Answered: Are your results accurate just because…

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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Question

Are your results accurate just because they were within 1 standard deviation of the mean?

Are your results incorrect if they deviate more than one standard deviation from the mean?

Explain why or why not

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: First Step:

Not necessarily. The standard deviation is a measure of how spread out the data is around the mean. A result that is within 1 standard deviation of the mean is likely to be accurate, but it is not guaranteed. There is always a chance that the result could be an outlier, even if it is within 1 standard deviation of the mean.
No, not necessarily. A result that deviates more than 1 standard deviation from the mean could still be accurate. It is important to consider the context of the data and the specific question being asked in order to determine whether or not a result is accurate. For example, if the data is normally distributed, then about 68% of the results will be within 1 standard deviation of the mean. However, there is still a 32% chance that a result will fall outside of 1 standard deviation of the mean, even if it is accurate.

In general, it is important to consider the standard deviation when interpreting results, but it is not the only factor to consider. Other factors such as the sample size, the distribution of the data, and the specific question being asked should also be considered.

Here are some additional things to keep in mind:

The standard deviation is a measure of the average distance of the data points from the mean. It does not take into account the direction of the deviation. For example, a result that is 1 standard deviation below the mean is just as likely as a result that is 1 standard deviation above the mean.
The standard deviation can be affected by outliers, which are data points that are far from the rest of the data. If there are outliers in the data, then the standard deviation may be higher than it would be if the outliers were not present.
The standard deviation is not always a reliable measure of accuracy. In some cases, the data may not be normally distributed, in which case the standard deviation may not be a good indicator of how spread out the data is.