Coefficient of Variation Calculator

The coefficient of variation calculator may help you make judgments about your data after you know its standard deviation and mean. For example, is the difference significant or minor? How close to the mean do you think you’d anticipate a fresh random observation to be? Here, you can find the definition of the coefficient of variation and coefficient of variation formula. Also, when to use the coefficient of variation.

What is the coefficient of variation?

The coefficient of variation (CV) is a statistical measure of data points’ dispersion around the mean in a data series. The coefficient of variation is helpful for assessing the degree of variation between two data series, even if the means are radically different. It indicates the ratio of the standard deviation to the mean.

Furthermore, the coefficient of variation measures how variable data in a sample is in comparison to the population mean. Because the coefficient of variation is a financial term that helps investors to assess how much volatility, or risk, is taken in relation to the projected return on investments. The better the risk-return trade-off, the lower the standard deviation to mean return ratio produced by the coefficient of variation formula. The coefficient of variation may be deceptive if the projected return in the denominator is negative or zero.

When considering the risk/reward ratio to choose investments, the coefficient of variance is useful. A risk-averse investor, for example, may wish to examine assets that have historically low volatility relative to return in comparison to the broader market or sector. On the other hand, risk-takers may want to invest in assets with a history of high volatility.

Coefficient of variation formula

We can calculate the coefficient of variation using two different formulas. Later, the sample coefficient of variation is the same as the population coefficient of variation. In statistics, population refers to the entire group being studied. To put it another way, the population refers to the entire data collection. Generally, the sample is a portion of this population that has been picked at random. We use a sample to represent the study’s whole population. Also, the sample mean and the population mean will always be equal. The formula for the coefficient of variation is:

Coefficient of Variation = (Standard Deviation / Mean) x 100

How to find the coefficient of variation? 

When we need to compare data from two distinct surveys with different values, the coefficient of variation formula comes in handy. The CV formula, also known as relative standard deviation (RSD), is a normalized measure of a probability or frequency distribution dispersion in statistics. The smaller the coefficient of variation, the less variable and stable the data is.

Coefficient of variation and relative standard deviation

The Coefficient of Variation (CV) is a measure of point/price dispersion around the mean (Dispersion of a probability distribution). The coefficient of variation, we also know as the variation coefficient, unitized risk, or relative standard deviation in statistics (percent RSD). It is highly useful in assessing and comparing the volatility of different stocks since its value is standardized and dimensionless.

CV is measured in percentages and always has a positive value. It’s determined by calculating the standard deviation of N-previous prices and dividing it by the mean’s absolute value (of these N-past prices). The fact that the coefficient of variation is normalized and can be used to directly compare the volatility of various assets is one of the key advantages of using it instead of the standard deviation to quantify volatility. The standard deviation must be seen in relation to the data’s mean.

The key disadvantage is that when the mean is near zero, the coefficient becomes extremely sensitive to slight variations. As a result, this trading indicator isn’t suitable for determining the volatility of penny stocks.

Coefficient of Variation	Standard deviation
It is a relative measure of dispersion	Absolute measure of dispersion
Measures the ratio of the standard deviation to the mean	It measures how far a data point lies from the mean
Coefficient of variation is usually used to compare the variation of different data sets	Standard deviation is used to measure the dispersion of data in a single data set

Common uses for the coefficient of variation calculator

The standard deviation can be employed when comparing two data sets with comparable values. However, when comparing two data sets with different units, the coefficient of variation must be employed. The following are some examples of coefficient of variation applications:

• When an investor wishes to invest in a certain ETF, he utilizes the coefficient of variation to determine which one will provide the best risk-return trade-off.
• We may also use the coefficient of variation to assess data consistency. A distribution with a lower coefficient of variation (CV) is more stable than one with a higher CV.
• Perform a quality assurance audit
• Analyze a technique’s precision, such as an assay in analytical chemistry.
• Examine the risk/reward profile of investment alternatives like equities and bonds.
• Compare and contrast the variance of two datasets with different means.

When not to use the coefficient of variation

The coefficient of variation should not be used for data on an interval scale. A true zero on interval scales shows the lack of a quantity, such as a temperature (in degrees Celsius or Fahrenheit) or a calendar year. When a dataset contains both positive and negative values, the coefficient of variation is also improper.

If you keep track of net daily profits from a lemonade stand, for example, you may have positive net earnings on some days and negative net earnings on others. Additionally, the mean would be 0, and the coefficient of variation would be infinite if net earnings were $3.00 on two days and -$3.00 on the other two days, which doesn’t make much sense.

The mean will be closer to zero in any dataset having both positive and negative values without necessarily impacting standard deviation. As a result, the calculated coefficient of variation would be very high, and it would not adequately represent the dataset’s fluctuation.

Coefficient of a variation example

A researcher is comparing two multiple-choice exams with various settings. A typical multiple-choice test is given in the first test. Alternative alternatives (i.e. erroneous responses) are randomly provided to test-takers in the second exam. The following are the findings of the two tests:

Type	Regular Test	Randomized Answers
Mean	59.9	44.8
SD	10.2	12.7

It’s difficult to compare the two test findings. Because the means are also different, comparing standard deviations isn’t particularly useful. Furthermore, we use the formula to assist make sense of the data:

CV=(SD/Mean)*100

Type	Regular Test	Randomized Answers
Mean	59.9	44.8
SD	10.2	12.7
CV	17.03	28.35

Indeed, you would believe that the tests had comparable findings based on the standard deviations of 10.2 and 12.7. However, when the results are adjusted for the difference in means, the results become more significant:

Regular examination: 17.03 (CV)

CV = 28.35 (randomized responses)

Lastly note: On a ratio scale, we may only use the Coefficient of Variation to compare positive data. The CV has little or no value for measurements on an interval scale. Temperatures in Celsius or Fahrenheit are examples of interval scales. Still, the Kelvin scale is a ratio scale that starts at zero and cannot, by definition, take on a negative value (0 degrees Kelvin is the absence of heat).

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