(a) Calculate the coefficient of correlation for the ages of husbands and their respective wives.

| Age of husbands | 23 | 27 | 28 | 29 | 30 | 31 | 33 | 35 | 36 | 39 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Age of wives | 18 | 22 | 23 | 24 | 25 | 2

Question

(a) Calculate the coefficient of correlation for the ages of husbands and their respective wives.

| Age of husbands | 23 | 27 | 28 | 29 | 30 | 31 | 33 | 35 | 36 | 39 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Age of wives | 18 | 22 | 23 | 24 | 25 | 26 | 28 | 29 | 30 | 32 |

OR

(b) The annual demand for an item A is 800 units and unit price is ₹ 0.02. If ordering cost is ₹ 5 per order and annual holding cost is 10% of unit price, then determine the following :
(i) EOQ in units.
(ii) Minimum inventory cost.
(iii) EOQ in Rupees.
(iv) EOQ in years of supply.
(v) Number of orders per year.

Accepted Answer

>

> [!TLDR]
> **(a)** Karl Pearson's $r \approx 0.995$, a near-perfect positive correlation between husbands' and wives' ages. **(b)** EOQ $=2000$ units, min. inventory cost ₹4, EOQ ₹40, 2.5 years of supply, 0.4 orders/year.
>
> **Part (a): Correlation of husbands' ($X$) and wives' ($Y$) ages** (assumed means $A_X=30$, $A_Y=25$; $n=10$).
>
> | $X$ | $Y$ | $dx=X-30$ | $dy=Y-25$ | $dx^2$ | $dy^2$ | $dx\,dy$ |
> | --- | --- | --- | --- | --- | --- | --- |
> | 23 | 18 | -7 | -7 | 49 | 49 | 49 |
> | 27 | 22 | -3 | -3 | 9 | 9 | 9 |
> | 28 | 23 | -2 | -2 | 4 | 4 | 4 |
> | 29 | 24 | -1 | -1 | 1 | 1 | 1 |
> | 30 | 25 | 0 | 0 | 0 | 0 | 0 |
> | 31 | 26 | 1 | 1 | 1 | 1 | 1 |
> | 33 | 28 | 3 | 3 | 9 | 9 | 9 |
> | 35 | 29 | 5 | 4 | 25 | 16 | 20 |
> | 36 | 30 | 6 | 5 | 36 | 25 | 30 |
> | 39 | 32 | 9 | 7 | 81 | 49 | 63 |
> | | | $\Sigma dx=11$ | $\Sigma dy=7$ | $\Sigma dx^2=215$ | $\Sigma dy^2=163$ | $\Sigma dx\,dy=186$ |
>
> $$r = \frac{n\Sigma dx\,dy - \Sigma dx\,\Sigma dy}{\sqrt{[n\Sigma dx^2-(\Sigma dx)^2][n\Sigma dy^2-(\Sigma dy)^2]}} = \frac{10(186)-(11)(7)}{\sqrt{[10(215)-121][10(163)-49]}}.$$
> $$= \frac{1860-77}{\sqrt{(2029)(1581)}} = \frac{1783}{\sqrt{3{,}207{,}849}} = \frac{1783}{1791.05} \approx 0.995.$$
>
> **Part (b): EOQ problem.** Annual demand $D=800$ units, unit price ₹0.02, ordering cost $C_o=₹5$/order, holding cost $C_h = 10\%$ of unit price $= 0.10	imes0.02 = ₹0.002$/unit/year.
>
> *(i) EOQ (units):* $\ Q^* = \sqrt{\dfrac{2DC_o}{C_h}} = \sqrt{\dfrac{2(800)(5)}{0.002}} = \sqrt{4{,}000{,}000} = 2000$ units.
> …

$X$	$Y$	$dx=X-30$	$dy=Y-25$	$dx^2$	$dy^2$	$dx\,dy$
23	18	-7	-7	49	49	49
27	22	-3	-3	9	9	9
28	23	-2	-2	4	4	4
29	24	-1	-1	1	1	1
30	25	0	0	0	0	0
31	26	1	1	1	1	1
33	28	3	3	9	9	9
35	29	5	4	25	16	20
36	30	6	5	36	25	30
39	32	9	7	81	49	63
		$\Sigma dx=11$	$\Sigma dy=7$	$\Sigma dx^2=215$	$\Sigma dy^2=163$	$\Sigma dx\,dy=186$

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