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# Linear Correlation, Chebyshev's Theorem, and Z score

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1. You are given the following frequency distribution for the number of errors that students made in a test

Errors Frequency
0-2 13
3-5 17
6-8 0
9-11 16
12-14 3

Find the mean, variance, and standard deviation.

2. You are given the following data.

x y
2 11
3 19
4 4
5 19
5 2
7 14
7 6

Find:
- SS(x)
- SS(y)
- SS(xy)
- The linear correlation coefficient, r
- The slope b1
- The y-intercept, b0
- The equation of the line of best fit.

- Use Chebyshev's theorem to find what percent of the values will fall between 75 and 205 for a data set with mean of 140 and standard deviation of 13.
- Use the Empirical Rule to find what two values 67% of the data will fall between for a data set with mean 85 and standard deviation of 14.

4. Nine households had the following number of children per household:

1, 7, 0, 4, 1, 8, 8, 5, 3

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

5. An aptitude test has a mean of 74 and standard deviation of 5. Find the corresponding z scores for:
- a test score of 80
- a test score of 11

6. Find P84 for the following data:
3 8 1 1 1 8 6 9 4 4 1 1

7. A class of 15 kindergarteners had the following weights in pounds:
53 39 46 36 39 52 49 52
46 47 48 51 48 51 41

Find the mean, variance, and standard deviation.

8. Starting with the data values 70 and 100, add three data values to the sample so that the mean is 90, the median is 91, and the mode is 91.