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# Chebyshev's Theorem, Empirical Rule, Correlation, etc.

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1. For a particular sample of 50 scores on a psychology exam, the following results were obtained.
First quartile = 39 Third quartile = 71 Standard deviation = 10 Range = 62
Mean = 62 Median = 61 Mode = 68 Midrange = 69
Answer each of the following; show all work.
- What score was earned by more students than any other score? Why?
- What was the highest score earned on the exam?
- What was the lowest score earned on the exam?
- According to Chebyshev's Theorem, how many students scored between 42 and 82?
- Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 42 and 82?

- If the correlation coefficient is 0.80, what is the sign of the slope of the regression line?
- As the correlation coefficient increases from 0.85 to 0.90, do the points of the scatter plot move toward the regression line, or away from it?

3. A math test was given; a sample of the scores yielded the following results:
32, 17, 83, 42, 32, 70, 94, 88, 27, 10, 76, 27, 98, 7, 7, 53
Find the range, standard deviation, and variance for the sample scores.

4. In terms of the mean and standard deviation:
- What does it mean to say that a particular value of x has a standard score of +4.4?
- What does it mean to say that a particular value of x has a z-score of -1.6?

5. A student scored 81 percent on a test, and was in the 67th percentile. Explain these two numbers.

6. An animal trainer obtained the following sample data (Table A) in a study of reaction times of dogs (in seconds) to a specific stimulus. He then selected another group of dogs that were much older than the first group and measure their reaction times to the same stimulus. The sample data is shown in Table B.
Table A Table B
Classes Frequency Classes Frequency
2.3-2.9 25 2.3-2.9 14
3.0-3.6 18 3.0-3.6 19
3.7-4.3 14 3.7-4.3 27
4.4-5.0 20 4.4-5.0 9
5.1-5.7 0 5.1-5.7 25
5.8-6.4 16 5.8-6.4 29

Find the variance and standard deviation for the two distributions above. Compare the variation of the data sets. Decide if one data set is more variable than the other.

7. You are given the following data.
Number of Absences Final
0 93
1 90
2 79
2 77
3 77
3 66
4 60
5 56
6 47
? Make a scatter plot for the data; submit it through the Dropbox.
? Find the correlation coefficient for the data.
? Find the equation for the regression line for the data, and predict the final grade of a student who misses 3.5 days.

8. Indicate which would be the independent variable and which would be the dependent variable:
Microprocessor chip speed = dependent, Cost of microprocessor = independent
Microprocessor chip speed = independent, Cost of microprocessor = dependent

9. Indicate which would be the independent variable and which would be the dependent variable:
Distance = dependent, Travel time required = independent
Distance = independent, Travel time required = dependent

##### Solution Summary

The solution provides step-by-step calculations involving Quartile, Percentile, Range, Mid-Range, Mean, Median, Mode, Standard Deviation, Variance, Frequency, Dispersion, Chebyshev's Theorem, Empirical Rule, Scatter Plot, Correlation Coefficient, Regression Equation, Z-Score, and Standard Score. Calculations have been perfomed in Excel and the formulas, explanation and analysis have been provided in text attachment.

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###### Education
• MSc, Osmania University
• MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
• BSc, Banaras Hindu University
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