# Using Chebyshev's Theorem and Other Statistic Rules

1. I. Use Chebyshev's theorem to find what percent of the values will fall between 162 and 292 for a data set with a mean of 227 and standard deviation of 13.

II. Use the Empirical Rule to find what two values 99.7% of the data will fall between for a data set with a mean of 246 and standard deviation of 16.

2. Nine college students had eaten the following number of times at a fast food restaurant for dinner in the last ten days:

5, 2, 4, 0, 4, 6, 4, 2, 3

Find the mean, median, mode, range, and midrange for these data.

3. A Math test has a mean of 38 and standard deviation of 9.0. Find the corresponding z scores for:

I. a test score of 80

II. a test score of 22

4. Rank the following data in increasing order and find the position and value of the 85th percentile.

0 8 6 1 9 7 1 0 1 7 5 4

5. The following data lists the average monthly snowfall for January in 15 cities around the US:

20 13 15 28 16 25 2 14

35 42 5 34 34 38 29

Find the mean, variance, and standard deviation. Please show all of your work.

6. Starting with the data values 70 and 100, add three data values to the sample so that the mean is 79, the median is 80, and the mode is 80.

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#### Solution Preview

Hi there,

1.

I. Use Chebyshev's theorem to find what percent of the values will fall between 162 and 292 for a data set with a mean of 227 and standard deviation of 13.

(227-162)/13=5

(292-227)/13=5.

According to Chebyshev's theorem, the percentage within 162 and 292:

1-1/5^2=96%

II. Use the Empirical Rule to find what two values 99.7% of the data will fall between for a data set with a mean of 246 and standard deviation of 16.

According to the empirical rule, 99.7% of data are within 3 standard deviation of the mean.

Upper limit: 246+16*3=294

Lower limit:246-16*3=198.

So the two values are 198 and 294.

2. Nine college students had eaten the following number of times at a fast ...

#### Solution Summary

Tne following posting helps with problems that apply Chebyshev's theorem and other statistical rules.

Statistics (The Empirical Rule vs. Chebyshev's Theorem)

How does the Empirical Rule work and how does it relate to the bell curve as illustrated in Figure 3.14 (a)? Then, explain Chebyshev's Theorem and how it is different from the Empirical Rule. Give a specific example of a population with which the Empirical Rule might be most effective and one with which Chebyshev's Theorem might be most effective.

Please take a look at the attached document for a description on the Empirical Rule.

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