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Chapter 3: Q. 3.145 (page 124)

How many standard deviations to either side of the mean must we go to ensure that for any data set, at least 99%of the observations lie within?

Short Answer

Expert verified

At least 99%of the data lies withink=10standard deviations of the mean.

Step by step solution

01

Given Information

We have been given that at least99%of the observation lie within.

02

Simplification

We know Chebyshev's Rule says that at least 100(1-1k2)%of the data values is within k standard deviations from the mean (k>1).

We are interested in finding the number of standard deviations k such that 100(1-1k2)%becomes 99%.

So, 100(1-1k2)=99

On simplifying, we get

k2=100

k=10

Thus Chebyshev's rule then tells us that at least 99%of the data lies within k=10standard deviations of the mean.

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Most popular questions from this chapter

Simple data sets have been given for you to try locating the descriptive metrics mentioned in this section. For each data set separately.

(a) Calculate the quartiles,

(b) calculate the interquartile range

(c)compile a five-number summary.

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State pertinent properties of boxplots for symmetric, left-skewed and right-skewed distributions.

A quantitative data set has mean 25and standard deviation 5.Fill in the following blanks:

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