Concepts of Statistics - Karl Pearson’s Coefficient of Correlation

If the rank correlation coefficient is `2/3` and `Σ"d"_1^2` = 55` , then find the number of  pairs of observations. (Assume that no rank is repeated.) 

Calculate the coefficient of correlation between X and Y series from the following data :

`n = 15 ,bar x = 25, bary = 18, σ_x = 3.01, σ_y = 3.03,`

`sum ("x"_i - bar x) ("y"_i - bar y) = 122`

A train travelled between two stations. The distance and time were recorded as below:

Draw scatter diagram and identify the type of correlation. 

A sample of 5 items is taken from the production of a firm. Length and weight of the five items arc given below :

Calculate Karl Pearson's coefficient of   correlation between the length and weight and interpret the result.

Compute rank correlation coefficient for the following data : 

For 10 pairs of observations on two variables X and Y, the following data are available:

`sum(x-2)=30, sum(y-5)=40, sum(x-2)^2=900, sum(y-5)^2=800, sum(x-2)(y-5)=480`

Find the correlation coefficient between X and Y.

If r = 0.5, σ_x = 1 and σ_y = 4, then find Cov.(X,Y).

Given that r = 0.4 , `Σ(x - barx)(y - bary) = 108 , σ_y = 3 and Σ(x - barx)^2 = 900` . Find the number of pairs of observations.