Dr. Veronika Alhanaqtah. Statistics



MIDTERM EXAM 1. EXEMPLARY QUESTIONSTopics you need to study: Introduction to data (Topic 1), Univariate analysis (Topic 2).You might need a calculator for the exam.Question 1. Fill the gap. “……………..” is a data table or a data matrix that is made up of rows and columns. data set;unit of observation;variable;density curve.Question 2. In the data set below, crime rates (per 100?000) are presented for various crime types.What is the unit of observation?criminal;citizen;state;type of a crime.Question 3. In the data set below information is provided on a subset of Titanic passengers. The first ten observations are listed. What is the unit of observation for this data set?ship;survival;passenger class;passenger.Question 4. Choose a correct answer. Categorical variables are those:which take numerical values;which do not usually take numeric values;which we could be put on a number line;with which we can make mathematical operations.Question 5. What in the list below is not an example of a numeric variable?cost of production;total output;consumer’s income;name of a product.Question 6. In the data set below, crime rates (per 100?000) are presented for various crime types. We updated the data set with a new variable specifying whether the state was East or West of the Mississippi river. East is coded 0, West is coded as 1. This new variable is of what type?categorical;numeric;normal;binomial.Question 7. In the data set below information is provided on a subset of Titanic passengers. The first ten observations are listed. Which of the following variables is categorical?siblings and spouses;age;fare;survived.Question 8. In the data set below information is provided on a subset of Titanic passengers. The first ten observations are listed. Which of the following variables is numeric?passenger class;sex;fare; (d) survived.Question 9. Fill the gap. A “…………” represents the proportion of times the variable takes particular valves using area:distribution;density curve;histogram.Question 10. Fill the gap. The “……….” means how often does the variable take on each particular value. distribution;density curve;z-score.Question 11. Fill the gap. In a histogram representing a “……………” distribution we can mentally draw a line down the middle of the histogram and fold it over, so the left and the right halves are exactly the same.right-skewed;left-skewed;symmetric.Question 12. Fill the gap. A histogram, representing a “…………… ” distribution, there is no mid-point. If such a histogram has a right long tail, we call it’ “…………….”. symmetric, right-skewed;symmetric, left-skewed;non symmetric, right-skewed;non symmetric, left-skewed.: Question 13. Fill the gap. A histogram, representing a “…………… ” distribution, there is no mid-point. If such a histogram has a left long tail, we call it’ “…………….”. symmetric, right-skewed;symmetric, left-skewed;non symmetric, right-skewed;non symmetric, left-skewed.Question 14. In order to draw a box plot we need 5 number summaries. Which ones?minimum, maximum, 25th percentile, median, 75th percentile;mean, mode, 25th percentile, 50th percentile, 75th percentile;minimum, maximum, mean, median, boundary fence;minimum, maximum, mean, median, standard deviation.Question 15. Calculate a right boundary fence for a box plot if we know that 25th percentile is 4 and 75th percentile is 5.5.5.52.257.756Question 16. Calculate a right boundary fence for a box plot if we know that 25th percentile is 2 and 75th percentile is 6.24612Question 17. Calculate a left boundary fence for a box plot if we know that 25th percentile is 4 and 75th percentile is 6.1246Question 18. Calculate a left boundary fence for a box plot if we know that 25th percentile is 8 and 75th percentile is 12.1246Question 19. Which set of number summaries does describe the spread of a distribution?range, inter-quartile range, standard deviation;mean, inter-quartile range, standard deviation;median, inter-quartile range, standard deviation;mean, median, mode;Question 20. For the normal distribution, the values less than one standard deviation from the mean account for 68 % of the set, while two standard deviations from the mean account for 95 %, and three standard deviations account for 99.7 %. This is a definition of:z-score;Empirical rule;Chebyshev theorem;no correct answer.Question 21. The Greek symbol sigma (σ) in statistical formulas stands for:mean;median;mode;standard deviation.Question 22. This kind of distribution is centered around the mean and can take various spreads:normal (bell-shaped);righ-skewed;left skewed;no correct answer.Question 23. Which transformation does center a distribution, in order it has a mean of 0 and a standard deviation of 1?when we add poit to a data set;when we subtract point out of a data set;standardization transformation;logarithmic transformation.Question 24. What kind of transformation does change the shape of a distribution?when we add poit to a data set;when we subtract point out of a data set;standardization transformation;logarithmic transformation.Question 25. What is for do we standardize variables?