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Chapter 3: Q. 3.113 (page 122)

A quantitative data set has size 80. At least how many observations lie within two standard deviation of the either side?

Short Answer

Expert verified

80 observations lie within two standard deviation of the either side .

Step by step solution

01

Given information.

We have been given that,

data size=80

We need to find the number of observations lie within two standard deviation of 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=2,we know that at least

1001-1K2%=1001-122%=1001-14%=10034%=75%

is within 2standard deviation from the mean.

The number of the observations within 2standard deviation of the mean is the product of the percentage and the sample size n.

75%×80=0.75×80=60

Thus ,at least 80observations lie within two standard deviation of the mean.

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