5.6.3 Interquartile range for the SIRDS data

Answer

Solution

The lower quartile birth weight (in kg) for the 27 children who died is given by

q_L = x _(¼(n+1)) = x ₍₇₎ = 1.230.

The upper quartile birth weight (in kg) is

q_U = x _(¾(n+1)) = x ₍₂₁₎ = 2.220.

The interquartile range (in kg) is

q_U – q_L = 2.200 – 1.230 = 0.970.

Answer

Solution

For the silica data, the sample size n is 22. The lower quartile is

So q_L is three-quarters of the way between

x ₍₅₎=26.39 and x ₍₆₎=27.08. That is

q_L = 26.39 + ¾(27.08 – 26.39) = 26.9075,

or approximately 26.91. The sample median is

This is midway between x ₍₁₁₎=28.69 and x ₍₁₂₎=29.36. That is 29.025, or approximately 29.03.

The upper quartile is

So q_U is one-quarter of the way between x ₍₁₇₎=33.28 and x ₍₁₈₎=33.40. That is

q_U = 33.28 + ¼(33.40 – 33.28) = 33.31

The interquartile range is

q_U – q_L = 33.31 – 26.9075 = 6.4025,

or approximately 6.40.