About Standard Deviation

In statistics, standard deviation (symbol: σ) is a measure of how spread out or dispersed the values in a dataset are. It shows the degree to which individual data points differ from the mean (average) value.

“When the standard deviation is low, most of the values stay close to the average, meaning there is little variation in the dataset.”

When the standard deviation is high, it means the data values differ significantly from the average and are spread out over a larger range.

This makes standard deviation an important tool in statistics, finance, research, and data analysis, as it helps in understanding the consistency and reliability of data.

Population Standard Deviation

The population standard deviation is calculated when data is taken from an entire population rather than just a sample. “It is found by taking the square root of the variance, and it clearly shows how far the values in a population deviate from the overall mean (μ).”

Where:

• xi is an individual value
• μ is the mean/expected value
• N is the total number of values

Sample Standard Deviation

An Example of a Standard Deviation Within statistics, it’s not always possible to access every individual constituent of a population to obtain data, so a random sample is used to estimate standard deviation. In this case, the ‘sample standard deviation’ is an adjusted nomenclature. It is highly adapted to express the degree of variability of values in a sample and is esteemed in research, data analysis, and business forecasting.

Where:

• xi is one sample value
• x̄ is the sample mean
• N is the sample size

Statistical Formulas

Count (n):
n = 3

Sum (Σx):
Σx = 6.0000

Mean (x̄):
x̄ = Σx / n = 6 / 3 = 2.0000

Variance (σ²):
σ² = Σ(x_i − x̄)² / n = 0.0000

Standard Deviation (σ):
σ = √σ² = 0.0000

Margin of Error (95%):
ME = Z × (σ / √n) = 1.96 × (0 / √3) = 0.0000