The following table contains the heights and weights of a sample of 5 women from a room. Find the approximate weight corresponding to 165 cm using interpolation.
Height (X, cm)Weight (Y, kg)1505416058170631756518070
61 kg
xyx−¯x(x−¯x)2(y−¯y)(x−¯x)(y−¯y)15054−17289−813616058−749−4281706339131756586432418070131698104∑=580∑=295
¯x=∑xn=8355=167
¯y=∑yn=3105=62
M=∑ni=1(xi−¯x)(yi−¯y)∑ni=1(xi−¯x)2=295580=0.51
B=¯y−M¯x=62−0.51×167=−23.17
y=0.51 x−23.17
Substituting 165 cm in the equation,
y=0.51×165−23.17=60.98
Weight corresponding to 165 cm is around 61 kg.