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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 26PFA

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Hello, could you please help me with this,

The mean temperature in New York City over last month was 80 degrees Fahrenheit with the standard deviation of 10. Assume that the distribution of NYC temperature is unimodal and symmetric.

a) Using the Empirical Rule, fill out the followings.

About 68% of the last month, the temperature in NYC was between ______ and ________.

About 95% of the last month, the temperature in NYC was between _______ and _________.

For almost all days in the last month, the temperature in NYC was between ________ and _______ .

If the temperature in NYC on a day was 81, would this be considered unusual? Explain.

No, 81 would not be considered unusual because it falls within one standard deviation of the mean.
Yes, 81 would be considered unusual because it falls within one standard deviation of the mean.

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If the temperature in NYC on a day was 54, would this be considered unusual? Explain.

Yes, 54 would be considered unusual because it is more than two standard deviations below the mean.
No, 54 would not be considered unusual because it is not more than two standard deviations from the 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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