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Chapter 3: Q. 3.115 (page 122)

A quantitative data set has size 50. At least how many observations lie within three standard deviation to either side of the mean?

Short Answer

Expert verified

45 observations lie within three standard deviation to either side of the mean.

Step by step solution

01

Given information.

We have been given that,

data size= 50, K=3

We need to find the number of observation lie within three standard deviation of the mean.

02

Simplify.

Chebyshev's Rule: At least 1001-1K2%of the data values is written kstandard deviation from the mean k>1.

Now,

Using Chebyshev's Rule with k=3,we know that at least

1001-1K2%=1001-132%=10089%=89%

is within three standard deviation from the mean.

The number of observations within three standard deviation of the mean is the product of the percentage and sample size n,

89%×50=.89×50=45

Thus, at least 45observations lie within three standard deviation of the mean.

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