Answered: Standard Deviation: A measure of the…

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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Standard Deviation: A measure of the dispersion of a set of data from its mean.
These are the steps to calculate it by hand. I recommend using a table to keep track
of your values; we will practice this below.
Step 1: List the values and find the mean (column 1).
Step 2: Find the distance between each value and the mean (column 2).
Step 3: Find the squares (second power) of all the deviations from the mean
(column 3).
Step 4: Add all the squares of the deviations from the mean (bottom of column 3).

Try this: The daily temperatures (in degrees Fahrenheit) one week in January were
32 36 29 34 31 33 27 34

Week 3 Lab Stapplet-2.docx
Page
Find the mean and the standard deviation of the temperature.
Temperatures
Distance from mean
Mean:
2
Square the distances
Step 5: Divide this sum by the total number of data values minus 1:
There are EIGHT temperatures, so we divide by SEVEN in Step 5.
exponent of .5:
◄ Previous
Sum of these:
of 2
Step 6: The standard deviation is the square root of this quotient.
The last step is to SQUARE ROOT the value from step 5. Use the √ key or use an
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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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