Researchers studying anthropometry collected body and skeletal diameter measurements, as well as age, weight, height, and sex for 507 physically active individuals.

The scatterplot below shows the relationship between height and shoulder girth (circumference of shoulders measured over deltoid muscles), both measured in centimeters.

- Mean shoulder girth: 107.20 cm
- Standard deviation of shoulder girth: 10.37 cm
- Mean height: 171.14 cm
- Standard deviation of height: 9.41 cm
- Correlation between height and shoulder girth: 0.67

Reference: Heinz et al., 2003

The z-scores for the weights 11kg, 7.9kg, and 12.2kg are respectively 1, -2.875, and 2.5 indicating they are 1 standard deviation above, about 2.875 standard deviations below, and 2.5 standard deviations above the mean weight 10.2 kg that has been measured.

Explanation:

In this question, we are asked to calculate the z-scores that correspond to certain weights of 80 cm girls in the reference population. The Z-Score formula is Z = (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation.

a. For 11 kg:
Using the formula, Z = (11 - 10.2) / 0.8 = 1. This means that a child weighing 11 kg is 1 standard deviation above the mean weight.

b. For 7.9 kg:
Z = (7.9 - 10.2) / 0.8 = -2.875. This means that a child weighing 7.9 kg is around 2.875 standard deviations below the mean weight.

c. For 12.2 kg:
Z = (12.2 - 10.2) / 0.8 = 2.5. This means that a child weighing 12.2 kg is 2.5 standard deviations above the mean weight.

Above or below the mean weight indicates if the particular weight is above or below the average weight measured.

Learn more about Z-Scores

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