# Common Statistical Formulas

Statistical formulas are used to calculate values related to statistical concepts or analyses. Here we will discuss common formulas and what they stand for.

# Population Mean

The term population mean, which is the average score of the population on a given variable, is represented by:

μ = ( Σ X_{i} ) / N

The symbol ‘μ’ represents the population mean. The symbol ‘Σ X_{i}’ represents the sum of all scores present in the population (say, in this case) X_{1 }X_{2} X_{3} and so on. The symbol ‘N’ represents the total number of individuals or cases in the population.

# Population Standard Deviation

The population standard deviation is a measure of the spread (variability) of the scores on a given variable and is represented by:

σ = sqrt[ Σ ( X_{i} – μ )^{2} / N ]

The symbol ‘σ’ represents the population standard deviation. The term ‘sqrt’ used in this statistical formula denotes square root. The term ‘Σ ( X_{i} – μ )^{2}’ used in the statistical formula represents the sum of the squared deviations of the scores from their population mean.

# Population Variance

The population variance is the square of the population standard deviation and is represented by:

σ^{2} = Σ ( X_{i} – μ )^{2 }/ N

The symbol ‘σ^{2’ }represents the population variance.

# Sample Mean

The sample mean is the average score of a sample on a given variable and is represented by:

x_bar = ( Σ x_{i} ) / n

The term “x_bar” represents the sample mean. The symbol ‘Σ x_{i}’ used in this formula represents the represents the sum of all scores present in the sample (say, in this case) x_{1} x_{2} x_{3 }and so on. The symbol ‘n,’ represents the total number of individuals or observations in the sample.

# Sample Standard Deviation

The statistic called sample standard deviation, is a measure of the spread (variability) of the scores in the sample on a given variable and is represented by:

s = sqrt [ Σ ( x_{i} – x_bar )^{2} / ( n – 1 ) ]

The term ‘Σ ( x_{i }– x_bar )^{2}’ represents the sum of the squared deviations of the scores from the sample mean.

# Sample Variance

The sample variance is the square of the sample standard deviation and is represented by:

s^{2} = Σ ( x_{i} – x_bar )^{2} / ( n – 1 )

The symbol ‘s^{2}’ represents the sample variance.

# Pooled Sample Standard Deviation

The pooled sample standard deviation is a weighted estimate of spread (variability) across multiple samples. It is represented by:

s_{p} = sqrt [ (n_{1} – 1) * s_{1}^{2} + (n_{2} – 1) * s_{2}^{2} ] / (n_{1} + n_{2} – 2) ]

The term ‘s_{p}’ represents the pooled sample standard deviation. The term ‘n_{1}’ represents the size of the first sample, and the term ‘n_{2}’ represents the size of the second sample that is being pooled with the first sample. The term ‘s_{1}^{2}’ represents the variance of the first sample, and ‘s_{2}^{2}’ represents the variance of the second sample.

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