Determine what percentage of your data is within 2 standard deviations of the mean. (Show your calculations). How does this seem to compare with the 68-95 99.7 rule? StatisticsN forVariableN N*MeanSE MeanStDevMinimumQ1MedianQ3MaximumMode ModeMiles3029.803.6820.165.0012.7527.00 43.5090.00123

Answered: Determine what percentage of your data…

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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Determine what percentage of your data is within 2 standard deviations of

the mean. (Show your calculations). How does this seem to compare with the 68-95

99.7 rule?

Statistics
N for
Variable
N N*
Mean
SE Mean
StDev
Minimum
Q1
Median
Q3
Maximum
Mode Mode
Miles
30
29.80
3.68
20.16
5.00
12.75
27.00 43.50
90.00
12
3

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 + ...

Expert Solution

Step 1

The Empirical Ruel:

It is a simple method to find the percentage of the normal distribution for certain values. Commonly, 3 percentages are found that 68%, 95%, 99.7%, for the standard deviation of the mean with 1,2,3 respectively.

That is, 1 standard deviation distance from the mean gives about 68% of the distribution,

2 standard deviations distance from the mean gives about 95% of the distribution,

3 standard deviations distance from the mean gives about 99.7% of the distribution.

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