A doctor works at a hospital estimate when to leave for work from his apartment; he decided to measure how long it takes him to go to the hospital every day. For one week, he records the time it gets him to drive from his apartment to the hospital, including searching for parking and reaching to his office. The data are as follows: M Eighty-one      Min T Fifty-four         Min W Seventy           Min R Fifty-two          Min F Forty-three      Min 1- Will you recognize these times as a sample or a population? and way 2- Obtain the mean and the standard deviation for the time it requires him to go to his office at the hospital. 3- Lets say his roommate, who is working with him at the same hospital and same office, takes the train to the hospital. She records the time it takes her to get to the office during the exact week and was that her mean was Sixty-two minutes, and the standard deviation was Five. Based on these measurements, it is convenient to drive or ride the train to the hospital? and why.

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 + ...