Self-Instruct
In statistics, it is common to use measures of central tendency to describe a set of data. The two most commonly used measures of central tendency are the average and the median. While both measures are often used interchangeably, they have different applications and meanings. This article will explain the difference between the average and median.
Average:
The average is a measure of central tendency that represents the sum of all the observations in a dataset divided by the number of observations. It is also known as the mean. For example, if a student’s grades in five subjects are 90, 85, 75, 80, and 70, the average of the grades can be calculated as follows:
Average = (90 + 85 + 75 + 80 + 70) / 5 = 80
The average can be used to provide an overall view of the data. However, it can be influenced by extreme values or outliers. For instance, if a student gets a grade of 20 in one of the subjects, that would affect the average significantly. A few outliers can skew the distribution, leading to a distorted representation of the data.
Therefore, the average should be used with caution, especially when working with a small dataset or when there are extreme values. It is also worth noting that the average can only be calculated for quantitative data, which can be counted and measured.
Median:
The median is a measure of central tendency that represents the middle value of a dataset. It is obtained by arranging the data in ascending order and identifying the value that is in the middle of the data. For example, if a student’s grades in five subjects are 90, 85, 75, 80, and 70, the median of the grades can be calculated as follows:
Arranging the values in ascending order: 70, 75, 80, 85, 90
The median is the middle value: 80
If there are an odd number of observations, the median is the value that is exactly in the middle of the dataset. If there are an even number of observations, the median is the average of the two middle values.
The median is not influenced by extreme values or outliers, as it only takes into account the middle value(s) of the dataset. Therefore, it is a more robust measure of central tendency than the average. Additionally, the median can be calculated for both quantitative and qualitative data.
To illustrate the difference between the average and median, consider the following example: A class of ten students took a math test, and their scores are listed below:
45, 50, 55, 60, 65, 70, 75, 80, 85, 95
The average score is calculated as follows:
Average = (45 + 50 + 55 + 60 + 65 + 70 + 75 + 80 + 85 + 95) / 10 = 68
The median score is identified as follows:
Arranging the scores in ascending order: 45, 50, 55, 60, 65, 70, 75, 80, 85, 95
The middle value is 65, which is the median.
The difference between the average and the median in this case is due to the presence of an outlier, which is the score of 95. The outlier pushed the average score higher, while the median score was not affected by the outlier. Therefore, if the goal is to identify the typical or representative score of the class, the median score would be a better measure of central tendency than the average score.
In conclusion, the average and median are both measures of central tendency, but they have different meanings and applications. The average represents the sum of all the values in the dataset divided by the number of observations, while the median represents the middle value of the dataset. The average can be influenced by outliers or extreme values, while the median is not affected by them. Therefore, the choice between the average and median as a measure of central tendency depends on the nature of the data and the research question being asked.