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The sample range in statistics is a measure of how spread out the values in a dataset are. It is the simplest measure of variability and is determined by finding the difference between the largest and smallest numbers in your dataset. In the case of the sample data provided, consisting of oxygen consumption by firefighters, this involves identifying the maximum value, which is 49.3, and the minimum value, which is 23.5.

To compute the range, subtract the smallest value from the largest:

• Range = 49.3 - 23.5 = 25.8

This result tells us that there is a 25.8 mL/kg/min difference in oxygen consumption between the firefighters with the highest and lowest measurements.

Using the range gives you a basic but insightful understanding of the data's distribution, indicating the spread between the extremities of your data points. However, it does not tell you how the rest of the values are distributed between these two points.

Standard deviation represents the average amount by which values in a data set differ from the mean. It is a more refined measure of spread than the range, providing insight into how clustered or dispersed the values are around the average. In our data set for the firefighters' oxygen consumption, the sample standard deviation was calculated as 7.777.

This process involves several steps:

• Calculate the mean of the data set.
• Determine the deviations of each data point from the mean.
• Square each of these deviations.
• Compute the average of these squared deviations by dividing the sum by one less than the number of data points (known as degrees of freedom in this context).
• Finally, take the square root of this average to obtain the standard deviation.

The standard deviation helps us understand the degree to which each firefighter's oxygen consumption varied from the group's average. A smaller standard deviation would indicate that most values are close to the mean, whereas a larger standard deviation points to a wider spread from the mean.

The mean, or average, is a central measure used to summarize a set of values. For the oxygen consumption data, the mean is computed by adding all the values and dividing by the number of data points (10, in this case). The result is 31.03 mL/kg/min.

Calculating deviations involves determining how each individual value differs from the mean. To do this, subtract the mean from each data point. For instance, one firefighter's consumption is 29.5, which deviates from the mean by

• 29.5 - 31.03 = -1.53

This value tells us that the firefighter consumes less oxygen than the average.

By analyzing these deviations, we gain insights into the consistency of data or variability among the measurements. Large deviations (either positive or negative) indicate that a data point is far from the mean, highlighting significant differences in behavior or conditions influencing the measurement.