What is Variability?

Variability is like finding the range and the average score in a class’s test results…

A teacher gives their class a test and wants to gauge if each student has a similar understanding of the content he or she has taught. One way to do this is by finding the difference between the lowest score and average score and the highest score and average score. The smaller the gap, the lower the variability and the closer each student’s comprehension is to each other’s.

Variability is a way that you can measure the difference between individual pieces of data and the average in a dataset. When you do something, you can usually predict how it’s going to turn out. For example, you might know that if you play a round of golf, your average score is 80. The variability in your scores helps you predict how far your actual score might fall from that average. If you have low variability in your scores, you might score between 75 and 85. If you have high variability, your score could range from 60 to 100.

One way to think about variability is as a graph of a normal distribution. The wider the distribution on the chart, the more variability there is in the results. The thinner the distribution, the less variability there is.

There are many ways to measure variability, such as finding the standard deviation or range for a set of data.

Understanding variability is vital in a variety of situations. In a field where consistency is essential, people make the variability in their results is as low as possible. An example of this is medical care. In situations where extreme outcomes are acceptable or desirable, such as trying to grow a record-setting vegetable, variability is less of an issue, or possibly even a good thing.

In the world of finance, variability is essential for investors who are choosing assets in which to invest. Different types of assets offer various potential risks and returns. Typically, assets with higher variability must offer higher returns to offset the potential for loss.

One example of variability can be seen in a bowler’s scoring history. Throughout a season, a bowler might average a score of 200 over 10 frames. Their worst score was 150, and their best was a perfect 300. One measure of variability, range, would find the difference between the highest and lowest score, 150. The wide range indicates high variability in the bowler’s scores.

If an online shopper orders a package, he or she may experience variability in how long it takes the shipment to arrive. Parcels may take an average of three days to arrive but as little as two, or as many as four, days.

Patrons at a fast-food restaurant can experience variability in how long it takes the restaurant to fill their orders. If they visit during the lunch rush, it can take a long time for them to receive their food. If they go during a less busy time, they can place an order and receive their food much more quickly.

There are four main measures of variability.

Range is the most straightforward measure of variability, finding the difference between the largest value and the smallest value in a set.

For example, if 20 students in a class take an exam, there will be 20 resulting scores. If one student gets a perfect score of 100 and the lowest-scoring student receives a 64, the range for the test scores will be 36 (that is, 100 – 64). The downside of using the range to measure variability is that outliers have a significant impact on the range. If 19 of the students scored 100 and one student scored 64, the range is still 36. However, the range might not show the full picture, which is that almost every student scored 100.

Related to the range is the interquartile range. You can find the interquartile range by breaking a dataset into four parts. Start by dividing the data into two parts by finding the median value. Then divide each of the resulting halves into half again by finding their medians. For example, using the following dataset:

2, 4, 6, 8, 10, 12, 14, 16,

You would divide the data set into two halves, which look like this:

2, 4, 6, 8,

And

10, 12, 14, 16

Call the point that divides the two datasets Q2.

Then, divide the first half of the dataset in half again, so you get

2, 4

And

6, 8

The point dividing those two datasets is Q1.

Finally, divide the second half of the original dataset to get.

10, 12

And

14, 16

Call the point dividing the resulting datasets Q3.

Finally, to find the interquartile range, subtract Q1 from Q3.

Because each half of the original dataset has an even number of data points, you have to find the average of each data point on either side of dividers to calculate Q1, Q2, and Q3.

In this example:

Q1 = (4 + 6) / 2 = 5 Q2 = (8 + 10) / 2 = 9 Q3 = (12 + 14) / 2 = 13

The interquartile range is calculated as such: 13 – 5 = 8

Interquartile ranges reduce the impact that outliers have on the calculation, providing a more accurate picture of the variability in a dataset.

Variance measures each data point’s distance from the average. Then it squares the differences, adds them together and divides them by the number of data points in a set. This offers a measure of how far each data point tends to be from the average.

The formula for variance is:

Standard deviation is a measurement based on the variance in a dataset. It is the square root of the variance, so you can find standard deviation using the following formula:

Variance is a specific measurement of variability. It helps measure each data point's distance from the average in a set of data.

A variation is any difference between two similar things. For example, there could be a variation in the price of fruit between two grocery stores. In biology, variation occurs between different organisms or cells. For example, humans can have blonde, black, brown, red, or another color of hair.

Variability is vital for a variety of reasons.

In statistics, researchers often use small sample sizes to infer information about large populations. For example, a researcher may use 1,000 survey results to infer the results for a city with hundreds of thousands of residents. If there is low variability in the survey results, it could indicate that it shows the characteristics of the larger population accurately. High variability means the sample might not be sufficient to make broader inferences.

In other fields, where consistency of results is essential, measuring variability helps ensure that consistency. For example, a baseball pitcher would want to reduce variability in how they deliver a pitch, guaranteeing accurate and powerful throws each time.

Variability is essential in investing because it’s impossible to predict how most investments will play out. Investing in an individual stock could produce significant gains, significant losses, or anything in between.

One goal of many investors is to reduce the variability of their investing strategy so they can have some ability to predict their results. For example, constructing a diversified portfolio and holding stocks for the long-term can reduce variability. All investing, of course, carries risk; always keep investment objectives in mind.

Even for investments where reducing variability is difficult, understanding variability is important when choosing in what to invest. Typically, investors seek higher returns from investments with higher variability, such as stocks or options. Those higher returns may offset the increased potential for losses.

Options trading entails significant risk and is not appropriate for all investors. Certain complex options strategies carry additional risks. To learn more about the risks associated with options trading, please review the options disclosure document entitled Characteristics and Risks of Standardized Options, available here or through https://www.theocc.com/about/publications/character-risks.jsp. Investors should consider their investment objectives and risks carefully before trading options.