Question

Body mass index (bmi) is a medical screening tool that measures body fat in an individual based on height and weight. the following data sets include the bmi measurements for random samples of 7 individuals. use the range rule of thumb to estimate the standard deviation, then determine which sample has the least amount of variation.

a) sample 1 25.8,39.2,32.2,18.7,22.7,28.8,25.4
b) sample 2 24.5,33.3,31.7,45.9,23.4,28.2,25.8
c) sample 3 30.8,19.2,29.9,25.6,28.8,31.0,27.3
d) sample 4 31.8,23.9,29.1,52.6,23.6,31.1,20.6

Answer 1

To estimate the standard deviation using the range rule of thumb, calculate the range for each sample and divide it by 4. Sample 3 has the least amount of variation with an estimated standard deviation of 2.95.

Step-by-step explanation:

To estimate the standard deviation using the range rule of thumb, you need to find the range of each sample. The range is calculated by subtracting the smallest value from the largest value in each sample. Then, divide the range by 4 to get an estimate of the standard deviation. Let's calculate the ranges and estimate the standard deviations:

Sample 1: Range = 39.2 - 18.7 = 20.5, Estimated Standard Deviation = 20.5 / 4 = 5.125

Sample 2: Range = 45.9 - 23.4 = 22.5, Estimated Standard Deviation = 22.5 / 4 = 5.625

Sample 3: Range = 31.0 - 19.2 = 11.8, Estimated Standard Deviation = 11.8 / 4 = 2.95

Sample 4: Range = 52.6 - 20.6 = 32, Estimated Standard Deviation = 32 / 4 = 8

The sample with the least amount of variation (i.e., smallest estimated standard deviation) is Sample 3 with an estimated standard deviation of 2.95.