Data from a state indicate that scores on the SAT test are normally distributed with a mean of 994 and a standard deviation of 204. Scores on the ACT test are normally distributed with a mean of 20 and a standard deviation of 5.1. It is assumed that the two tests measure the same aptitude, but use different scales. If a student gets an SAT score that is the 77 percentile, find the actual SAT score. Round answer to a whole number. SAT score =  What would be the equivalent ACT score for this student? Round answer to 1 decimal place. ACT score =  If a student gets an SAT score of 1280, find the equivalent ACT score. Round answer to 1 decimal place. ACT score =

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 + ...