Researchers are trying to see if the English AP scores from four different Massachusetts private schools are different. From each school, a random sample of students in the past year was taken and compared. Here are the results from the samples: Results School              n         Mean       StDev      BB&N             23          4.3            0.4 Roxbury Latin     25          3.9            0.6      Winsor           26          4.2            0.3   Belmont Hill      29          3.1            0.3 Is there any significant difference between these schools’ AP English scores? (Assume that the populations are normally distributed)

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 + ...