When should one of mean, mode, and median be used over the other
In: 15
All three of these measures can be used to think about what a ‘normal’ value for a variable is.
**When should you use the mean?**
I’m going to disagree with many of the other posts and say that in many real-world situations, the mean is not a very good measure to use to describe what a ‘normal’ value is.
* A lot of real-world variables, and I’m mainly thinking about money-related examples here, are not symmetrically distributed and the mean is a poor descriptor for what is normal.
* Many real-world problems involve taking a single sample from a distribution.
Want to know what a normal income is? What is a normal price to pay for a house? How long to people spend commuting to work? The mean would be awful for these because they are all going to be heavily influenced by a few extremely large values.
So when should you use the mean?
* The mean is great for when you need to understand what a variable does in the long term or if you are accumulating things over time. For example, given the distribution of daily rainfall, the mean is a good measurement to use to understand the expected amount of total rain over a month or a year.
* The mean can be good for describing properties of groups of things based on their individual properties. E.g. On average, 1 in every 400 widgets will fail within two years.
* The mean is a measurement that minimises how badly you can be wrong, so use it when you want a descriptor for the ‘middle’ of a data set that has this property.
**When should you use the median?**
The median is a great measure to use to describe what an average person’s experience is like. It is the ‘middle of the pack’ and is influenced by where the pack is, not what happens at the extremes.
**When should you use the mode?**
Others have stated this pretty well. This measure is most useful with categorical variables to answer the question of what the ‘most likely’ result is. E.g. What is the most common colour of car?
Latest Answers