n a city with three high schools, all the ninth graders took a Standardized Test, with these results: High School Mean Test Score Number of ninth graders (Frequency) Glenwood 78 258 Central 96 303 Lincoln 69 159 The city's PR manager, who never took statistics, claimed the mean score of all ninth graders in the city was the average of 78, 96, and 69, which is 81. Of course, that is incorrect. What is the mean score for all ninth graders in the city? Round to one decimal place. Mean of all ninth grader's scores =

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 + ...