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Introduction
The mean, median, and mode are important measures of central tendency in statistics, and they can be calculated in a given statistical data set to make inferences and draw conclusions. While the values of the mean, median, and mode can be different, they can also be the same, especially in a normally distributed sample.
Discussion
When the data set in question is in the form of normal distribution, then the median, mean, or mode can be used as the main measure of central tendency. Also known as the Gaussian distribution, the normal distribution is a type of statistical distribution that has a symmetrical shape about the mean. In a graphical format, the normal distribution takes the form of a bell curve (Ranganathan & Gogtay, 2019). In essence, all the provided data in a given statistical data set occur frequently around the mean.
A prime example of data where the mean, median, and mode are the same would be the scores on a given test. Consider a class where there 20 students took a mathematics test that was marked out of 100 and their scores were 80, 80, 81, 79, 80, 80, 81, 79, 80, 80, 80, 80, 80, 85, 75, 79, 81, 80, 80, and 80. From these grades, the mean score for the whole class is 80. Similarly, the mode is 80 as that was the most common score for the whole class. Lastly, the median is also 80 because arranging the data chronologically from the highest to the lowest would also see 80 as the value in the middle. Similarly, a distribution curve for the above test scores would also yield a bell curve.
Conclusion
In essence, the math test scores are not only a good example of a normal distribution, but also of how a given data set could have the same value of its mean, mode, and median.
Reference
Ranganathan, P., & Gogtay, N. J. (2019). An Introduction to Statistics – Data Types, Distributions and Summarizing Data. Indian journal of critical care medicine : peer-reviewed, official publication of Indian Society of Critical Care Medicine, 23(Suppl 2), S169–S170.
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