Fitness Machine A fitness center bought a new exercise machine called the Mountain Climber. They decided to keep track of how many people used the machine over a 3 -hour period. Here X is the number of people who used the machine. X 0 1 2 3 4 PX 0.3 0.2 0.2 0.1 0.2 Find the mean. Round your answer to one decimal place as needed. Mean: =μ Find the variance. Round your answer to one decimal place as needed. Variance: σ2= Find the standard deviation. Round your answer to one decimal place as needed. Standard deviation: σ=

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 + ...