Measures of Variation: Types, Examples and Careers

Updated March 10, 2023

Measures of variation can help convey meaningful information about sets of data. Because variability can provide useful information about data, it's important to know the different measures of variation. Learning about the measures of variation helps you understand how to use this data effectively.

In this article, we discuss what the measures of variations are, define the types of measures of variation and provide jobs that use variation statistics.

What are measures of variation in statistics?

Measures of variation in statistics are ways to describe the distribution or dispersion of data. It shows how far apart data points are from one another. Statisticians use measures of variation to summarize their data. You can draw many conclusions by using measures of variation, such as high and low variability. High variability can mean that the data is less consistent while low variability data is more consistent. You can use measures of variation to measure, analyze or describe trends in your data, which can apply to many careers that use statistics.

Types of measures of statistics

Here are some types of measures of statistics that you can use to describe your data:

Range

Range is one of the simplest measures of variation. It's the lowest point of data subtracted from the highest point of data. For example, if your highest point is 10 and your lowest point is three, your range would be seven. The range tells you a general idea of how widely spread your data is. Because range is so simple and only uses two pieces of data, consider using it with other measures of variation so you have a variety of ways to measure and analyze the variability of your data.

Variance

Variance is the average squared variations of values from the mean. It compares every piece of value to the mean, which is why variance differs from the other measures of variation. Variance also displays the spread of the data set. Typically, the more spread out your data is, the larger the variance. Statisticians use variance to compare pieces of data to one another to see how they relate. Variance is standard deviation squared, which denotes that values of variance are larger than the other values. To calculate the variance, simply square your standard deviation. Here's an example of this calculation, where "S" stands for standard deviation:

S = 8

S2= 8 × 8 = 64

If your standard deviation is 8, then your variance would be 64.

Quartiles

Quartiles divide your data into four equal sections, or quarters. They divide the data in ascending order, meaning there are the lower two quartiles and the higher two quartiles. Statisticians divide their data by percentage: the lowest and the second-lowest 25% and the highest and second-highest 25%, which are respectively called the first quartile, second quartile, third quartile and fourth quartile. The symbols Q1, Q2, Q3 and Q4 represent the quartiles. Statisticians use quartiles to organize data, and they often use quartiles in many different equations.

Interquartile range

Interquartile range (IQR) refers to the middle of your data distribution or the middle of your four quartiles, meaning that the IQR is in the middle of the upper and lower quartiles. The IQR measures how the data spreads around the average. To find the IQR, you need to know the values of Q1 and Q3. To do this, you simply find the median of the Q1 and Q3 quartiles. Once you do that, you can calculate the IQR with this equation:

IQR = Q3 − Q1

For example, if the median of your Q3 was 10 and the median of your Q1 was 6, your IQR would be 4, as shown by the following:

IQR = 10 − 6

IQR = 4

Statisticians use IQR to measure the distribution of your data. IQR is valuable for measuring the variability of both skewed and consistent data sets.

Standard deviation

Standard deviation is the average or standard distance between each point of data and the mean. It's the standard amount of variability in your data set. If you know the variance of your data set, then you can take the square root of that value to find the standard deviation. However, you can also calculate the standard deviation by using equations. This equation is if you have the data for a total population:

σ = √ ∑ (X − µ)2 ÷ N

Where:

σ: population standard deviation
∑: sum of
X: each value
µ: population mean
N: number of values in the population

If you only have data for a sample, you can use this equation to find the standard deviation:

S = √ ∑(X − x̅)2÷ n − 1

Where:

S: sample standard deviation
∑: sum of
X: each value
x̅: sample mean
n: number of values in the sample

If the values in your dataset are closer together, you have a smaller standard deviation. If your values are far apart, then your standard deviation is larger.

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3 careers that use variation statistics

There are many careers that use variation statistics, such as the following three roles. For the most up-to-date salary information from Indeed, visit indeed.com/salaries.

1. Marketing analyst

National average salary: $65,240 per year

Primary duties: A marketing analyst studies marketing trends to help decide what a company should sell to boost profits. Their roles could include researching consumer behavior, the current market or even competitor strategies. Marketing analysts can use variation statistics to analyze the variability of a company's sales to see what products sell the most. They could do this by calculating the standard deviation of the company's sales profits. Variation statistics help marketing analysts make important decisions about what products, advertisements or sales tactics they should invest in to increase profits.

2. Sales representative

National average salary: $70,358 per year

Primary duties: A sales representative works closely with the sales team to support customers. They may process orders, provide price quotes or keep records of customers. Sales representatives can use variation statistics to analyze a variety of data sets they may have while working, such as sales records or the population of customers. They can use variation statistics to organize that data to help them decide how to improve sales or customer satisfaction. They could use variance or even range to denote the spread or average mean of the data set.

3. Financial planner

National average salary: $81,439 per year

Primary duties: A financial planner works with clients to create budgets to help ensure their future financial stability. Their roles may include performing market research, handling money or offering strategic financial advice. Financial planners can use variation statistics to organize and analyze their customer's financial information. For example, they could organize a customer's biweekly paychecks into quartiles to see how they compare to calculate the interquartile range. This may help the financial planner create a budget that best fits the needs of their customer.