Basic Statistics and Other Finance Terms
A brief explanation of various statistics used in finance and how to understand them.
Average, Mean, Median
Average (Generic Term)
The term “average” is a generic term that refers to a central value of a dataset. It is most often used interchangeably with “mean,” but in broader terms, it can also refer to other measures of central tendency, such as the median and mode.
There are several types of averages that can be used in finance and each has its strengths.
Mean (Arithmetic Mean)
The mean is a type of average, often called the arithmetic mean. The Mean is most likely what most people consider as the definition of when you say “average”. It is calculated by summing all the values in a dataset and then dividing by the number of values. For a simpler explanation and visuals, see How to Calculate the Mean Value (mathsisfun.com).
Median
The median is also a type of average that returns the middle value of the whole data set after sorting it from lowest value to highest value. As a result, there will be the same (or as close as possible) number of data points below the median number as above it. For a simpler explanation and visuals, see How to Find the Median Value (mathsisfun.com).
Example: Different Stories
Imagine you have the following group of 10 people and their net worth values.
| Data Set |
| – |
| – |
| 25,000 |
| 50,000 |
| 75,000 |
| 125,000 |
| 150,000 |
| 275,000 |
| 300,000 |
| 20,000,000 |
Applying the Mean: If you were to calculate the average (mean) of the net worth of everyone in the data set, you would come up with a mean net worth of $2,100,000.
Wow! Everyone must be doing really well. But looking at the data set, anyone can see that this is not necessarily the case.
In fact, nine out of 10 are below that average. The reason for the high average is the single data point that where the net worth is $20,000,000 (called an outlier).
Applying the Median: When you calculate the median, you are seeking to find the central value. Since there are 10 values, you would actually take the average of 5 and 6 ($75,000 and $125,000) to get a median net worth of $100,000.
That is a very different picture.
Key Concept: Using different metrics can help reveal underlying distortions in the data and paint a different picture.
Standard Deviation
Standard deviation is a statistical measure that describes how different each data point in the set is from the average (mean). What Standard Deviation attempts to tell you is what is the most likely range of values that should be expected in a data set. For a simpler explanation, see Standard Deviation and Variance (mathsisfun.com).
Standard deviation is a normalized statistic meaning that it may not accurately describe the true underlying deviation within a data set. For example, if the stock market has an average (mean) return of 10% and a standard deviation of 18%, we can expect that…
68% of the time annual returns will be between -8% and +28%,
95% of the time annual returns will be within -26% and +46%, and
99.7% of the time annual returns will be within -44% to +64%.
This example is for illustrative and educational purposes and does not represent guarantees of future returns.
Simple Interest vs Compound Interest
Simple Interest: Simple interest is calculated on the initial amount you invest, and the interest earned remains the same every year. This means that if you invest $1,000 at a 10% annual interest rate, you’ll earn $100 each year, resulting in a total of $3,000 after 20 years.
Compound Interest: Compound interest, on the other hand, earns interest not just on the initial amount but also on the interest accumulated over time. With the same $1,000 investment at a 10% annual interest rate, the value of your investment grows each year as you earn interest on both the initial amount and the interest that has already been added. After 10 years, your investment could grow to approximately $6,727 over twice the value of simple interest.
