Central Tendency Explained: Mean, Median, Mode

The arithmetic mean is the most common way to find the average of a dataset.Let's look at a simple dataset with the numbers 2, 4, 6, 8, and 10.To find the mean, we first add all the numbers together.Then we divide the sum by the count of numbers, which is 5.The mean of our dataset is 6, which represents the average value.Now, let's see how an outlier can affect the mean.Notice how the mean has shifted significantly due to just one outlier.This sensitivity to outliers is important to consider when choosing the mean as a measure of central tendency.The median is the middle value when data is arranged in order from lowest to highest.For an odd-numbered dataset like this one with 5 numbers, we find the exact middle position by adding 1 to the count and dividing by 2.This gives us position 3, making 5 our median value.For even-numbered datasets, like these four numbers, we need to take the average of the two middle values.Here, we take 4 and 6, add them together, and divide by 2 to get our median of 5.The median is particularly useful when dealing with outliers. Let's look at a dataset with an extreme value.When we have an outlier like 100, the mean is heavily affected, jumping to 23.4.However, the median remains at 5, making it a more reliable measure of central tendency in this case.Let's look at a real-world example with house prices in a neighborhood.In this neighborhood, most houses are priced between 150 thousand and 260 thousand dollars, but there's one luxury home at 1.5 million.The median price better represents what a typical home in this neighborhood costs, as it isn't skewed by the luxury property.The mode is the value that appears most frequently in a dataset.Let's look at a unimodal dataset, where there is one clear mode. In this case, 4 appears three times, making it the mode.A dataset can also be bimodal, having two modes. Here, both 1 and 5 appear three times each.Sometimes, a dataset has no mode at all. This happens when all values appear the same number of times.The mode is particularly useful for categorical data, like colors or names, where mean and median don't make sense.The mode has many practical applications in real-world scenarios.Let's review the key points about mode.Thanks for learning about mode with Spark.E!