Name: Yule's Coefficient of Association
Uploaded: 2019-07-19
Duration: 19 min 49 s
Description: This video explains the meaning of the 'association of attributes' by describing the notations, terminology and difference between association and correlatio...

Question

Find the Karl Pearson’s coefficient of correlation for the following data.

$\begin{matrix} Wages & 100 & 101 & 102 & 102 & 100 & 99 & 97 & 98 & 96 & 95 \\ Cost of living & 98 & 99 & 99 & 97 & 95 & 92 & 95 & 94 & 90 & 91 \end{matrix}$

Accepted Answer

Given that,

$\begin{matrix} Wages & 100 & 101 & 102 & 102 & 100 & 99 & 97 & 98 & 96 & 95 \\ Cost of living & 98 & 99 & 99 & 97 & 95 & 92 & 95 & 94 & 90 & 91 \end{matrix}$

Let $x$ indicate wages and $y$ indicate cost of living.

Let $A = 99, B = 95, c = 1, d = 1$ .

Here, $u_{i} = \frac{x_{i} - A}{c}, v_{i} = \frac{y_{i} - B}{d}$ , value of $n = 10$ .

If the width between the values of the variables are not equal then take $c = 1, d = 1$ and $A, B$ are the arbitrary values.

Calculation:

wages $(x_{i})$ cost $(y_{i})$ $u_{i} = \frac{x_{i} - A}{c}$ $V_{i} = \frac{x_{i} - B}{d}$ ${u_{i}}^{2}$ ${v_{i}}^{2}$ $u_{i} v_{i}$

$100$ $98$ $1$ $3$ $1$ $9$ $3$

$101$ $99$ $2$ $4$ $4$ $16$ $8$

$102$ $99$ $3$ $4$ $9$ $16$ $12$

$102$ $97$ $3$ $2$ $9$ $4$ $6$

$100$ $95$ $1$ $0$ $1$ $0$ $0$

$99$ $92$ $0$ $- 3$ $0$ $9$ $0$

$97$ $95$ $- 2$ $0$ $4$ $0$ $0$

$98$ $94$ $- 1$ $- 1$ $1$ $1$ $1$

$96$ $90$ $- 3$ $- 5$ $9$ $25$ $15$

$95$ $91$ $- 4$ $- 4$ $16$ $16$ $16$

$\sum_{i = 1}^{10} u_{i} = 0$ $\sum_{i = 1}^{10} v_{i} = 0$ $\sum_{i = 1}^{10} {u_{i}}^{2} = 54$ $\sum_{i = 1}^{10} {v_{i}}^{2} = 95$ $\sum_{i = 1}^{10} u_{i} v_{i} = 61$

We know that, $r (u, v) = \frac{n \sum_{i = 1}^{n} u_{i} v_{i} - \sum_{i = 1}^{n} u_{i} \sum_{i = 1}^{n} v_{i}}{\sqrt{n \sum_{i = 1}^{n} u_{i}^{2} - {(\sum_{i = 1}^{n} u_{i})}^{2}} \sqrt{n \sum_{i = 1}^{n} v_{i}^{2} - {(\sum_{i = 1}^{n} v_{i})}^{2}}}$

$= \frac{10 \times 61 - 0 \times 0}{\sqrt{10 \times 54} \sqrt{10 \times 95}} = 0.847$

$∴ r = 0.847$ , wages and cost of living are highly positively correlated.

Find the Karl Pearson’s coefficient of correlation for the following data.

$\begin{matrix} Wages & 100 & 101 & 102 & 102 & 100 & 99 & 97 & 98 & 96 & 95 \\ Cost of living & 98 & 99 & 99 & 97 & 95 & 92 & 95 & 94 & 90 & 91 \end{matrix}$

Important Points to Remember in Chapter -1 - Correlation Analysis from Tamil Nadu Board Statistics Standard 12 Solutions

Learn and Prepare for any exam you want !

Find the Karl Pearson’s coefficient of correlation for the following data. Wages 1001011021021009997989695 Cost of living 98999997959295949091

Important Points to Remember in Chapter -1 - Correlation Analysis from Tamil Nadu Board Statistics Standard 12 Solutions

Learn and Prepare for any exam you want !

Find the Karl Pearson’s coefficient of correlation for the following data.

$\begin{matrix} Wages & 100 & 101 & 102 & 102 & 100 & 99 & 97 & 98 & 96 & 95 \\ Cost of living & 98 & 99 & 99 & 97 & 95 & 92 & 95 & 94 & 90 & 91 \end{matrix}$