Fill-In Review Sheet for AP Stat. Test #1 / Mr. Hansen

rev. 9/26/1998

#	Description	Official name	Standard notation
1.	Observed y value minus predicted y value		y - yhat [yhat means y with a ^ on top]
2.	Add up the x values	sum of observations
3.	Total number of observations	sample size
4.	If n is odd, the middle observation; if n is even, the mean of the two middle ones
5.	The smallest observation
6.	The largest observation
7.	The most common observation		[none]
8.	The median of the set from #5 up to (but not including) #4
9.	The median of the set from #6 down to (but not including) #4
10.	#9 minus #8
11.	#2 divided by #3
12.	A distribution’s center of mass
13.	A distribution’s equal-area point (i.e., the point at which half of the area lies to the left, and half of the area lies to the right)
14.	Take the deviations from the mean, square them, add them all up, and divide by n
15.	Similar to #14, except with n–1 instead of n in the denominator
16.	Square root of #14
17.	Square root of #15
18.	A value from –1 to 1, depending on whether the observations trend upward, downward, or have no linear trend at all
19.	A value from 0 to 1 that gives a rough idea of how well a line fits the observations
20.	A graph in which an explanatory variable is plotted on the x axis and a response variable is plotted on the y axis
21.	A special type of #20 in which the y axis shows values for #1 instead		How do you read it?
22.	A special type of #20 in which the values of interest are plotted on the x axis, and the z values of n uniformly spaced quantiles are plotted on the y axis.		How do you read it?
23.	An observation that departs significantly from the overall distribution pattern		Rule of thumb:

True or false?

24. An influential observation in the regression setting is an observation with a large residual that affects the regression line significantly.

25. A regression outlier (i.e., an observation that lies far from the regression prediction) must be an influential observation.

26. An influential observation must be a regression outlier.

27. All normal distributions are symmetric.

28. All symmetric distributions are normal.

29. All symmetric distributions have a mean that does not significantly differ from the median.

30. In a distribution that is skewed to the right, the median is lower than the mean.

31. Any statistic that is normally distributed will still be normally distributed when subjected to a linear transformation.

32. The median is a resistant measure of central tendency.

33. The standard deviation is a resistant measure of dispersion.

34. It is easy to spot the standard deviation of a skewed distribution.

35. Approximately 99.7% of all observations in a data set will fall within 3 standard deviations of the mean.

36. Measurements of a variable taken at regular intervals are called seasonal adjustments.

37. The numbers in the five-number summary are affected by linear transformations such as changes in units.

38. The standard deviation and IQR are affected by changes in units involving scale factors (e.g., pounds to kilograms).

39. The standard deviation and IQR are affected by changes in units involving both scaling and shifting (e.g., Fahrenheit to Celsius).

40. The standard deviation and IQR are affected by changes in units involving only a shift (e.g., Celsius to Kelvin).

41. If the regression model has a "good" residual plot, then extrapolation is valid for prediction purposes.

42. If the normal quantile plot shows a mostly linear pattern, except that the largest observations fall to the right of the line, then the distribution is skewed to the right. If the smallest observations fall to the left of the line, then the distribution is skewed left.

43. Although human judgment is better, the "1.5 IQR" rule is useful in cases where automated determination of outliers is needed.

44. A box plot is more useful than a histogram in providing a quick summary of a two-peaked distribution.

Transformation skills:

45. Be able to convert between any two normal distributions and draw conclusions. For example, to convert test scores from an N(800,50) distribution into an N(82,10) format, you should _______________________________________________ . In the new scale, approximately _____ % of the students will score between 72 and 92.

Pencil-and-paper skills:

46. Be able to transcribe calculator plots onto paper, capturing the essence of the drawing.

47. Be able to prepare stem plots (a.k.a. stem-and-leaf plots) by hand.

48. Optional: Be able to make a dot plot (same as a histogram, except using dots or pictographs to indicate frequencies).

Calculator-related skills:

49. Find the mean, standard deviation, and five-number summary of any data set.

50. Prepare a box plot (a.k.a. box-and-whiskers plot), modified box plot, histogram, or scatterplot for any data set.

51. Optional: Use the DOTPLOT program to make a dot plot.

52. Compute the z score for any observation in a normal distribution.

53. In a normal distribution, compute the probability that Z is less than z, that Z is greater than z, that Z is more than a certain number of standard deviations from the mean, that Z is between any two z values, or the complement of any of these.

54. Be able to work with the inverse normal distribution. In other words, be able to find the z value that corresponds to a desired normal quantile, the range of z values that capture a desired percentage of the normal distribution, or the z value beyond which a desired percentage of the normal distribution will lie.

55. Convert z scores into observation values.

56. Be able to combine skills #52 through 55 as needed.

57. Compute the linear least-squares regression model with or without certain influential observations. Be able to graph at least two regression lines on the same screen as the scatterplot. Be able to discuss the steepness (i.e., slope) and intercepts.

58. Make and analyze a residual plot.

59. Compute r and r² for a linear regression fit and be able to say whether the correlation is positive or negative, weak or strong.

60. If the y values for a normal quantile plot are linked into your calculator, be able to build and analyze a normal quantile plot.