Answered: Suppose a normally distributed set of…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 11PPS

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Question

Suppose a normally distributed set of data has a mean of 170 and a standard deviation of 16. Use the 68-95-99.7 rule (sometimes called the Empirical rule or the Standard Deviation rule) to determine the percentage of scores in the data set expected to be between the scores 122 and 186.

Answer = (Write your answer in decimal form, not percentage form. For example, if your percentage is 99%, enter 0.99, not 99. Keep all decimal places.)

Caution: Using tables or Excel for this may produce a wrong answer. Use the 68-95-99.7 rule.

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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