Solution to Exercise 1.44.

  Problem Statement: 44. The article ``Oxygen Consumption During Fire Suppression: Error of Heart Rate Estimation" reported the following data on oxygen consumption (ml/kg/min) for a sample of ten firefighters performing a fire suppression simulation:

$$29.5 \quad 49.3 \quad 30.6 \quad 28.2 \quad 28.0 \quad 26.3 \quad 33.9 \quad 29.4 \quad 23.5 \quad 31.6$$

Compute the following:

a. The sample range.

Solution: The range is 49.3 - 23.5 = 25.8.

b. The sample variance s² from the definition (i.e. first computing deviations, then squaring them, etc.).

Solution: The variance is 49.3112.

c. The sample standard deviation.

Solution: s = 7.02219.

d. s² using the shortcut method.

Solution: Same numerical value as b.