The average 20 to 29 year old male is 696 inches tall with a

The average 20 to 29 year old male is 69.6 inches tall, with a standard deviation of 3 inches, while the average 20 to 29 year old female is 64.1 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 67 inch tall man or a 62 inch tall woman?

Solution

The relative tallness can be judged by scalinging the two person in an uniform way.

One of the method is Z-scaling ,where the underline assumption is that the distribution of the underlying variable (here height ) follows same distribution for the two groups differeing only in their mean and variance.

So, Z-score for the 67 inch tall man is given by , Z₁ = (67-69.6)/3 = -0.867 .

For the woman having height 62 inch is , Z₂ = (62-64.1)/3.8 = 0.553 .

Now the comparision in this method is drawn in this way that higher the score taller the person.

So, the woman is relatively taller than the man.