Question

The following table contains the quantity of goods supplied by a firm at different prices. Use interpolation to find what quantity of goods would the firm supply at a price of Rs 85.

$\begin{array}{cc}Price\left(X\right)& Quantity\left(Y\right)\\ 25& 19\\ 50& 32\\ 75& 39\\ 100& 48\\ 125& 63\\ 150& 68\end{array}$

• A. 42
• B. 44
• C. 46
• D. 47

Answer 1

The correct option is B

44

$\begin{array}{cccccc}x& y& x-\overline{x}& (x-\overline{x}{)}^2& (y-\overline{y})& (x-\overline{x})(y-\overline{y})\\ 25& 19& -62.5& 3906.25& -25.83& 1614.38\\ 50& 32& -37.5& 1406.25& -12.83& 481.13\\ 75& 39& -12.5& 156.25& -5.83& 72.88\\ 100& 48& 12.5& 156.25& 3.17& 39.63\\ 125& 63& 37.5& 1406.25& 18.17& 681.38\\ 150& 68& 62.5& 3906.25& 23.17& 1448.13\\ & & & \sum =10937.5& & \sum =4337.53\end{array}$

$\overline{x}=\frac{\sum x}{n}=\frac{525}{6}=87.5$
$\overline{y}=\frac{\sum y}{n}=\frac{269}{6}=44.83$

$M=\frac{{\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{{\sum }_{i=1}^n(x_i-\overline{x}{)}^2}=\frac{4337.53}{10937.5}=0.4$
$B=\overline{y}-M\overline{x}=44.83-0.4\times 87.5=9.83$

The line of best fit is $y=0.4x+9.83$
Substituting 85 in the equation, we have
$y=0.4\times 85+9.83$
which is approximately equal to 44.