Chapter 3: Q. 3.111 (page 122)

A quantitative data set has mean $30$ and standard deviation $4$ . At least what percentage of the observations lie between $10$ and $50$ $?$

Short Answer

Expert verified

$96 %$ of the observations lie between $10$ and $50$ .

Step by step solution

Given information.

We have been given that,

Mean = $30$ ,Standard deviation= $4$

We need to find the percentage of observations lie between $10$ and $50$ .

Simplify.

Chebyshev's Rule: At least $100 (1 - \frac{1}{K^{2}}) %$ of the data is within $k$ standard deviation from the mean $(k > 1)$ .

Let us determine the number of standard deviation that $10$ and $50$ are from the mean,

$\frac{10 - m e a n}{s \tan d a r d d e v i a t i o n} = \frac{10 - 30}{4} = - 5 \frac{50 - m e a n}{s \tan d a r d d e v i a t i o n} = \frac{50 - 30}{4} = 5$

Thus, $10$ and $50$ are $5$ standard deviation from the mean.

Using Chebyshev's Rule with $k = 5$ ,we know that at least

$100 (1 - \frac{1}{K^{2}}) % = 100 (1 - \frac{1}{5^{2}}) % = 100 (1 - \frac{1}{25}) % = 96 %$

is within $5$ standard deviation from the mean.

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A quantitative data set has mean $30$ and standard deviation $4$ . At least what percentage of the observations lie between $10$ and $50$ $?$

Short Answer

Step by step solution

Given information.

Simplify.

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A quantitative data set has mean 30and standard deviation 4. At least what percentage of the observations lie between 10and50?

Short Answer

Step by step solution

Given information.

Simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

A quantitative data set has mean $30$ and standard deviation $4$ . At least what percentage of the observations lie between $10$ and $50$ $?$