Mathematics is a vast as well as a challenging subject. It includes many concepts that apparently seem similar but have significant differences. Students often get confused about such measures and need expert help to clear their confusion.
The median and mean are also perplexing concepts in math. Although both are used to calculate the center of a data distribution, they have key dissimilarities in the calculation. They differ not just in the measurement process but also in the intended usage.
That’s why it is essential to learn how they differ and when they fit best to use. For your convenience, we have crafted this article to guide you through the basics and correct use of median and mean. Therefore, make sure you read this article till the end. Ready to dive in? Let’s roll.
What Is Median?
In mathematics, the median is the point of an ordered dataset that divides it into two halves: the higher half and the lower half. In other words, the median is simply the central value of a dataset that is either arranged in either ascending order or descending order.
How Median Is Calculated?
The calculation of media depends on whether the components of the provided data are odd or even. If the number of values in a dataset is odd, then you just need to arrange the values in ascending order, and the central value will be the median of the dataset.
However, if the given group of numbers is even, then the median will be the mean of the central two values after arranging them ascendingly or descending. For example, the median of an odd dataset 4,5,3,7,8 is 5, and the median of an even dataset 5,3,6,8 is 5.5.
Well, when dealing with large datasets, you might fall victim to inaccuracies as a human. In such situations, you can rely on a reliable online median calculator like https://mediancalculator.info/. No matter how large a group of numbers you have, a median calculator quickly processes the data and accurately calculates the median.
When To Use Median?
Calculating the median depends on the type of dataset and the purpose of analysis. Here are circumstances when using median fits best.
- Median can be helpful in situations when you have a skewed distribution of a group of numbers. Since this type of distribution includes instances of asymmetry in data, the median provides the best central tendency.
- Another application of the median is when your dataset contains outliers. Outliers are extremes that highly differ from the rest of the values of a dataset. In their presence, the median proves best for finding the center of the dataset without affecting the results by skewness.
- Median is mainly used when the order of the numbers of a group matters. As mentioned earlier, the median involves arranging the dataset in ascending or descending orders; it better predicts the ordinal center of a large dataset.
What Is Mean?
Mean is another calculation of the central tendency of a large dataset that is significantly different from the median. However, the mean is not as complex as the median is. To put it simply, the mean is the average of all the components of a group of numbers.
How Mean Is Calculated?
When it comes to calculating the mean of a given dataset, there is a simple formula that makes it easy to find the mean of a group of numbers. This formula directs you to take a sum of all the given values and divide them by the total number of values in a dataset.
Mathematically, it is written as,
X̄ = (x1 + x2 + x3 +….+xn)/n
Here, the bar over X represents the mean, and n refers to the total number of values in the dataset. If you have a dataset, X = 2, 5, 3, 9, 5, 6, 7, 3, its mean will be calculated as follows:
X̄ = (2 + 5 + 3 +9+5+6+7+3)/8
X̄ = 5
When To Use Mean?
Just like the median, the mean is also useful in particular situations, especially when you deal with athematic datasets. Here is when you should prefer using mean instead of median.
- Opposite to the application of the median, the mean is beneficial when you deal with the symmetric distributions. This is because the mean involves taking the average of all the numbers, and the average might be affected by skewness in the data.
- Where the median is used when the outliers are present, the mean is used when the outliers are absent from a dataset. As discussed earlier, outliers are highly different from the other numbers in the group, so they might affect the central tendency.
- Mean is preferred when you need to perform a quantitative analysis of datasets. This is helpful in fields where real-time measurements are taken. For example, the mean can be used to find the average of a student’s marks, employees’ salaries, and geometrical values.
To Sum Up
After going through the above article, we hope that you now have no confusion about the concepts of median and mean. Now that you know the difference between their definitions, method of calculation, and especially purpose of use, we expect that you will easily decide which to use.