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Chapter 3: Q. 3.111 (page 122)

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

Short Answer

Expert verified

96% of the observations lie between10and50.

Step by step solution

01

Given information.

We have been given that,

Mean =30,Standard deviation= 4

We need to find the percentage of observations lie between10and50.

02

Simplify.

Chebyshev's Rule: At least 1001-1K2%of the data is within kstandard deviation from the meank>1.

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

10-meanstandarddeviation=10-304=-550-meanstandarddeviation=50-304=5

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

Using Chebyshev's Rule withk=5,we know that at least

1001-1K2%=1001-152%=1001-125%=96%

is within 5standard deviation from the mean.

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Most popular questions from this chapter

Is an extreme observation necessary an outlier? Explain your answer.

The data set has mean 10 and standard deviation3 . Fill in the following blanks:
a. Approximately 68% of the observations lie between_ and _
b. Approximately95% of the observations lie between_ and _
c. Approximately99.7% of the observations lie between _and _

Which measure of variation is preferred when

(a) the mean is used as a measure of center?

(b) the median is used as a measure of center?

Explain what each of symbol represents:

a)鈭�b)nc)x-

A quantitative data set has size 80has mean 30and standard deviation 5. At least how many observations lie between20and40?
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