(a) to make a distribution more symmetric;(b) to make a distribution more asymmetric;(c) to move on to the standard normal distribution, for which we may apply z-score table to calculate probabilities of events;(d) to make our minds busy.Question 26. What is for do we apply logarithmic transformations? (a) to standardize a variable;(b) to make a distribution more symmetric;(c) to make a distribution more asymmetric;(d) to practice our mathematical skills.Question 27. Find the mean for the following sample: 4, 4, 4, 4, 4, 4, 5, 6, 10.1.94532Question 28. Find the standard deviation for the following sample: 4, 4, 4, 4, 4, 4, 5, 6, 10.1.95932Question 29. Find the range for the following sample: 1, 2, 3, 4.0134Question 30. A “………” is the most common value in a data set. It is a definition of:meanmedian;mode;range.Question 31. For the 1st value of a sample 0,0,2,2 compute z-score:2-110Question 32. For the 4th value of a sample 0,0,2,2 compute z-score:01-12Question 33. A data set with a normal distribution has the mean 6 and standard deviation 2. Find the approximate proportion of observations in the data set that lie between 2 and 10:68 %75 %95 %99.7 %Question 34. A data set has the mean 6 and standard deviations 2. Find the minimum proportion of observations in the data set that must lie between 2 and 10:68 %75 %95 %99.7 %Question 35. A data set has the mean 6 and standard deviations 2. Find the minimum proportion of observations in the data set that must lie between 4 and 8:068 %75 %99.7 %Question 36. A sample data set of size n= 30 has the mean 6 and the standard deviations 2. What is the maximum number of observations in the data set that can lie outside the interval (2, 10)? 77.2522.523Question 37. A sample data set of size n= 30 has the mean 6 and the standard deviations 2. What can be said about the number of observations in the data set that are below 2?0-70-7.257.25-22.5more than 23Question 38. A sample data set of size n= 30 has the mean 6 and the standard deviations 2. What can be said about the number of observations in the data set that are above 10? 0-70-7.257.25-22.5more than 23Question 39. An instructor announces to the class that the scores on a recent exam had a normal distribution with mean 75 and standard deviation 5. What is the median score? 5707580Question 40. An instructor announces to the class that the scores on a recent exam had a normal distribution with mean 75 and standard deviation 5. Approximately what proportion of students in the class scored above 85? 95 %5 %2.5 %0Question 41. Make a histogram for the data set: 10, 30, 70, 70, 80, 80, 80, 80, 90, 90, 90Question 42. Make a box plot for the data set: 30, 30, 30, 40, 40, 40, 40, 60, 80, 90Question 43. Which boxplot does represent a skewed distribution? (a)(b)(c)Question 44. There are two histograms showing the distribution of men’s heights and a histogram of women’s heights. How would you compare the various aspects of the two distributions?histogram of men’s heights has a normal distribution, histogram of women’s heights shows errant points towards tails;histogram of women’s heights has a normal distribution, histogram of men’s heights shows errant points towards tails;both histograms have normal distribution;both histograms are left-skewed.Histogram of women’s heightHistogram of men’s heightQuestion 45. The box plot for the Mathematics exam for the 13 students is drawn on the grid below. What conclusion we can make about students’ performance? Check all that apply.the distribution of scores is symmetric;the distribution of scores is left skewed;the distribution of scores is right skewed;the mean score is 61;the median score is 61;the mode is 55;there is more small scores in the distribution;there is more large scores in the distribution;the minimum achieved score was 45.Question 46. The distribution of daily average wind speed on an island over a period of 120 days is displayed on this box-and-whisker diagram.(a) Write down the median wind speed. …………...(b) Write down the minimum wind speed. ……….......(c) Find the interquartile range. ………………………………………Question 47. 155 people were asked how much money they would pay for particular three-course meal in a special restaurant. The histogram shows the results of the plete the frequency table for information shown in the histogram.Amount (? x)0<x≤10Frequency20Bonus question: Use your frequency table to calculate an estimate of the mean amount these people would pay for the meal.Question 48. What is a necessary condition for using the empirical rule (or 68-95-99.7 rule)?all values of a variable must be even numbers;all values of a variable must be uneven numbers;distribution must be normal;distribution must be bimodal.Question 49. Biologists gather data on a sample of fish in a large lake. They capture, measure the length of, and release 1000 fish. They find that the standard deviation is 5 centimeters, and the mean is 25 centimeters. They also notice that the shape of the distribution (according to a histogram) is very much skewed to the left (which means that some fish are smaller than most of the others). Approximately what percentage of fish in the lake is likely to have a length within one standard deviation of the mean?68 %95 %99,7 %cannot be determined with the information given.Question 50. Look at a histogram of students’ scores in the exam. What can you say about the mode?7;17;17 and 20;20.What can you say about the distribution of scores?distribution is symmetric;distribution is right skewed;distribution is left skewed.Question 51. Look at a histogram of students’ scores in the exam. What can you say about the mode?10;12;14;19 and 20.What can you say about kurtosis?it is about zero;it is large and positive;it is large and negative;it is small and positive;it is small and negative.Question 52. Distribution is symmetric when skewness:0>0<0Question 53. For normally distributed variables kurtosis (tail weight) is:0>0<0Question 54. Table shows the mean and standard deviation for total scores on the SAT and ACT exams. The distribution of SAT and ACT scores are both nearly normal. Suppose Ahmad scored 1800 and Hamza scored 24 on his ACT. Who performed better?SATACTMean150021SD3005Question 55. Using Z-table determine the probability that:a variable is no more than 0.51 SD above the mean;a variable is less than 1.5 SD above the mean;a variable is within the range -1.16 to 1.32 SD. ................
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