Standard deviation Excel: functions and formula examples

This tutorial clarifies the distinction between standard deviation and standard error of the mean, guiding you on the optimal Excel functions for standard deviation calculations.

In descriptive statistics, the mean and standard deviation are intrinsically linked. While the mean is widely understood, the standard deviation often remains less clear. This tutorial aims to demystify standard deviation and demonstrate its Excel calculation.

Key Concepts:

• Standard Deviation: A measure quantifying data dispersion around the mean. A low standard deviation indicates data clustered near the mean, while a high standard deviation signifies greater variability. This helps determine the mean's representativeness of the data. A standard deviation of zero implies all data points are identical to the mean.

• Sample vs. Population Standard Deviation: The calculation differs based on whether the data represents the entire population or a sample. Sample standard deviation uses Bessel's correction (dividing by n-1 instead of n) to account for bias in estimating the population mean from a sample.

• Standard Deviation Formula:

  Sample Standard Deviation	Population Standard Deviation

  Where: x_i represents individual data points, x̄ is the mean, and n is the data count.

• Step-by-Step Calculation:

  1. Calculate the Mean: Sum the data points and divide by their count. Excel's AVERAGE function simplifies this.
  2. Calculate Deviations and Square: Subtract the mean from each data point and square the result.
  3. Sum Squared Deviations: Add the squared deviations.
  4. Divide by n or n-1: Divide by n for population standard deviation, n-1 for sample standard deviation.
  5. Take the Square Root: The result is the standard deviation.

• Excel Functions:

  Function	Description	Sample/Population	Includes Text/Logical?	Excel Version
  STDEV	Older sample standard deviation function	Sample	No	2003-2019
  STDEV.S	Improved sample standard deviation function	Sample	No	2010-2019
  STDEVA	Sample standard deviation, includes text/logical	Sample	Yes	2003-2019
  STDEVP	Older population standard deviation function	Population	No	2003-2019
  STDEV.P	Improved population standard deviation function	Population	No	2010-2019
  STDEVPA	Population standard deviation, includes text/logical	Population	Yes	2003-2019

• Adding Standard Deviation Error Bars to Charts: Select the chart, click "Chart Elements," choose "Error Bars," and select "Standard Deviation."

• Standard Deviation vs. Standard Error of the Mean (SEM): Standard deviation measures data variability; SEM estimates how much a sample mean differs from the true population mean. SEM = Standard Deviation / √(Sample Size). Excel formula: =STDEV.S(range)/SQRT(COUNT(range))

This enhanced explanation provides a more comprehensive understanding of standard deviation and its practical application within Excel. Remember to select the appropriate Excel function based on your data type (sample or population) and whether non-numeric values are present.

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