Consider this scenario:  A cereal-packing company where the content of cereal boxes must have a mean of 368 grams to satisfy the labeling on the box. Because it is expensive to weigh every box produced at the factory, a sample of boxes is used to estimate the actual mean. After analyzing the data sample, the operations manager must decide whether or not the manufacturing process is working as expected. Suppose a sample of 49 boxes is taken from thousands produced during an 8-hour shift and the standard deviation (σ) of the cereal-filling process is 15, what is the standard error of the mean? Use the equation, σX̅   = σ /(square-root of n), where n is the sample size.  Enter your result as a value with one digit after the decimal point (e.g. 1.7).

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 + ...