Basic Statistics for Economics (Correlation of Coefficient (r), Coefficient of Variation (COV), Arithmetic Mean (AM).......

Basic Statistics for Economics...... 

1. Arithmetic Mean (AM): AM or average is the ratio of the sum of the series of observations of the values of a given variable unweighted or weighted and the total no. of observations or values.

Mathematically speaking,

AM = ∑f_ix_i / ∑f_i = ∑w_ix_i ; ∑f_i = N,

This is what is called the Weighted Arithmetic Mean where w_i (=f_i/N) represents the weight of the i-th item. When w₁ = w₂ = ................ = w_n = 1/N, the formula for simple AM can be derived.

1. Coefficient of Variation (COV): COV of a series of observation of values of a given variable represents the ratio of standard deviation (SD) and arithmetic mean (AM) in percentage term.

Mathematically speaking,

COV = SD/AM x 100 , where SD is the positive square root of variance.COV is one of the relative measures of dispersion in descriptive statistics. COV is positively and negatively related with SD and AM respectively. One of the interesting features of COV is that its value is significantly small and positive.

1. Correlation of Coefficient (r): Correlation of Coefficient (r) can be adopted as a statistical measure in the case of bivariate observations of a phenomenon. The value of r lies within the close interval of -1 and +1 i.e. r[-1,+1]. It can hold the values of -1, 0 and 1 in case of perfectively negative, zero and positive correlation respectively.

Mathematically speaking,

Correlation Coefficient (r_xy) = σ(xy) / σ_x . σ_{y ;} σ(xy) is covariance

Where, σ(xy) = 1/N ∑ (x- x̄) (y-ȳ)

σ_x = { 1/N ∑ (x- x̄)² }^1/2

σ_y = { 1/N ∑ (y-ȳ)² }^1/2