Silver's Gym Case Study

At the Silver's Gym, as an analyst the body fats versus weight calculations for statistical principles are outline as the following:

Body Fat Weight

Mean= 18.79 Mean=173.01

Median=17.4 Median=167.00

Range=45.1 Range=244.65

Standard deviation= 4.33 Standard deviation=13.15

Out of the 252 men that attend the Gym the average, mean of those men, that has body fat of 18.79 with a weight of 173.01. The median calculated by finding the middle number for the body fat and weight numbers. For this observation, the middle number for the body fat is 17.4 and weight is 167.00. These ranges for the calculations show for the body fat shows the difference between the highest and lowest values of the distribution. The body fat calculations are 45.1 minus 0.00, which will results as a range of 45.1. Now the range in weight is calculated the same and those results come up with 244.65.

In real-world situations, the importance of measuring central tendency reflects on the data that has measured. For example, the calculations from 252 men body fat and weight shows the average on the data calculated on a daily basis in the Silver's Gym. "Statistics geared toward measuring central tendency all focus on this concept of average. The mean also known as average calculated as the sum of all the data divided by a number."(Price, 2000) The median better described as the middle value, which the value is the equal number. These numbers are arranging from the smallest to largest. For example, in the gym the median out of 252 men equals 126 that represent men that where in the half way point. The mean is more applicable in the case with Silver's Gym. The 252 men calculated by adding all values, and then divided by the 252 men for each data set under body fat and the weight. "Importance of the range shows difference between the highest value and the lowest."(Price, 2000) When time to calculate the body fat. The largest number, the smallest subtracted, and the difference showed the range and this concept also applied to determine the range for the weight out of the data sets. "The standard deviation provided an approximate measure of the mean distance between each data point and the mean of all the data points."(Price, 2000) For example, the above calculation determine for the standard deviation is the square root of whatever the mean value equal to.

The null and alternative hypothesis test determines by the boss interpretation that 20 percent of the 252 men have body fat. The statistics shows from the calculations that the average out of 252 men, who comes into the Silver Gym, has 19 percent of body fat. For example, the hypothesis test is Ho=20,