Question

Assume that IQ scores follow a Normal distribution with µ=100 and σ=16. Using our IQR rule for determining IQ score outliers, what IQ scores would establish the lower and upper fences for determining outliers?

Answer 1

we have given the mean of IQ score  µ=100  

and standard deviation of IQ scores σ=16

from the properties of normal distribution

first quartile (Q₁) =  µ -0.6745σ = 100 - 0.6745*16 = 100-10.792 =89.208

third quartile (Q₃) =  µ + 0.6745σ = 100 + 0.6745*16 = 100+ 10.792 = 110.792

interquartile range (IQR) = Q₃ -Q₁ = 110.792 - 89.208 =21.584

lower fences for determining outliers = Q₁ -1.5* IQR = 89.208 -1.5*21.584 = 89.208-32.376 = 56.832

upper  fences for determining outliers = Q₃ -1.5* IQR = 110.792 -1.5*21.584 = 110.792-32.376 =78.416