Standard Deviation

calender iconUpdated on May 16, 2024
corporate finance and accounting
financial ratios

Standard deviation is a measure of statistical dispersion that quantifies the variability or spread of a set of data around its mean. It is calculated by the square root of the variance.

Formula:Standard deviation (σ) = √[Variance (Var) = Σ(x - μ)² / n - 1]

where:* σ is the standard deviation* Var is the variance* x is each element in the data set* μ is the mean of the data set* n is the number of elements in the data set

Interpretation:

  • Standard deviation measures the degree of variation in a data set.
  • A high standard deviation indicates a wide range of values, while a low standard deviation indicates a narrow range of values.
  • The standard deviation is an important measure of data dispersion, alongside the range, variance, and coefficient of variation.

Significance:

  • Standard deviation is used to:
    • Describe the variability of a data set.
    • Compare the variability of different data sets.
    • Calculate confidence intervals and hypothesis tests.
    • Evaluate the performance of statistical models.

Example:

“`Data: [10, 12, 14, 16, 18]

Mean (μ) = (10 + 12 + 14 + 16 + 18) / 5 = 16

Variance (Var) = [(10 – 16)² + (12 – 16)² + (14 – 16)² + (16 – 16)² + (18 – 16)] / (5 – 1) = 8

Standard Deviation (σ) = √8 = 2.828“`

Therefore, the standard deviation of the data set is 2.828.

FAQ's

What is standard deviation?

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Standard deviation is a measure of the spread or dispersion of a set of numbers. It shows how much the numbers in a data set deviate from the mean (average). A small standard deviation means the numbers are close to the mean, while a large one indicates that they are spread out over a wide range of values.

What is an example of standard deviation in real life?

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