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). Question 1 15 pts 9 1 The 5-number summary for a data set is as follows: - 46 - 4 18 26 66 a. The range of the dataset = b. The third (upper) quartile = c. The interquartile range, IQR = and it represents the range of the middle of the data. d. The 50" percentile = e. About 75% of the data are greater than f. There are about of the data between 26 and 66.I Question 2 E 6 pts '52) 1 A computer password is required to be 3 characters long. How many passwords are possible if the password requires 2 letteris} followed by 5 digits [numbers 0-91, where no repetition of any letter or digit is allowed? There are C] possible passwords. . Question 3 10 pts 0 1 Given the following table of scores, calculate the indicated locator and percentile. Do not round your results. 6 7 10 11 13 15 16 17 18 22 23 24 27 32 33 35 37 38 41 48 a) Calculate the locator for the 42th percentile, L42. L42 = b) Determine the 42th percentile, P42. P42= c) Approximately, what percent of the scores in a dataset are above the 42th percentile? %Question 4 4 pts 0 1 0 Details 4 points possible Choose the best description for the given variable: a. purchase price of an item plus tax O quantitative-discrete O quantitative-ordinal O qualitative-continuous O quantitative-nominal O quantitative-continuous O qualitative-ordinal O qualitative-nominal b. number of mobile devices owned O quantitative-nominal O quantitative-discrete O qualitative-nominal O qualitative-continuous O qualitative-ordinal O quantitative-ordinal O quantitative-continuous. Question 5 3 pts 5 1 In a study, the data you collect is Number of traffic tickets. What is the level of measurement? O nominal O ordinal O interval Oratio. Question 6 8 pts 0 1 Match each of the following to the type of sampling technique used: - A company groups the batches of a product made in a month into which shift they were made. The number of defective items is counted in randomly selected batches in each shift. - A company chooses every 15th batch of a product off the assembly line and counts the number of defective items in each chosen batch. A company lists all of the batches of a product made in a given month. The number of defective items is counted in randomly selected batches. - A company divides the batches of a product made in a month into which day they were made. Then certain days are picked and every batch made that day is counted to determine the number of defective items. - A company takes the first 10 batches of a product made and counts the number of defective items in each of these batches. a. stratified sample b. simple random sample c. convenience sample d. systematic sample e. cluster sampleI Question 3' E 3 pts '52) 1 A regression was run to determine if there is a relationship between hours of TV watched per day [at] and number of situps a person can do {3*}. The results of the regression were: 3} 2 be: l o. b = 0.937 a = 30.927 R2 = [1.6889 a] Use this to predict the number of situps a person who watches 5 hours of TV can do [to 3 decimal places} C} b} What is the 1Iralue of the correlation coefficient [to 3 decimal places} ? C} . Question 8 8 pts 5 1 Suppose you want to know what high school incoming freshman at a particular college came from. To estimate the percentage of incoming freshman from each of the area's high schools you take a sample of 200 incoming college freshman. Match the following: - van incoming college freshman - 200 incoming college freshman - percentage of the 200 incoming college freshmen who graduated from each area high school - percentage of all incoming freshman who graduated from each area high school - > all incoming college freshmen - high school graduated from a. variable b. sample c. population d. statistic e. individual f. parameter