# Formula & Function: How to Calculate Standard Deviation in Excel

The Excel standard deviation function is a statistical powerhouse. It expresses how much values within datasets deviate from the mean (average) data point. A dataset with a low standard deviation indicates which values are tightly clustered around the mean data point, while a high standard deviation indicates much greater variation.

By using Excel to calculate standard deviation, finance professionals can simplify an otherwise complex calculation process to find logical and error values. Excel offers several built-in functions that handle all of the math for users—the trick is learning how to use them properly. In the following section, we will provide a comprehensive walkthrough of these functions, demonstrating their application and offering guidance on interpreting the outcomes to gain enhanced insights.

## What is Standard Deviation?

By definition, standard deviation is a statistical calculation used to quantify the amount of variations within a set of values. Essentially, this calculation indicates how far individual data points are from the mean value within a specific data set.

Generally speaking, the standard deviation is the culmination of the following:

1. Calculation of the mean: When calculating standard deviation, look for the dataset’s average.
2. Deviation from the Mean: For each data point, the mean is subtracted to find how far it is from the center.
3. Squaring of the deviations: Squaring in this calculation helps eliminate negative values.
4. The average of squared deviations: The mean of these squared deviations is then calculated to find what is called the variance.
5. Square Root: Taking the square root of the variance brings the calculation back to the original units of measurement, resulting in the standard deviation.

## Using the Standard Deviation Function in Excel

While Excel does most of the heavy lifting, understanding the formula behind it is essential:

Formula Breakdown:

STDEV = ( Σ(x µ)² / N)

Where:

• Σ (Sigma): Means “sum of”
• x: Each data point in the set
• µ (Mu): The mean (average) of the data
• N: The total number of data points

### The Two Primary Formulas for Standard Deviation in Excel

Excel streamlines its standard deviation calculations with two dedicated functions and a few additional functions.

Here’s a quick overview of these functions:

• STDEV.S (Sample Standard Deviation): Use this formula when the dataset represents a sample of a larger population. It provides a slightly higher standard deviation, accounting for the uncertainty of not having data for the entire population.
• STDEV.P (Population Standard Deviation): If the data includes the entire population, use this function.
• STDEVA and STDEVPA: These functions work similarly to STDEV.S and STDEV.P, respectively, but they also include logical values (TRUE/FALSE) and text representations of numbers within their calculations.

## The Difference Between Using STDEV.S and STDEV.P

A crucial choice when calculating standard deviation in Excel is deciding whether to use STDEV.S or STDEV.P. How should finance professionals choose the correct formula?

The general rule of thumb is to use STDEV.S when obtaining a sample of a larger population. Remember, samples often provide an incomplete representation of the bigger picture, so expect the results to be slightly inflated due to data gaps. For robust representation of the entire analytical dataset, STDEV.P is recommended.

## Using the Syntax Function

The syntax for the standard deviation function is as follows:

=FunctionName(Number1, [Number2],…)

• FunctionName: Replace “FunctionName” with the chosen function (STDEV.S, STDEV.P, etc.)
• Number1: Plot the first data point here
• Number2: Enter any additional data points up to 255 here.

#### An example standard deviation using sample data:

Let’s use the example of tracking exam scores:

• Student A – 85
• Student B – 76
• Student C – 92
• Student D – 88
• Student E – 69
1. Choose the function: Since we’re likely working with a sample of the overall student population, we’ll use STDEV.S.
2. Enter the formula: Assuming scores are in cells B2:B6, the formula would be: =STDEV.S(B2:B6)
3. Result: Excel performs standard deviation computation automatically. In the provided scenario, the outcome is approximately 9.65, signifying a moderate distribution of scores from the average.

Important Note: If the data represents the entire class population, use STDEV.P instead.

## Alternative Ways to Input Data into the Excel Standard Deviation Formula

Beyond typing individual numbers, Excel also offers flexibility in feeding data into standard deviation functions via:

• Cell Ranges: Reference a range of cells (e.g., =STDEV.S(A2:A15))
• Arrays: Create an array within the formula (e.g., =STDEV.P({78,83,77,91}))
• Named Ranges: Define a named range and use it in the formula for greater adaptability.

