Body Fat Vs Weight Silvers Gym

I am a statistical analyst and have been hired by Silver's gym. My supervisor would like me to determine the difference, or relationship, of the body fat and the weight in the men that exercise there. We compiled the data of 252 willing volunteers and plan to examine the statistical measures in great detail. I will perform a hypothesis test, regression analysis and will present my findings of the relationship between body fat and weight in the 252 men.

First we will begin by determining the mean, median, range and standard deviation of the body fat and weight results of the 252 men at Silvers Gym.

A. Statistical Measures

I. Calculate the statistical mean of the body fat and the actual weight for each subject.

Body fat mean = 18.9

Weight mean = 178.9

II. Calculate the statistical Median of the body fat and the actual weight for each subject.

Body fat median = 19.0

Weight median = 176.50

III. What is the importance of finding the mean/median?

The importance of the mean and median is that you can show two different ways of determining the most typical value in a given dataset, such as body fat versus weight in 252 men at Silver's Gym. If there are many outliers and the data is extremely skewed then it is recommended to use the median (Dr. Evans archive chat). If you want to determine a value in a data set with a lot of variability and not a lot of outliers then it is best to determine the mean.

IV. What is the usefulness of determining the median versus the mean?

Both the median and the mean produced very similar results. In the case of determining which is better to use, the median or the mean, at Silver's gym I would use the median because the range in the data set has significant outliers. If you wanted to show the typical house price in an area such as Los Angeles and used the average the result would be a very high price because of all the multi-million dollar homes in Beverly Hills. The result would be skewed because of the ridiculously high prices of those homes. If you use the median it would take into account the rich people's homes and give you a more appropriate measure.

V. Calculate the statistical Range of the body fat and the actual weight for each subject.

Body fat range = 0.00 (min) - 45.1 (max)

Weight range = 118.5 (min) - 363.2 (max)

VI. Calculate the standard deviation of the body fat and the actual weight for each