Question

If the inter-quartile range is the distance between the first and third quartiles, then the inter-decile range is the distance between the first and ninth decile. (Deciles divide a distribution into ten equal parts.) If IQ is normally distributed with a mean of 100 and a standard deviation of 16, what is the inter-decile range of IQ?

Answer 1

Solution:

We are given

µ = 100

σ = 16

D9 = µ + Z*σ

Z for D9 = 1.281552

[Find the value for the Z score for probability 0.9 by using z-table or other software]

D9 = 100 + 1.281552*16

D9 = 120.5048

D1 = µ + Z*σ

Z for D1 = -1.281552

[Find the value for the Z score for probability 0.1 by using z-table or other software]

D1 = 100 - 1.281552*16

D1 = 79.49517

Inter-decile range = D9 - D1 = 120.5048 - 79.49517 = 41.00963

Inter-decile range = 41.00963

Inter-decile range = 41 (approximately)