Explain why the tandart deviation would likely not be reliable measure of variability for a distribution of data that includes at least one extreme outlier.

Question
Data distributions
asked 2021-01-02
Explain why the tandart deviation would likely not be reliable measure of variability for a distribution of data that includes at least one extreme outlier.

Answers (1)

2021-01-03
To analyse the standard deviation that will not be reliable based on the measure of variability that includes the data distribution with atleast one extreme outlier as follows.
The particular data set in an extreme is defined as an outlier. It is many a time that includes the statistical analysis that is being dominated.
The outliers are not present since the mean and standard deviation are different. The Standard deviation is calculated by the formula as,
\(\displaystyle\sigma=\sqrt{{\frac{{{\sum_{{{i}={1}}}^{{n}}}{\left({X}_{{i}}-\overline{{X}}\right)}^{{2}}}}{{n}}}}\)
Here, sigma is the Standard deviation. It involves the mean deviation in which the value is affected based on the presence of the outliers in which the Standard deviation is affected. It is not reliable that includes the variability measure forming the data distribution that includes the one outlier. It is measured based on the squared difference in which the single extreme value results in having the disproportionate effect.
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Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
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Black - 60
White - 67
Hispanic - 38
Total - 165
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Hispanic - 416
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This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
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Let's compare the percentage of unarmed shot for each race.
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f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
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