Question

economics statistics class 11 correlation x=19,24,12,23,19,16 and Y=9,22,20,14,22,18​

Answer 1

Answer:

r = 6.907

Explanation:

Since the question doesn't ask to solve this using any particular method, I'm using Karl Pearson's Coefficient of Correlation.

The formula for calculating correlation using this method by the short-cut way is as below.

$r = \dfrac{\Sigma dxdy -\dfrac{(\Sigma dx) \times (\Sigma dy)}{N}}{\sqrt{\Sigma dx^2 - \dfrac{(\Sigma dx)^2}{N} \times \sqrt{\Sigma dy^2 - \dfrac{(\Sigma dy)^2}{N}}}}$

The formula may look complicated at first, but it is not...trust me.

And to use this method, you will need to make the following columns.

$\begin{tabular}{|c|c|c|c|c|c|c|}\cline{1-7}X & dx = x-a & dx^2 & Y & dy = y-a & dy^2 & dxdy\\\cline{1-7}\end{tabular}$

This table for the given data is created in the attachment. Please refer to the attachment.

In the attachment, the yellow numbers are the numbers I randomly chose to be 'a'. They don't need to be in the same row. This is just how I like to do it. You can assume different values for 'a' and still get the same answer.

The bottom-most row shows the total of the columns, which are required by the formula.

Now, from the table, we have

$\Sigma dx = -25\\\\\Sigma dx^2 = 203\\\\\Sigma dy = 21\\\\\Sigma dy^2 =205\\\\\Sigma dxdy = -98\\\\N = \text{6 (number of observations, ie, number of values in x or y)}$

Putting these values in the formula, we get

$r = \dfrac{\Sigma dxdy -\dfrac{(\Sigma dx) \times (\Sigma dy)}{N}}{\sqrt{\Sigma dx^2 - \dfrac{(\Sigma dx)^2}{N} \times \sqrt{\Sigma dy^2 - \dfrac{(\Sigma dy)^2}{N}}}}\\\\\\\\\implies r = \dfrac{-98 - \dfrac{-25 \times 21}{6}}{\sqrt{203 - \dfrac{(-25)^2}{6}}- \sqrt{205 - \dfrac{(21)^2}{6}}}\\\\\\\\\implies r = \dfrac{-98 - (-87.5)}{\sqrt{203 - 104.16} - \sqrt{205 - 73.5}}\\\\\\\\\implies r = \dfrac{-98 + 87.5}{\sqrt{98.84} - \sqrt{131.5}}\\\\\\\\\implies r = \dfrac{-10.5}{9.94-11.46}$

$\implies r = \dfrac{-10.5}{-1.52}\\\\\\\\\implies r = \dfrac{-105 \times 100 \times -1}{-152 \times 10 \times -1}\\\\\\\\\implies \boxed{\boxed{\underline{\bold{r = 6.907}}}}}$

Therefore, r = 6.907