How To Calculate Standard Deviation Excel 2013

Standard deviation is a fundamental statistical measure that quantifies the amount of variation or dispersion in a set of values. In Excel 2013, calculating standard deviation is straightforward once you understand the different functions available and when to use each one.

Understanding Standard Deviation

Standard deviation measures how spread out numbers are in a data set. A low standard deviation indicates that the values tend to be close to the mean (average), while a high standard deviation indicates that the values are spread out over a wider range.

Key Concepts:

• Population Standard Deviation (σ): Used when your data set includes all members of a population
• Sample Standard Deviation (s): Used when your data is a sample of a larger population
• Variance: The square of the standard deviation
• Mean: The average of all numbers in the data set

Excel 2013 Standard Deviation Functions

Excel 2013 offers several functions for calculating standard deviation, each designed for specific scenarios:

1. STDEV.P (Population Standard Deviation)

Calculates standard deviation for an entire population. The formula is:

STDEV.P(number1,[number2],...) = √(Σ(xi - x̄)² / N)

Where:

• xi = each individual value
• x̄ = mean of all values
• N = number of values

2. STDEV.S (Sample Standard Deviation)

Calculates standard deviation for a sample of a population. The formula is:

STDEV.S(number1,[number2],...) = √(Σ(xi - x̄)² / (N - 1))

Note the division by (N – 1) instead of N, which is known as Bessel’s correction.

3. Legacy Functions (for compatibility)

Excel 2013 also includes older functions that were replaced in Excel 2010:

• STDEV (same as STDEV.S)
• STDEVP (same as STDEV.P)

Step-by-Step Guide to Calculate Standard Deviation in Excel 2013

1. Prepare your data:

   Enter your data set in a column or row. For example, enter values in cells A2 through A10.

2. Determine your data type:

   Decide whether your data represents a population (all possible observations) or a sample (subset of a population).

3. Choose the appropriate function:
   • For population data: Use STDEV.P
   • For sample data: Use STDEV.S
4. Enter the function:

   Click on the cell where you want the result to appear, then:

   1. Type “=STDEV.P(” or “=STDEV.S(“
   2. Select your data range (e.g., A2:A10)
   3. Close the parenthesis and press Enter
5. Format the result (optional):

   Right-click the result cell → Format Cells → Number → Set decimal places as needed.

Practical Example

Let’s calculate the standard deviation for the following test scores: 85, 92, 78, 90, 88, 76, 95, 89, 83, 91

1. Enter the scores in cells A2 through A11
2. Assume this is a sample of a larger population
3. In cell B2, enter: =STDEV.S(A2:A11)
4. Press Enter – the result should be approximately 5.67

Common Mistakes to Avoid

Mistake	Why It’s Wrong	Correct Approach
Using STDEV.P for sample data	Underestimates the true population standard deviation	Use STDEV.S for samples to apply Bessel’s correction
Including text or blank cells in range	Excel ignores these but may cause confusion	Clean your data first or use data validation
Not anchoring cell references	Formula breaks when copied to other cells	Use absolute references (e.g., $A$2:$A$11)
Confusing standard deviation with variance	Variance is standard deviation squared	Remember: SD = √variance

Advanced Techniques

1. Calculating Standard Deviation with Conditions

To calculate standard deviation for values that meet specific criteria, you can combine standard deviation functions with array formulas or helper columns.

2. Creating a Dynamic Standard Deviation Calculation

Use Excel Tables (Ctrl+T) to create ranges that automatically expand when new data is added. Your standard deviation formula will then automatically include new data points.

3. Visualizing Standard Deviation

Create a column chart with error bars to visualize the mean ±1 standard deviation:

1. Create a column chart of your data
2. Click on any data point → Error Bars → More Options
3. Set “Error Amount” to “Custom” and specify your standard deviation value

Standard Deviation vs. Other Statistical Measures

Measure	Purpose	When to Use	Excel Function
Standard Deviation	Measures dispersion from the mean	When you need to understand variability	STDEV.P, STDEV.S
Variance	Square of standard deviation	In advanced statistical calculations	VAR.P, VAR.S
Mean	Average of all values	When you need central tendency	AVERAGE
Median	Middle value	With skewed distributions or outliers	MEDIAN
Range	Difference between max and min	Quick measure of spread	MAX – MIN

Real-World Applications

Standard deviation has numerous practical applications across various fields:

1. Finance

• Measuring investment risk (volatility)
• Portfolio optimization
• Financial modeling and forecasting

2. Quality Control

• Monitoring manufacturing processes (Six Sigma)
• Setting control limits
• Detecting anomalies in production

3. Education

• Analyzing test score distributions
• Grading on a curve
• Identifying students who need extra help

4. Science and Research

• Analyzing experimental results
• Determining measurement precision
• Calculating confidence intervals

Authoritative Resources

For more in-depth information about standard deviation and its calculation:

• National Institute of Standards and Technology (NIST) – Engineering Statistics Handbook with comprehensive coverage of standard deviation
• NIST/SEMATECH e-Handbook of Statistical Methods – Detailed explanations of statistical concepts including standard deviation
• Seeing Theory by Brown University – Interactive visualizations of standard deviation and other statistical concepts

Frequently Asked Questions

Why does Excel have two different standard deviation functions?

Excel provides both STDEV.P and STDEV.S because the calculation differs slightly depending on whether your data represents an entire population or just a sample. For populations, we divide by N (number of data points). For samples, we divide by N-1 to correct for bias in the estimation.

Can I calculate standard deviation for non-numeric data?

No, standard deviation can only be calculated for numeric data. If your range includes text, logical values, or empty cells, Excel will ignore them in the calculation.

How do I interpret the standard deviation value?

The standard deviation tells you how spread out your data is around the mean. As a rule of thumb:

• About 68% of data falls within ±1 standard deviation of the mean
• About 95% within ±2 standard deviations
• About 99.7% within ±3 standard deviations

This is known as the 68-95-99.7 rule or empirical rule for normal distributions.

What’s the difference between standard deviation and average deviation?

Standard deviation squares the deviations before averaging (which gives more weight to larger deviations), while average deviation uses absolute values of deviations. Standard deviation is more commonly used because it has nice mathematical properties and works well with probability distributions.

How can I calculate a rolling standard deviation in Excel?

To calculate standard deviation over a moving window of data:

1. Enter your data in a column (e.g., A2:A100)
2. In the first result cell (e.g., B10), enter: =STDEV.S(A2:A10)
3. Drag the formula down, changing the range to A3:A11, A4:A12, etc.
4. For a dynamic solution, use the OFFSET function