K300 Practice Exam 1 Note: This gives you an idea of the types of questions I ask. The length of the exam may differ. The questions are meant to be representative but not all-inclused (i.e. this is a sample of all possible material to cover, not the population). In the actual exam, you will be given more space to work each problem, so work these problems on separate sheets. 1) After 5 points are added to every score in a distribution, the mean is calculated and found to be µ = 30. What was the value of the mean for the original distribution? 2) Consider the following set of scores: 2, 8, 4, 5, 5, 5, 2, 4, 7, 8 a) Compute the mean. b) Compute the median. c) Compute the mode. d) Compute the inter-quartile ravnge (don't need to do this one). 3) The value of one score in a distribution is changed from X = 20 to X = 30. Which measure(s) of central tendency is/are certain to be changed (choose from mean, median and/or mode)? 4) The students in a class have the following grades on a quiz (out of 10): 2, 4, 3, 4, 5, 10, 2, 4, 2, 3, 4, 2 a) What scale are these number on (nominal, ordinal, interval, ratio)? b) Display the quiz scores on a frequency distribution graph and label the axes.
c) Is this distribution positively skewed, negatively skewed, or symmetric? d) Which measurement of central tendency is best? 5) For the next set of questions, refer to the following table, which is the information from the nascar series this year: Position Driver Points Wins Top 5 Top 1 0 Winnings 1 Jeff Gordon 3768 5 16 18 $5,509,200 2 Ricky Rudd 3546 2 11 18 $3,737,500 3 Dale Jarrett 3375 4 10 13 $3,640,300 4 Tony Stewart 3356 3 10 14 $2,663,500 5 Sterling Marlin 3302 1 7 13 $2,368,300 6 Bobby Labonte 3267 1 6 14 $2,981,480 7 Dale Earnhardt Jr 3244 1 6 11 $3,376,110 8 Kevin Harvick * 3230 2 5 12 $2,769,260 9 Rusty Wallace 3225 1 7 12 $3,341,680 1 0 Johnny Benson 3098 0 5 11 $2,718,000 1 1 Jeff Burton 2979 1 3 10 $2,708,560 1 2 Mark Martin 2948 0 3 10 $2,626,770 1 3 Bill Elliott 2917 0 4 8 $2,405,350 1 4 Steve Park 2859 1 5 12 $2,385,970 1 5 Jimmy Spencer 2838 0 3 8 $1,836,100 1 6 Matt Kenseth 2829 0 1 5 $1,611,820 1 7 Ward Burton 2712 1 3 6 $2,428,100 1 8 Elliott Sadler 2629 1 2 2 $1,914,870 1 9 Bobby Hamilton 2608 1 2 5 $1,728,760 2 0 Ken Schrader 2597 0 0 5 $1,717,450 a) The position column lists the rank of each driver. Is this on a nominal, interval, ordinal or ratio scale? Determine nature of the scale for the Points, Wins, Top 5 wins, Top 10 wins, and Winnings columns as well. b) The Wins column lists the number of wins for each driver. Draw the frequency distribution for these 20 numbers.
c) Are the Wins on an interval, ordinal, nominal or ratio scale? If possible, compute the mean, median and mode. d) Is the distribution of Wins positively skewed, negatively skewed or symmetric? e) What is the median number of Top 10 finishes for these top 20 drivers? Which driver(s) is/are at the median? f) What is the range of Top 10 finishes? g) What proportion of drivers have 10 or more Top 10 Finishes? 6) For the following sample of scores: 23, 42, 35, 26, 39, 27 a) Compute the mean b) Compute SS using the computational formula. c) Compute the standard deviation. d) Suppose you add a score at the mean. Would the mean change? (yes or no, no computation is necessary, but explain why) e) Suppose you add a score at the mean. Would the standard deviation change? (yes or no, no computation is necessary, but explain why) 7) Explain why the sample variance tends to be smaller than the population variance.
8) Consider all the voters in an election. Does this represent a sample or a population if the data (the votes) are used to pick a president (ignoring the electoral college and assuming instead that the popular vote determines the winner). 9) Lots of things (e.g. salaries, taxes, housing prices) tend to be positively skewed, in part because they can't have negative values (if your house was worth -$100,000, that would mean that you would have to pay someone to live in your house). They also tend to have no upper bound, because salaries and house prices can keep going up. See Bill Gates as an example. It is harder to think of things that have a negatively-skewed distribution. Come up with an example. Hint: think of things that have an upper bound with scores that tend to cluster toward the top. 10) Imagine an experiment that randomly surveys 50 P101 students from each of two classes and asks them how tall they are. a) What is the population of interest? b) What is the independent variable? c) Is the independent variable discrete or continuous? d) What is the dependent variable? e) Is the dependent variable discrete or continuous? f) What scale is the dependent variable measured on? 11) For the following set of scores 5, 5, 0, 6, 4 a) Find ( X X) 3.
b) Find ( 2X + 1) 12) A sample has a mean of X =45. a) If a new score of X=50 is added to the sample, what will happen to the sample mean? (increase, decrease, stay the same) b) If a new score of X=45 is added to the sample, what will happen to the standard deviation? (increase, decrease, stay the same) 13) Two sections of a stats class have exam means of X 1 =24 and X 2 =20. The first class has 20 students, and the second has 30. What is the overall class mean? 14) Describe why the sample variance tends to underestimate the population variance. 15) IQ scores have a mean of 100 and a standard deviation of 10. Suppose we give a drug to everyone in the population that raises their IQ by 10 points. Does this change the mean? Does this change the standard deviation? 16) Explain why the sample standard deviation and the sample variance cannot both be unbiased estimates of the population standard deviation and variance respectively.