## The Importance of Data Cleaning Before Using Standard Deviation Formulas

Data cleaning is the process of fixing or completely removing incorrect data to get the most accurate results from Excel’s calculations. Before inputting the information into Excel’s standard deviation formula, be sure to assess:

• Incorrect Formatting: Ensure numbers are formatted as numbers, not text. The text won’t be calculated.
• Errors and Outliers: Address typos or extreme outliers, as they can significantly skew standard deviation results.

## Applying Standard Deviation in Real-Life Scenarios

Standard deviation isn’t just used in theory. In real-life scenarios, we have populations of particular subjects to which this formula applies.

Here are a few examples of how standard deviation is used every day:

• Quality Control: In manufacturing, standard deviation helps monitor process consistency. If the standard deviation of component weights is high, it signals possible production issues.
• Investment Analysis: Assessing the standard deviation of stock returns provides insight into volatility and risk, allowing investors to make more informed trading decisions for clients.
• Comparing Datasets: Analyzing the standard deviation of sales in different regions to see where performance variability is highest. This allows businesses to improve their sales performance where needed through financial analysis.
• Hypothesis Testing: Standard deviation is also a key component in statistical tests to determine the significance of differences between groups. This includes test groups in just about everything from clinical trials to focus groups.

## Creating Visuals for Standard Deviation in Excel

Charts can also be used to create a visual representation of the margin of error or margin analysis in standard deviation calculations. The two most common types of charts include:

• Error Bars: Easily add error bars to bar charts or column charts representing the standard deviation. This visually showcases the range of possible values in relation to averages.
• Distribution Curves: Distribution curves allow users to create data histograms. Overlaying a bell-shaped normal distribution curve calculated using the mean and standard deviation. This can help demonstrate how closely data matches a standard distribution.

## Standard Deviation and the 68-95-99.7 Empirical Rule

For normally distributed data, the standard deviation helps us understand how much of our data falls within certain distances of the mean. This is also known as the Empirical Rule.

The Empirical rule simply means that:

• 68%: Approximately 68% of data will fall within one standard deviation of the mean.
• 95%: About 95% falls within two standard deviations.
• 99.7%: Nearly all (99.7%) fall within three standard deviations.

The Empirical Rule is used because it allows users to estimate probabilities quickly while calculating with a normal distribution. Essentially, users can use this rule to create data ranges to determine which percentage of cases will inform their analyses.

## Dynamic Calculations with Tables & Named Ranges

When datasets grow or change frequently, Excel allows users to make standard deviation calculations flexible:

• Excel tables: Easily structure data as an Excel Table. When adding new data, formulas using table references will automatically expand the calculation.
• Named ranges: Define named ranges for the data. Using named ranges with standard deviation formulas ensures they adapt as the range changes.

## Troubleshooting: When Results Don’t Make Sense

Frequently, it’s necessary to recalculate the standard deviation when initial results are inconclusive—underscoring the importance of cleaning data before feeding information into Excel formulas. If datasets prove inconclusive, consider the following:

• Data formatting: Double-check that the data is formatted as numbers. Text values won’t be included in the calculations.
• Check for outliers: Extreme outliers have the potential to substantially inflate datasets’ standard deviations. It’s essential to ensure that datasets utilize valid data points or, if necessary, explore alternative techniques for managing outliers.
• Check for an incorrect function: Using STDEV.S for samples and STDEV.P for populations is vital to ensure accurate results. Employing the wrong function can consistently lead to inaccurate outcomes.

## Taking Standard Deviation One Step Further

Ready to go further with standard deviation? Here are some advanced concepts to consider:

• Weighted standard deviation: Calculate the standard deviation when each value has a different weight (for instance, student grades with varying credit hours).
• Standard deviation for groups: Use functions like SUBTOTAL in combination with standard deviation functions to calculate standard deviations for sub-groups.
• Rolling standard deviation: Calculate the standard deviation over a moving window of data points (e.g., the standard deviation of the last 10 sales figures) to identify more localized trends in variability.

Remember, the chosen standard deviation concept should be applicable to the situation.

## Standard Deviation in Excel Doesn’t Have to Be Complicated

Calculating the standard deviation in Excel can provide finance professionals with valuable insights regarding data distribution. Excel offers a straightforward process that uses specific functions that can quickly determine entire datasets or sample values to help users make sense of numerical data and make more informed decisions for the future.

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