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. Price (X) Quantity (Y)251950327539100481256315068

A

42

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B

44

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C

46

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D

47

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Solution

## The correct option is B 44 xyx−¯x(x−¯x)2(y−¯y)(x−¯x)(y−¯y)2519−62.53906.25−25.831614.385032−37.51406.25−12.83481.137539−12.5156.25−5.8372.881004812.5156.253.1739.631256337.51406.2518.17681.381506862.53906.2523.171448.13∑=10937.5∑=4337.53 ¯x=∑xn=5256=87.5 ¯y=∑yn=2696=44.83 M=∑ni=1(xi−¯x)(yi−¯y)∑ni=1(xi−¯x)2=4337.5310937.5=0.4 B=¯y−M¯x=44.83−0.4×87.5=9.83 The line of best fit is y=0.4 x+9.83 Substituting 85 in the equation, we have y=0.4×85+9.83 which is approximately equal to 44.

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