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Chapter 3: Q. 3.114 (page 122)

A quantitative data set has size 60. At least how many observations lie within three standard deviation to either side of the mean ?

Short Answer

Expert verified

53observations 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 = 60, K=3

We need to find the number of observations to either side of the mean.

02

Simplify.

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

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 from the mean is the product of the percentage and sample size n.

89%×60=53

Thus, at least 53observations lie within three standard deviation of the mean.

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