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Chapter 3: Q. 3.112 (page 122)

A quantitative data set has size 40. At least how many observations lie within two standard deviation to either side of the mean?

Short Answer

Expert verified

At least 30 observations lie within two standard deviation .

Step by step solution

01

Given information

We have been given that,

data size= 40

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 is 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%=100×34%=75%

is within 2standard deviation rom 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%×40=30

Thus, at least 30observations lie within 2standard deviation of the mean.

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