What's the difference between mean and median?
The main difference between a mean and a median is that a mean is calculated by taking all of the data in a set and then dividing it by how many numbers there are, while the median is the point at which 50% of the data falls above and 50% falls below.
This blog post will also go over many other differences that you should know about mean vs median!
What is a Mean?
It is the sum of all observations divided by the number of total observations or sample size (average). A mean is a calculation of the average value for a dataset. This means that all the values in your data set are added up and then divided by how many items there were to come up with an overall value.
A good example would be if you had the price of every home sold within a year, this would give you a much better idea as to what most people paid because it takes into account everyone's purchase price rather than just those at one end or another.
What is a Median?
It is the middle observation when grouped into a numerical sequence (intermediate point). Median is found from dividing your dataset in half based on size - this will tell us where exactly 50% of our data lies when we put them in order from smallest to largest (or vice versa).
If we take our housing prices example again, the median price would be the value that falls exactly in the middle when all of our homes are lined up from cheapest to most expensive. Many people find it a more representative measure than the mean as it isn't skewed by outliers at either end of the spectrum.
Key Differences between Mean & Median
The difference in interpretation
The mean is pulled higher by outliers while the median is not. Consider the example below with 20, 30, 40, 50, 100 as the data set.
The mean of this data set would be 48 (20 + 30 + 40 + 50 + 100 divided by five). However, the median would be 40 since it ignores that outlier at 100. This can make a big difference in interpretation when looking at data sets.
The difference in central tendency
Another key difference between these two measures of central tendency is how they are affected by extra values added to or removed from the data set. When you add an extra value to a data set, the mean will change but the median will remain unchanged.
The mean shows greater influence from extreme values (outliers), while medians don’t change very much with outlying points — though they can still be pulled in that direction due to their positioning relative to other values within the dataset. This makes them better for identifying actual central tendency than measures such as mode and midrange which also include outliers, thus making them less dependent on those types of extreme values.
The difference in the role of outliers
There are some major differences between mean vs median that make them very different from each other. For example, here's why they can give us completely different information about our data:
The most common use for both measures is to summarize skewed distributions; however, mean's tend to be more influenced by outliers than medians are. If you have a small sample size, then the median is usually more representative of your data than the mean since it doesn't depend on outliers as much as means do and will be closer to most or all of your observations.
The role of outliers is also different between the mean and median. An outlier will change the mean considerably in comparison to a median. So a median, in general, is not that sensitive to the addition of an outlier than a mean.
Similarities between Mean & Median
Bot Mean and Median are two statistical averages. The mean of a set is the average value while the median is an intermediate point in the range of data values, with half having higher values and half lower.
So which one should you use?
Well, this really depends on what you're trying to achieve with your data and also how much information is available to you. In general, if there's a lot of variation in your dataset then using median will give you a better picture - whereas if everything is relatively close together then the mean might be more accurate. Whichever calculation you choose, always make sure that you've taken into account every piece of data that you're working with!
Which is more accurate?
Median is a better measure of central tendency than mean if outliers are present. This happens when you have the presence of extremely large or small values that skew the average higher or lower, respectively. However, if your data set does not contain many outliers, then the mean and median will be equally accurate at representing central tendency in most cases.
What is the formula for the median?
The median can be found by arranging all of the values in ascending order and then finding the middle value. If there is an odd number of values, the middle value will be located in the middle position. If there is an even number of values, then the two middle values will be averaged to find the median.
What is the formula for mean?
The mean can be found by adding all of the values together and then dividing them by how many data points are in your list. This will give you an average value, which may not always reflect what is at the center of a dataset if there are outliers present. If this is the case, then you will likely want to use median instead of the mean for your calculations.
In conclusion, mean and median are two different measurements that should be used in appropriate scenarios depending on the type of data being analyzed. The meaning behind both statistics is important to understand when analyzing a situation because it can have an impact on how you approach your analysis.