example, suppose we have a data set that consists of the following values: 10, 20, 30, 40, and 50. The median of this data set is 30.

Median has the following strengths:

• It is not affected by outliers or extreme values in a data set.
• It is a representative measure of central tendency when the data set is skewed.

However, median has the following limitations:

• It does not take into account all the values in a data set.
• It may not be a reliable measure of central tendency when the data set has a normal distribution.

Mode:

Mode is the most frequently occurring value in a data set. For example, suppose we have a data set that consists of the following values: 10, 20, 30, 40, 40, and 50.

The mode of this data set is 40.

Mode has the following strengths:

• It is a representative measure of central tendency when the data set has a large number of values with the same value.
• It is not affected by outliers or extreme values in a data set.

However, mode has the following limitations:

• It may not exist in a data set if all the values are unique.
• It may not be a reliable measure of central tendency when the data set has a normal distribution.

In conclusion, measuring central tendency using mean, median, and mode has its own strengths and limitations. It is important to choose the appropriate measure of central tendency based on the characteristics of the data set being analyzed.