Quiz #13 Answer: Statistics - Z-score

A newborn (weight 3 kg, Length 50 cm) has aortic valve annulus of 6.0 mm. One published report states the following values for aortic valve annulus in newborns of the same body size: Mean 7.3 mm & Range of 6.38 – 8.22 mm. Range is reported as 2 standard deviations from the mean.

Question 1: What is the Z-score of the aortic valve in our patient with 6.0 mm diameter?

Answer: Z-score is (- 2.8)

Bonus Question: Please provide the steps of deriving the Z-score
Answer: Z-score is the represents the observed value as a the number of standard deviations away from the population mean. So, to calculate the Z-score for a given observed value, one has to know the population mean and SD.

Here the mean is 7.3 mm.
We need the SD. The given range is 2 SD on either sides of the mean. Therefore, 8.22 - 7.3 = 0.92 (which is equal to 2 SD).
SD = (0.92 ÷ 2) = 0.46

Given value for aortic valve diameter is 6.0 mm.
6.0 - mean = deviation from the mean.
i.e. 6.0 - 7.3 = (-1.3)

Deviation from mean ÷ SD = Z-score
i.e. (-1.3) ÷ 0.46 = (-2.8)
Z-score is (-2.8).