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Learn the fundamentals of median, quartiles and mode -Statistics

Updated: Nov 8, 2023



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Once upon a time, in a quiet village, nestled between hills and a river there lived a girl named Lily. She spent her afternoons exploring the woods, collecting stones and arranging them in sequences. Her favorite numbers were 9, 17 and 22.



One sunny morning, Lily heard the villagers talking about the annual Harvest Festival. One of the games would be a grand math contest where the sharpest minds in the village could compete. Lily wanted to take part in the contest.



She started forming a pattern with her stones, with 9, 17 and 22 at the center. She imagined a peaceful village with 22 houses along a winding road. The youngest child in the village was 9 years old. The carpenter who could mend anything was 17 years old.



She introduced the baker, the farmer and a teacher, each with their own age. Explaining the data, she said, the median is like the center dividing the data into two equal parts. Quartiles divide the data into 4 equal parts.



In her data, the first quartile was where the younger folks live. The third quartile was where the older folks lived and the 2nd quartile was the median. Finally, explaining the mode, she said the mode is the value which occurs the most.



In the math contest, the judges were impressed by Lily's creativity. Not only did Lily win the contest, she also left a lasting impression on the villagers. Most mathematical concepts can be made accessible through story telling.






A beginner's guide to median, mode and quartiles. This post should answer your basic questions about median, quartiles and mode and how to evaluate them. I am a math educator teaching mathematics to high school students and college students for the past 3 decades.


I can tell you exactly what you need to be studying to understand median, quartiles and mode. In this age of ChatGpt where AI takes over teaching as well, I cannot stress how important it is for you to avoid common mistakes which students make. So, that's me, adding a humane approach to learning math.


If you want to learn Arithmetic Mean.


Median, Quartiles and Mode. How to calculate it?



In layman's language, a median is the middle value of a set of observations arranged in ascending or descending order. For a set of discrete values, you have to first arrange the data in ascending or descending order. Then depending on whether you have odd number or even number of values, you calculate the median.





My students generally find it easy to calculate the median for odd number of observations. Even number of values require a little more of work, but with a little help, they usually get it right. What happens for a frequency distribution?


Basically, you can divide frequency distributions into 2 types. One, is a simple frequency distribution without class intervals. Here, you first calculate the cumulative frequency. I usually recommend using the lesser than cumulative frequency.


I tell my students to divide n ( the sum of the frequencies) by 2 and then look at the frequency table and identify the median. For a grouped frequency distribution, there are 2 methods of calculating the median.


First, you draw, the cumulative frequency curve using the ogive and then using the ogive, you determine the median. As I tell my students, you need a high degree of accuracy here. Alternately, there is a formula to calculate the median which makes it very easy, provided you remember it right.







Quartiles are the values which divide the data into 4 equal parts


There are 4 quartiles, the lower quartile, the second quartile also called the median and the third quartile. The difference between the third and the first quartile is called the inter quartile range.


How will you calculate the quartiles. Again, for a set of discrete values, you arrange the data in ascending or descending order. You then calculate the quartiles using the formula. I make my students practice the case when you have a fractional value as well.





Again, for a simple frequency distribution, you calculate the cumulative frequency. Then using this you will calculate the quartiles. For a grouped frequency distribution with equal class intervals, you can either use the ogive or the formula for calculating.



In simple language, mode is the value which occurs the most frequently


Calculating the mode is one of the easiest things to do. My students just love calculating the mode for a discrete set of values. Just take the value which occurs most frequently. In this context, note that you can also have 2 modes, called a bimodal distribution.


Coming to a frequency distribution, if the frequency distribution is simple, just take the value with the highest frequency as the mode. For a grouped frequency distribution, there are two ways of calculating the mode. My students just love the graphical method, where you plot a histogram and then move on to evaluating the mode.


The second method of calculating the mode is using the formula which is again quite simple. I have enclosed a few formulas as images in this blog.


Still needing help?


I have given you a basic idea of median, quartiles and mode and how to evaluate them. In case you need some more help, you can contact me for online tutoring


You can choose between one to one tutoring or group classes. Again, you can tutor topic wise or for the entire course.


You can choose whichever suits you best.


I hope this blog can serve the purpose of educating you. Would you like to share this piece of advice to your friends who may need it? Free resource on Statistics.


Empower yourself and others!














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