Statistical Formula

Statistical formula can be defined as the group of statistical symbols used to make a statistical statement. This webpage will discuss popular statistical formulas and what they stand for.

The term population mean, which is the parameter of a given population, is represented by the statistical formula

μ = ( Σ X_i ) / N

In this statistical formula, the symbol
‘μ’
represents the population mean. The symbol ‘Σ X_i’ represents the overall sum of all variables present in the population (say, in this case) X₁ X₂ X₃ and so on. The symbol ‘N’ in the statistical formula represents the overall size of the population.

The parameter called population standard deviation is represented by the statistical formula

σ = sqrt[ Σ ( X_i - μ )² / N ]

In this statistical formula, 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 squares of the deviation of the variables from their population mean.

The parameter called population variance is represented by the statistical formula

σ² = Σ ( X_i – μ )² / N

In this statistical formula, the symbol ‘σ^2’ represents the population variance.

A subject called applied statistics is one branch of statistics that involves statistical formulas for simple random sampling.

The statistic called sample mean is used in simple random sampling and is represented by the statistical formula

, = ( Σ x_i ) / n

In this statistical formula, the symbol represents the sample mean. The symbol ‘Σ x_i’ used in this statistical formula represents the overall sum of variables present in the sample (say, in this case) x₁ x₂ x₃ and so on. The symbol ‘n,’ which is divided by the overall sum in the statistical formula, represents the overall size of the sample.

The statistic called sample standard deviation, used in simple random sampling, is represented by the statistical formula

s = sqrt [ Σ ( x_i -)² / ( n - 1 ) ]

The term ‘Σ ( x_i -  )²’ used in the statistical formula represents the sum of the squares of the deviation of the variable from their sample mean.

The statistic called variance of the sample proportion is represented by the statistical formula

s_p² = pq / (n – 1)

The symbol ‘s_p²’ used in the statistical formula represents the variance of the sample proportion. The term ‘p’ in this statistical formula represents the proportion of the sample that acquires a particular characteristic or an attribute. The term ‘q’ in the statistical formula represents that proportion of samples that do not acquire that particular characteristic or  attribute. The term ‘q’ also has a statistical formula, and it is q=(1-p).

The statistic called pooled sample standard deviation is represented by the statistical formula

s_p = sqrt [ (n₁ - 1) * s₁² + (n₂ - 1) * s₂² ] / (n₁ + n₂ – 2) ]

The term ‘s_p’ in the statistical formula represents the pooled sample standard deviation. The term ‘n₁’ in the statistical formula represents the size of the first sample, and the term ‘n₂’ in the statistical formula represents the size of the second sample that is being pooled with the first sample. The term ‘s₁²’ in the statistical formula represents the variance of the first sample proportion, and ‘s₂²’ in the statistical formula represents the variance of the second sample proportion.