The normal monthly rainfall in a city is given in the following table.MonthJan.Feb.Mar.Apr.MayJuneInches0.60.60.80.20.10.1MonthJulyAug.Sept.Oct.Nov.Dec.Inches0.71.10.90.80.81.1(a) Find the mean and standard deviation of the monthly rainfall in the city. (Round your answers to two decimal places.)mean instandard deviation in(b) What percent of the year will the monthly rainfall be within one standard deviation of the mean? (Round your answer to the nearest whole number.) %(c) What percent of the year will the monthly rainfall be within two standard deviations of the mean? (Round your answer to the nearest whole number.) %

Name: The normal monthly rainfall in a city is given in the following table.
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Description: The normal monthly rainfall in a city is given in the following table.MonthJan.Feb.Mar.Apr.MayJuneInches0.60.60.80.20.10.1MonthJulyAug.Sept.Oct.Nov.Dec.Inches0.71.10.90.80.81.1(a) Find the mean and standard deviation of the monthly rainfall in the ci

Mean = (Summation Xi)/n Here n=12 Mean = (0.6+0.6+0.8+0.2+0.1+0.1+0.7+1.1+0.9+0.8+0.8+1.1)/12 Mean = 0.65 (Summation Xi2)/n = (0.6^2+0.6^2+0.8^2+0.2^2+0.1^2+0.1^2+0.7^2+1.1^2+0.9^2+0.8^2+0.8^2+1.1^2)/12 = 0.535 Standard deviation = √{(summation Xi2)/n - (mean2)} = √(0.535-0.4225) = 0.335According to Empirical rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean. (b) 68% of the year will the monthly rainfall be within one standard deviation of the mean. (C). 95% of the year will the monthly rainfall be within two standard deviation of the mean.

Answered: The normal monthly rainfall in a city…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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The normal monthly rainfall in a city is given in the following table.

Month	Jan.	Feb.	Mar.	Apr.	May	June
Inches	0.6	0.6	0.8	0.2	0.1	0.1

Month	July	Aug.	Sept.	Oct.	Nov.	Dec.
Inches	0.7	1.1	0.9	0.8	0.8	1.1

(a) Find the mean and standard deviation of the monthly rainfall in the city. (Round your answers to two decimal places.)

mean	in
standard deviation	in

(b) What percent of the year will the monthly rainfall be within one standard deviation of the mean? (Round your answer to the nearest whole number.)
%

(c) What percent of the year will the monthly rainfall be within two standard deviations of the mean? (Round your answer to the nearest whole number.)
%

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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