MATH 131 Lab 2 8/16 The goal of this lab is to organize your data from Lab 1 into frequency distributions and graphs. Graphs should be made by hand, using a ruler. Part 1: V1, Qualitative Data (3 points) A. Prepare a frequency and relative frequency distribution for your qualitative data V1 in the format noted below. Fill in the appropriate data values and frequencies for your data from Lab 1. V1:_Movement Direction Qualitative categories Up Frequency, f 13 Relative frequency, rf .325 Down Same None 23 2 2 .575 .05 .05 B. Prepare a Pareto chart for your data. 25 20 15 23 10 13 5 0 Down Up Series 3 1 2 2 None Same MATH 131 8/16 Lab 2 C. Write a one-sentence explanation about what these charts tell you about your data and whether you expected this result. The data shows that most of the songs went down, same or no movement in direction was pretty close. Also, movement direction going up was a little less than movement direction going down. Part 2: V2, Quantitative Data (3 points) A. List the name for V2, the quantitative variable for this part of the lab. Organize your data into a frequency distribution using between 5 and 10 groups or single values, as appropriate for your data. V2:_Peak Position_________________ V2 values or V2 data groups 1-10 11-20 21-30 31-40 If data groups are used, list class midpoints Frequency, f 27 8 4 1 Relative frequency, rf .675 .20 .125 .025 B. Prepare a relative frequency histogram for your data. Be sure to label clearly. 2 MATH 131 Lab 2 8/16 Chart Title 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1 thru 10 11 thru 20 21 thru 30 30 thru 40 Column3 C. Comment about your histogram. Use words like "symmetric", "skewed left or right", as appropriate. It's skewed to the right of the graph because it goes down as the numbers get higher. Part 3: V3, Quantitative Data (4 points) A. Prepare a frequency distribution for your data, using between 5 and 10 groups. V3:___Weeks on the Chart_______________ V3 data groups 1-20 21-40 41-50 51-70 71-90 91-110 111-130 131-150 Class midpoints 10.5 30.5 40.5 60.5 80.5 100.5 120.5 140.5 3 Frequency, f 6 1 3 3 5 8 4 10 MATH 131 Lab 2 8/16 B. Prepare a frequency polygon using class midpoints. Label carefully. Weeks on the chart 40 35 30 25 20 15 10 5 0 10.5 30.5 40.5 60.5 80.5 100.5 120.5 Column3 C. What does the graphs communicate to you about your data? 10 songs have been on the charts for the highest amount of weeks. 4 140.5 MATH 131 Lab 3 8/16 The goal of this lab is to find descriptive statistics for your quantitative data. Part 1: V2, Quantitative Data (3 points) Use the list of all 40 numbers from Lab 1, column V2 for this part of the lab. A. Identify the name of the quantitative variable V2 that you are using _Peak Position_______. B. Use StatCrunch or Minitab to find Mean Median Mode Standard Deviation 7.9 Minimum Value Maximum Value Q1 Q3 C. Using the appropriate numbers from B above, make a box-and-whisker plot for your data. What does this plot tell you about your data? (2 Points) D. Looking at your list in B, list your Minimum, Maximum and Mean data values. List below and then find the z-score for each. Data Value, x z-score ( z= xx ) s Minimum Maximum Mean E. How do -scores indicate a data value is above the mean? _______________________. z below the mean? _________________________. What -score always corresponds to the mean? ___________________________. z 1 MATH 131 Lab 3 8/16 (2 Points) F. Use Chebychev's Theorem to write a statement about the interval from 2 standard deviations below the mean to 2 standard deviations above the mean. List the specific interval you used for your data. Interpret the result in the context of your data. Part 2: V3, Quantitative Data (3 Points) A. What is the name of your V3 variable? ____Weeks On Chart________________________ B. Fill in the values in the chart below using the frequency distribution in Lab 2, Part 3. You may not need all of the rows below. C. Use the appropriate values in the table to find the mean for your grouped data. Show your computations. Remember Data Groups, using V3 (x f ) x = Frequenc y f Class Midpoint n x f =n D. Use StatCrunch or Minitab to find the mean and standard deviation of the raw data. (from Lab 1). E. Compare the answers in C and D. What accounts for any difference? StatCrunch directions Minitab directions 1. Stat 2. Summary stats 3. Columns 1. Stat 2. Basic Stat 3. Display descriptive statistics 2 xf (xf ) MATH 131 Lab 3 8/16 3 Billboard Top 100 Artists Artist/Group Migos Ed Sheeran Peak Position Weeks on Chart Movement Direction Random Number Information (from previous week) 1 17 up 3 Billboard Music Chart (Top 100 Artists) 1 130 same 4 http://www.billboard.com/charts/artist 100 Brantley Gilbert 3 42 up The Weeknd 1 121 down Drake 1 136 down 15 up means the artist moved up in the rankings from the previous week 5 For week of February 18, 2017 Bruno Mars 1 124 down The Chainsmokers 2 62 down 16 down means the artist moved down in the rankings from the previous week 17 same means the artist didn't move in the rankings from the previous week Rihanna 2 132 down Taylor Swift 1 132 up 23 twenty one pilots 1 94 down 25 Kehlani 11 6 none 28 Adele 1 105 down 29 Shawn Mendes 1 104 down 32 Train 14 7 up 33 Ariana Grande 1 134 down 34 Zayn 1 41 up 39 Alessia Cara 12 74 down 40 Sam Hunt 5 129 up 41 Maroon 5 1 136 down 43 New Edition 20 2 up 45 Big Sean 2 78 down 46 Justin Bieber 1 135 down 48 J. Cole 1 95 down 50 Rae Sremmurd 5 100 down 55 Beyonce 2 134 up 57 Lil Uzi Vert 16 31 down 61 Sia 5 136 down 64 Bell Biv Devoe 28 1 none 67 Metallica 2 86 down 74 Jon Bellion 25 17 down 75 Niall Horan 11 19 up 77 Camila Cabello 29 19 up 78 Marian Hill 33 3 up 79 Eminem 11 136 down 86 John Legend 15 90 down 88 Amine 27 16 up 91 Justin Timberlake 5 90 same 92 Keith Urban 8 97 down Panic! At The Disco 3 63 down 99 Gucci Mane 6 17 up 100 9 21 none means the artist was not ranked in the Top 100 the previous week 96 1 MATH 131 Lab 3 8/16 The frequency distribution you used gives a very different mean. You can use this if you wish or if you have not submitted lab 2 Class 0.5-20.5 20.5 -40.5 40.560.5 60.580.5 80.5100.5 100.5120.5 120.5140.5 Frequenc midpoin y t x*f 11 10.5 115.5 1 30.5 30.5 2 50.5 101 4 70.5 282 7 90.5 633.5 2 110.5 221 13 130.5 1696.5 Total 40 mean = 77 3080 1 MATH 131 Lab 3 8/16 The goal of this lab is to find descriptive statistics for your quantitative data. Part 1: V2, Quantitative Data (3 points) Use the list of all 40 numbers from Lab 1, column V2 for this part of the lab. A. Identify the name of the quantitative variable V2 that you are using _Peak Position_______. B. Use StatCrunch or Minitab to find Mean Median Mode Standard Deviation 7.9 3 1 9.35 Minimum Value Maximum Value Q1 Q3 1 33 1 11.75 Descriptive Statistics: Peak Position Variable Peak Position N 40 N* 0 Mean 7.90 SE Mean 1.48 StDev 9.35 Minimum 1.00 Q1 1.00 Median 3.00 Q3 11.75 Maximum 33.00 Mode 1 C. Using the appropriate numbers from B above, make a box-and-whisker plot for your data. What does this plot tell you about your data? Boxplot of Peak Position 35 30 Peak Position 25 20 15 10 5 0 1 MATH 131 Lab 3 8/16 The data is positively skewed. (2 Points) D. Looking at your list in B, list your Minimum, Maximum and Mean data values. List below and then find the z-score for each. Data Value, x z-score ( z= Minimum 1 -0.726 Maximum 33 2.642 Mean 7.9 0 xx ) s E. How do -scores indicate a data value is above the mean? z __positive__value___________________. below the mean? _________negative value________________. What -score always corresponds to the mean? ________zero___________________. z (2 Points) F. Use Chebychev's Theorem to write a statement about the interval from 2 standard deviations below the mean to 2 standard deviations above the mean. List the specific interval you used for your data. Interpret the result in the context of your data. Based on chebyshevs theorem, about 75% of the data should be within two standard deviations from the mean. interval for my data Lower bound= -10.88 Upper bound =26.6 Values within the interval = 36 % of values within the interval = 90% The data is not consistent with chebyshevs theorem. Part 2: V3, Quantitative Data (3 Points) 2 MATH 131 8/16 Lab 3 A. What is the name of your V3 variable? ____Weeks On Chart________________________ B. Fill in the values in the chart below using the frequency distribution in Lab 2, Part 3. You may not need all of the rows below. C. Use the appropriate values in the table to find the mean for your grouped data. Show your computations. Data Groups, using V3 (x f ) x = Remember Frequenc y f n Class Midpoint x f =n 20-Jan Class midpoin ts 10.5 21-40 30.5 1 41-50 40.5 3 51-70 60.5 3 71-90 80.5 5 91-110 100.5 8 111-130 120.5 4 131-150 140.5 V3 data groups Frequenc y, f 6 Total mean= x* f 10 63 30.5 121.5 181.5 402.5 804 482 1405 40 3490 87.25 D. Use StatCrunch or Minitab to find the mean and standard deviation of the raw data. (from Lab 1). Descriptive Statistics: Weeks on Chart Variable Weeks on Chart N 40 N* 0 Mean 77.28 StDev 49.64 E. Compare the answers in C and D. What accounts for any difference? 3 xf (xf ) MATH 131 8/16 Lab 3 For the frequency distribution, the result is an estimate as compared to that of the Minitab output which is exact as it is based on individual scores StatCrunch directions Minitab directions 1. Stat 2. Summary stats 3. Columns 1. Stat 2. Basic Stat 3. Display descriptive statistics 4 MATH 131 Lab 3 8/16 The frequency distribution you used gives a very different mean. You can use this if you wish or if you have not submitted lab 2 Class 0.5-20.5 20.5 -40.5 40.560.5 60.580.5 80.5100.5 100.5120.5 120.5140.5 Frequenc midpoin y t x*f 11 10.5 115.5 1 30.5 30.5 2 50.5 101 4 70.5 282 7 90.5 633.5 2 110.5 221 13 130.5 1696.5 Total 40 mean = 77 3080 1 MATH 131 Lab 3 8/16 The goal of this lab is to find descriptive statistics for your quantitative data. Part 1: V2, Quantitative Data (3 points) Use the list of all 40 numbers from Lab 1, column V2 for this part of the lab. A. Identify the name of the quantitative variable V2 that you are using _Peak Position_______. B. Use StatCrunch or Minitab to find Mean Median Mode Standard Deviation 7.9 3 1 9.35 Minimum Value Maximum Value Q1 Q3 1 33 1 11.75 Descriptive Statistics: Peak Position Variable Peak Position N 40 N* 0 Mean 7.90 SE Mean 1.48 StDev 9.35 Minimum 1.00 Q1 1.00 Median 3.00 Q3 11.75 Maximum 33.00 Mode 1 C. Using the appropriate numbers from B above, make a box-and-whisker plot for your data. What does this plot tell you about your data? Boxplot of Peak Position 35 30 Peak Position 25 20 15 10 5 0 1 MATH 131 Lab 3 8/16 The data is positively skewed. (2 Points) D. Looking at your list in B, list your Minimum, Maximum and Mean data values. List below and then find the z-score for each. Data Value, x z-score ( z= Minimum 1 -0.726 Maximum 33 2.642 Mean 7.9 0 xx ) s E. How do -scores indicate a data value is above the mean? z __positive__value___________________. below the mean? _________negative value________________. What -score always corresponds to the mean? ________zero___________________. z (2 Points) F. Use Chebychev's Theorem to write a statement about the interval from 2 standard deviations below the mean to 2 standard deviations above the mean. List the specific interval you used for your data. Interpret the result in the context of your data. Based on chebyshevs theorem, about 75% of the data should be within two standard deviations from the mean. interval for my data Lower bound= -10.88 Upper bound =26.6 Values within the interval = 36 % of values within the interval = 90% The data is not consistent with chebyshevs theorem. Part 2: V3, Quantitative Data (3 Points) 2 MATH 131 8/16 Lab 3 A. What is the name of your V3 variable? ____Weeks On Chart________________________ B. Fill in the values in the chart below using the frequency distribution in Lab 2, Part 3. You may not need all of the rows below. C. Use the appropriate values in the table to find the mean for your grouped data. Show your computations. Data Groups, using V3 (x f ) x = Remember Frequenc y f n Class Midpoint x f =n 20-Jan Class midpoin ts 10.5 21-40 30.5 1 41-50 40.5 3 51-70 60.5 3 71-90 80.5 5 91-110 100.5 8 111-130 120.5 4 131-150 140.5 V3 data groups Frequenc y, f 6 Total mean= x* f 10 63 30.5 121.5 181.5 402.5 804 482 1405 40 3490 87.25 D. Use StatCrunch or Minitab to find the mean and standard deviation of the raw data. (from Lab 1). Descriptive Statistics: Weeks on Chart Variable Weeks on Chart N 40 N* 0 Mean 77.28 StDev 49.64 E. Compare the answers in C and D. What accounts for any difference? 3 xf (xf ) MATH 131 8/16 Lab 3 For the frequency distribution, the result is an estimate as compared to that of the Minitab output which is exact as it is based on individual scores StatCrunch directions Minitab directions 1. Stat 2. Summary stats 3. Columns 1. Stat 2. Basic Stat 3. Display descriptive statistics 4