Measures of Dispersion

Difference Between Variance and Standard Deviation

Variance and standard deviation are both measures of how spread out a data set is. They are closely related, but not the same.

🔹 Variance

Variance measures the average squared deviation from the mean. It gives a general idea of how data points differ from the mean value.

Formula for variance of a sample:

\[ s^2 = \frac{1}{n - 1} \sum_{i=1}^{n} (x_i - \bar{x})^2 \]

🔹 Standard Deviation

Standard deviation is the square root of the variance. It is expressed in the same units as the original data, which makes it easier to interpret.

Formula for standard deviation of a sample:

\[ s = \sqrt{s^2} = \sqrt{ \frac{1}{n - 1} \sum_{i=1}^{n} (x_i - \bar{x})^2 } \]

🔍 Key Difference

• Variance is in squared units (e.g., m², $²), which makes it less intuitive.
• Standard deviation brings the result back to the original unit, making it easier to understand and compare.

📊 In Excel

Variance (sample): =VAR.S(rango) or =VAR.M(rango) (in Spanish)

Standard deviation (sample): =STDEV.S(rango) or =DESVEST.M(rango) (in Spanish)