# Math 219: CH03 (up to 3.2)

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1. mean
The mean of a variable is computed by adding all the values of the variable in the data set and dividing by the number of observation.
2. population mean
The population mean is computed using all the individuals in a population. The population mean is a parameter.
3. What is μ?
The population mean.
4. What does the following equation compute?
μ=the population mean
5. Is the population mean a parameter or statistic?
parameter
6. What does the following equation compute?
=the sample mean
7. Is the sample mean a parameter or statistic?
statistic
8. What is the value that lies in the middle of the data when arranged in ascending order?
The median of a variable (M)
9. What are the steps in finding the Median of a Data Set?
Step 1 Arrange the data in ascending order.

Step 2 Determine the number of observations, n.

Step 3 Determine the observation in the middle of the data set.
10. What is the Median if the number of observations is odd?
If the number of observations is odd, then the median is the data value exactly in the middle of the data set. That is, the median is the observation that lies in then (n + 1)/2 position.
11. What is the Median if the number of observations is even?
If the number of observations is even, then the median is the mean of the two middle observations in the data set. That is, the median is the mean of the observations that lie in the n/2 position and the n/2 + 1 position.
12. Define Resistant.
A numerical summary of data is said to be resistant if extreme values (very large or small) relative to the data do not affect its value substantially.
13. What is the distribution shape if the Mean is substantially smaller than the Median?
• Skewed Left
14. What is the distribution shape if the Mean is roughly equal to the Median?
• Symmetric (bell-shaped)
15. What is the distribution shape if the Mean is substantially larger than the Median?
• Skewed Right
16. What is the most frequent observation of the variable that occurs in the data set?
The Mode of a Variable.
17. True/False:  A data set can have no mode, one mode, or more than one mode.
True
18. What are the three Measures of Central Tendencies?
Mean, Median, Mode
19. What is the Range (R) of a variable?
The range, R, of a variable is the difference between the largest data and the smallest data value.
20. True/False:  The variance is based on the deviation about the mean.
True
21. What is the deviation about the mean for the ith observation for Population?
22. What is the deviation about the mean for the ith observation for a Sample?
23. True/False: The sum of all the deviation about the mean must equal zero.
True
24. True/False: To treat positive differences and negative difference, we square the deviation for population and for samples.
True
25. What is The Population Variance?
The population variance, σ2, of a variable is the sum of these squared deviations divided by the number of observations in the population, N. In other words, it is the average of the squared deviations about the population mean.
26. What is the formula for The Population Variance?
27. What is the Sample Variance?
The sample variance, s2, or a variable is the sum of these squared deviation divided by the number of observations in the sample, n, minus one. In other words, it is the average of the squared deviations about the sample mean.
28. What is the formula for The Sample Variance?
29. Why do we have (n-1) in the denominator for the Sample Variance?
If we used n in the denominator for the sample variance calculation, we would get a biased result, or we would tend to underestimate the true variance.
30. What is the Standard Deviation of a variable?
The standard deviation is the square root of the variance, but when it comes to applications and the data given, we think of the the standard deviation as “the average distance from the mean.”
31. What is the formula for the Population Standard Deviation?
32. What is the formula for the Sample Standard Deviation?
33. True/False:  We can use the Empirical Rule for all shapes of distributions.
False, the Empirical Rule only applies to bell-shaped distributions.
34. Using the Empirical Rule on a bell-shaped distribution, we can determine the percentage of data that will lie within ____ standard deviation of the _____.
k, mean
35. pproximately _____% of the data will lie within 1 standard deviation of the mean. That is, approximately _____% of the data lie between _____ and _____.
• 68%
• 68%
• μ-1σ and μ+1σ
36. Approximately _____% of the data will lie within 2 standard deviations of the mean. That is, approximately _____% of the data lie between_____and_____.
• 95%
• 95&
• μ-2σ and μ+2σ
37. Approximately _____% of the data will lie within 3 standard deviations of the mean. That is, approximately ______% of the data lie between ______and _____.
• 99.7%
• 99.7%
• μ-3σ and μ+3σ
 Author: lazvertiigo ID: 283262 Card Set: Math 219: CH03 (up to 3.2) Updated: 2014-09-25 16:33:38 Tags: scc math219 statistics Folders: Description: Math 219 Ch03 from Stewart III's textbook on Stats and Prob. at SCC Show Answers: