STAT 200 ASS2 2023

1 STAT 200 Assignment 2 For On-Line Students, be sure to:  Do any Excel or JMP analysis first  You will then be asked a series of questions  For numerical questions, enter the exact number only, without symbols (like $ or %).  Use the proper rules of rounding Key Topics  Measures of Central Tendency  Measures of Spread and Dispersion  Stem & Leaf Plot and describing distributions  Using Excel to graph data 1. The following is a small data set of 27 observations. I want you to calculate some basic descriptive statistics for the data. I suggest that you use Excel to do this, but you can also do the work with a calculator. I will ask for the answers, but also that you know the formulas, including the computation formula for the variance that uses the Sum(X) and the Sum(X 2 ). For the computational formula, you will want to calculate a separate row of each value squared in order to calculate the Sum(X 2 ), Excel will also calculate this for you. The Excel file Basic Stat 2020.xlsx would be helpful for this assignment. The data below is in table form and can be copied directly into Excel. VAR1 43 56 56 54 47 56 48 48 49 42 38 45 61 55 64 65 58 48 58 44 56 47 38 40 49 43 60 a. Create a Stem and Leaf Plot of the data (it is easy to do in Word by making a two-column table and entering the numbers in there, bolding the stems) 1

Stem Leaf 3 8 8 4 0 2 3 3 4 5 7 7 8 8 8 9 9 5 4 5 6 6 6 6 8 8 6 0 1 4 5 b. Calculate the Sum(X) and the Sum(X 2 ). You want to be able to show the variance calculated from the computational formula generates the same result as using the VAR.S function in Excel. Sum(X) = 1368 Sum(X 2 )= 70898 c. Calculate the following:  Mean = 50.667  Median = 49  Mode = 56  Range = 27  Variance = 61  Std. Deviation = 7.810  Coefficient of Variation = 15.415 d. Calculate a z-score for a data value of 65 and 38. Describe these in words. 65 – z-score = 1.835 Both of these scores are less than 3 and greater than -3 so they are not not outliers. 35 – z-score = -1.622 2. The Super Bowl is one of the most watched sports events in the U.S. There have been 57 Super Bowls played since the first in 1967. The data below are in the form of the Stem and Leaf plots for the Winning score and the losing Score. I have also given you the Sum(X), the Sum(X 2 ), and some other summary data for each variable. You can solve for everything using the information given in the plots and the sums. The Excel file Basic STATs 2020.xlsx has a tab that helps to do this. The actual data is given at the end in a table. Winner Los er STEM LEAF COUNT STEM LEAF COUNT 0 0 0 3 3 2 0 0 0 6 7 7 7 7 7 8 9 9 9 1 3 4 2 1 0 0 0 0 0 0 0 0 3 3 4 4 4 13 1 6 6 6 7 4 1 6 6 6 7 7 7 7 7 7 7 7 9 9 9 14 2 0 0 0 1 1 1 3 3 3 4 4 4 4 13 2 0 0 0 1 1 1 1 3 4 4 4 11 2 6 7 7 7 7 7 8 9 8 2 5 6 8 9 4 3 0 1 1 1 1 1 1 2 2 3 4 4 4 4 14 3 1 1 3 3 3 5 5 5 7 8 8 8 9 8 3 5 1 4 1 2 3 3 4 0 4 6 8 9 3 4 0 5 2 1 5 0 5 5 1 5 0 3| 1 stands for 31 points 3| 1 stands for 31 points Sum(X) 1718.000 Sum(X) 939.0000 Sum(X^2) 56950.000 Sum(X^2) 18797.000 Q1 23.000 Q1 10.000 2

5 V Jan. 17, 1971 16 13 3 6 VI Jan. 16, 1972 24 3 21 7 VII Jan. 14, 1973 14 7 7 8 VIII Jan. 13, 1974 24 7 17 9 IX Jan. 12, 1975 16 6 10 10 X Jan. 18, 1976 21 17 4 11 XI Jan. 9, 1977 32 14 18 12 XII Jan. 15, 1978 27 10 17 13 XIII Jan. 21, 1979 35 31 4 14 XIV Jan. 20, 1980 31 19 12 15 XV Jan. 25, 1981 27 10 17 16 XVI Jan. 24, 1982 26 21 5 17 XVII Jan. 30, 1983 27 17 10 18 XVIII Jan. 22, 1984 38 9 29 19 XIX Jan. 20, 1985 38 16 22 20 XX Jan. 26, 1986 46 10 36 21 XXI Jan. 25, 1987 39 20 19 22 XXII Jan. 31, 1988 42 10 32 23 XXIII Jan. 22, 1989 20 16 4 24 XXIV Jan. 28, 1990 55 10 45 25 XXV Jan. 27, 1991 20 19 1 26 XXVI Jan. 26, 1992 37 24 13 27 XXVII Jan. 31, 1993 52 17 35 28 XXVIII Jan. 30, 1994 30 13 17 29 XXIX Jan. 29, 1995 49 26 23 30 XXX Jan. 28, 1996 27 17 10 31 XXXI Jan. 26, 1997 35 21 14 32 XXXII Jan. 25, 1998 31 24 7 33 XXXIII Jan. 31, 1999 34 19 15 34 XXXIV Jan. 30, 2000 23 16 7 35 XXXV Jan. 28, 2001 34 7 27 36 XXXVI Feb. 3, 2002 20 17 3 37 XXXVII Jan. 26, 2003 48 21 27 38 XXXVIII Feb. 1, 2004 32 29 3 39 XXXIX Feb. 6, 2005 24 21 3 40 XL Feb. 5, 2006 21 10 11 41 XLI Feb. 4, 2007 29 17 12 42 XLII Feb. 3, 2008 17 14 3 43 XLIII Feb. 1, 2009 27 23 4 44 XLIV Feb. 7, 2010 31 17 14 45 XLV Feb. 6, 2011 31 25 6 46 XLVI Feb. 5, 2012 21 17 4 47 XLVII Feb. 3, 2013 34 31 3 48 XLVIII Feb. 2, 2014 43 8 35 4

49 XLIX Feb. 1, 2015 28 24 4 50 L Feb. 7, 2016 24 10 14 51 LI Feb. 5, 2017 34 28 6 52 LII Feb. 4, 2018 41 33 8 53 LIII Feb. 3, 2019 13 3 10 54 LIV Feb. 2, 2020 31 20 11 55 LV Feb. 7, 2021 31 9 22 56 LVI Feb. 13, 2022 23 20 3 57 LVII Feb. 12, 2023 38 35 3 5