Answered: AP Exam A small class of five…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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AP Exam A small class of five statistics students received
the following scores on their AP Exam: 5, 4, 4, 3, 1.
a) Calculate the mean and standard deviation of these
five scores.
b) List all possible sets of size 2 that could be chosen
from this class. (There are 5C2 = 10 such sets.)

c) Calculate the mean of each of these sets of 2 scores
and make a dotplot of the sampling distribution of the
sample mean.

d) Calculate the mean and standard deviation of this sam-
pling distribution. How do they compare to those of

the individual scores? Is the sample mean an unbiased
estimator of the population mean?

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 + ...

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