A study was to be undertaken to determine if a particular training program would improve physical fitness. An SRS of 31 university students was selected to be enrolled in the fitness program. One important measure of fitness is maximum oxygen uptake. Measurements of oxygen uptake in untrained individuals are known to follow a Normal distribution with a mean of  45 ml/kg/min. The researchers wished to determine if there was evidence that their sample of students differed from the general population of untrained subjects. The measurements made on the subjects coming into this study produced a mean of 47.4 with a standard deviation of s = 5.3. Test at 0.05 alpha level showing understanding on how problem was solved.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...