Use a calculator or software where necessary instead of the formulas below. Excel formulas are shown in GREEN. Nature of data: Qualitative (categorical) data, quantitative (numeric) data (continuous or discrete) Levels of Measurement: nominal level, ordinal level, interval level, ratio level Organization of data: Frequency table, relative frequency, cumulative frequency class frequency Relative Frequency = sum of frequencies = n Number of intervals - use the 2* rule; 2* > n (sample size) where k = number of intervals range range Class width = - k or # of intervals Class Midpoint = Lower limit + upper limit 2 Measures of Location (Measures of Central Tendency) Population data Sample data Ex Arithmetic Mean U = X = =AVERAGE( ) N n N+ 1 n+1 Position of Median =MEDIAN( ) 2 2 Mode Most frequent observation =MODE.SNGL() or =MODE.MULT() [ w(x) Weighted Mean where w =weighting factor x = individual valueSW(x) Weighted Mean where w =weighting factor x = individual value Measures of position: deciles, quartiles, percentiles Location of percentile Lp = (n + 1) - n = number of observations in the data set p = desired percentile L = position of the percentile in the data set P-th percentile =PERCENTILE.EXC( ) Interquartile range IQR = Q3 -Q Winter 2021 BSTA 200 - Midterm FORMULA SHEET Measures of Variation (dispersion) Population data Sample data Range Highest value - lowest value =MAX( ) - =MIN() E ( X - 1) Standard deviation 6 = N E(x - F) S = S = n 7 - 1 n - 1 =STDEV.P( ) =STDEV.S( ) Variance =VAR.P( ) =VAR.S( )n - 1 n - 1 =STDEV.P( ) =STDEV.S( ) Variance =VAR.P( ) =VAR.S( ) Coefficient of Variation CV = CV = (CV) Correlation and Regression Coefficient of Correlation (r) r= =CORREL(Y, X ) Regression Equation D = a + bx where b = slope =SLOPE(Y, X ) a = y-intercept =INTERCEPT(Y, X ) explained variation SSR Coefficient of Determination (r]) r2 = or total variation SST Standard Error of Estimate s. = [y' - a( [y) - b( [ xy) SSE or n - 2 =STEYX(Y, X) n - 2 Counting Rules Factorial Permutation Rule Combination Rule Number of arrangements of n Selecting r items from n Selecting r items from n different objects = n! =FACT(n ) different items when order different items when order is When objects repeat is important. not important. n1, n2, ., nk times, number of n! n! arrangements is: nPr = n! (n - r)! ner = (n -r)!r! n1! 'nz! " nk! =PERMUT(n, r) =COMBIN(n, r)I Question Q E 3 pts '52) 1 Suppose 55 students were asked how many courses theyr were taking this semester. The results are shown in the {incomplete} table below. Fill in the blank cells to complete the table. Round relative frequencies to 3 decimal places. m_ I Question 10 E 5 pts 01 G) Details Scores on an exam appear bell-shaped with the middle 63 97.3 of the scores in the interval (112, 144). According to the empirical rule, the middle 95 97.3 of the scores will lie in which interval? Choose the closest: O (87, 160) O (96. 160) O (92, 161) O (81, 163) O (92, 171) O (37, 163) O (87, 161) O (96. 163) O (31, 171) I Question 11 E 1i] pts E) 1 1} Match each variable with its Level of Measurement. Age in years a. Ratio Ranking of top ten universities b. Interval Grams of fat in cookies c. Ordinal Year of birth d. Nominal Level of Pain (Bad, Moderate, No Pain} Gender 2] Are the following variables discrete or continuous? a] Speed [in kmlh} of a car: C) continuous C) discrete b} Number of students in a class: D discrete - Year of birth d. Nominal - Level of Pain (Bad, Moderate, No Pain) - v Gender 2) Are the following variables discrete or continuous? a) Speed (in km/h) of a car: O continuous O discrete b) Number of students in a class: O discrete O continuous c) A person's age: O continuous O discreteI Question 12 E 4 pts '52) 1 In a brand recognition study, 1213 consumers knew of Coke, and 4 did not. Use these results to estimate the probability that a randomly selected consumer will recognize Coke. Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "as" symbol. . Question 13 6 pts 9 1 The total number of observations n = 40 in the following cumulative frequency distribution table. Find the missing value cumulative frequency percent, denoted X. Note that the frequency of that class is provided. Cumulative Class Frequency Frequency Percent 5- 9 7.500% 10 - 14 5 X 15 - 19 35.000% 20 - 24 72.500% 25 - 29 90.000% 30 - 34 100.000% Do not round your answer. X = %. Question 15 4 pts 1 A CEO of Awesome Coolers owns 7 pairs of pants, 8 shirts, 8 ties and 4 jackets. How many different outfits can he wear to the office if he must wear one of each item? The CEO has different outfits.I Question 15 E 12 pts '0 1 The time needed to complete a math examination is bell-shaped with a mean of 120 minutes and a standard deviation of 15 minutes. a] What percentage of students will complete the exam in 105 minutes or less? b} Assume that the class has 19D students and that the examination period is 150 minutes in length. How many students do you expect will not be able to complete the exam in the allotted time? Round answer to the nearest whole numbers |:| c} A student is classified as extremer "efficient" if the amount of time spent on the exam is the lowest 2.5% for the distribution. What is the upper limit for the time it takes an extremely "efficient" student to finish the exam? minutes . Question 17 6 pts 9 1 0 Details A sample of size n = 21 has a mean of @ = 73. After one observation was removed from the sample, the sample mean becomes 72.975. What value was removed? Choose the closest: 074.25 070 O 65.5 074.75 071 O 80.5 073.5 078.75. Question 18 Given the following simple linear regression equation: y = 135 - 155x Match each of the following descriptions with its terms/values: - v independent variable a. y estimated value of the dependent value b. - 155 - v estimated y-intercept c. y - v estimated slope d. x e. 135