MATH 131 Lab 3 Ryan Smith Answers should be included on this lab. Use additional paper, if needed. 8/11 The goal of this lab is to find descriptive statistics for your quantitative data. Part 1: V2 Quantitative Data Use the list of all 40 numbers from Lab 1, column V2 for this part of the lab. (3 Points) A. B Identify the name of the quantitative variable V2 that you are using. ___Stroke Rates___ Use Minitab to find Mean _________________84.4_______ Median __________65.5_____________ Mode ______22, 29, 39, 112, 151, 163________ Standard Deviation _________________51.668________ Minimum Value ________22________________ Maximum Value ______________173__________ ____________39_________________ Q1 _______________140.5______________ Q3 You may find your statistics using Minitab. Open the worksheet where you saved your lab data or enter your data. Select Stat Basic statistics Display Descriptive Statistics Double click on the location of V2 in the lefthand box to select that data Statistics Check or uncheck to include all the statistics of interest. Minitab does not find the Mode. OK OK 1 C. Consider your values for mean, median and mode listed above. Which is the largest? - 3 of my Modes are larger than the second largest value which is the Mean. Consider the diagrams on p. 71, discuss the similarities and differences among your three measures - The mean is greater than the median making it a skewed right distribution. Which one of these measures of central tendency is most suitable for your data? Explain your choice. - The median is the most suitable measure because the data is skewed right (2 Points) D. Using the appropriate numbers from B above, make a box-and-whisker plot for your data. (See p. 103) What does this plot tell you about your data? - The data is skewed right (2 Points) E. Looking at your list in B, list your lowest, highest and mean data values. List below and then find the z -score for each. (See p. 105) Lowest Data Value, x 22 z - score 22 - 84.4 _______ = -1.21 51.668 Highest 173 Mean 84.4 F. 84.4 - 84.4 __________ = 0 51.668 How do -scores indicate a data value is above the mean? ___If the number is positive____ z below the mean? ____If the number is negative_____ What -score always corresponds to the mean? ________0________ z (3 Points) A. 173 - 84.4 _________ = 171.4 51.668 Part 2: V3, Quantitative Data What is the name of your V3 variable? _______Life Expectancy______________________ 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. Data Groups, using V3 frequency, f 50-56 57-63 64-70 71-77 78-84 4 2 4 14 16 Class Midpoint, x 53 60 69 74 81 xf 212 120 276 1,036 1,296 xX -12.5 -5.5 3.5 8.5 15.5 ( x X )2 156.25 30.25 12.25 72.25 240.25 ( x X )2 f 625 60.5 49 1,011.5 3,844 f n n =40 C. Use the appropriate values in the table to find the mean and standard deviation for your grouped data. Show your computations. (See p. 70 and 88) 2,940 _____ = 73.5 40 5,590 ______ = 143.3 n-1 D. 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. - Chebyshev's inequality says that at least 99.96% of the data values of any distribution must be within 51.668 standard deviations of the mean. NAME 1. Iraq 2. Armenia 3. Turkey 4. Hait 5. Morocco 6. Austria 7. Netherlands 8. Syria 9. Egypt 10. Chad 11. Jamaica 12. Venezuela 13. Mexico 14. Norway 15. Lebanon 16. Iceland 17. Thailand 18. Barbados 19. Guinea 20. Mongolia 21. Yemen 22. Estonia 23. Chile 24. Germany 25. Botswana 26. United States 27. Uganda 28. Vietnam 29. Dominica 30. Denmark 31. Benin 32. Malta 33. Saint Lucia 34. Spain 35. Nigeria 36. Saudi Arabia 37. Croata 38. Switzerland 39. United Kingdom 40. Georgia V1 - Continent Asia Asia Asia Americas Africa Europe Europe Asia Africa Africa Americas Americas Americas Europe Europe Europe Asia Americas Africa Asia Asia Europe Americas Europe Africa Americas Africa Asia Americas Europe Africa Europe Americas Europe Africa Asia Europe Europe Europe Asia V2 - Stroke Rates per 10,000 81 133 117 150 62 26 22 112 110 163 63 54 39 33 53 29 23 41 166 151 84 58 45 31 112 163 151 173 87 39 148 44 68 29 149 50 89 22 37 169 V3 - Life Expectancy 71 74 73 71 74 73 63 77 80 81 69 73 49 73 74 75 82 77 81 74 75 60 69 65 74 78 88 54 80 59 73 77 79 61 80 77 81 82 80 76 MATH 131 LAB 6 8/11 The goal of this lab is to standardize data, to compute probabilities using the standard normal distribution, and to find values given probabilities. (2 points) 1. Use Minitab to compute the mean and standard deviation of your RAW V3 data (as listed in Lab 1). The Minitab instructions are the same as in Lab 3. Mean __________________________________ Standard deviation ___________________________ 2. What are the mean and standard deviation you computed in Lab 3, Part 2? Mean __________________________________ Standard deviation ___________________________ Are these values close to those in question 1? Explain clearly why they could be different. _______________________________________________________________ ______________________________________________________________ *** For the remainder of the labs, use the mean and standard deviation from question 1**** (1 point) 3. Sort the list of 40 data values from smallest to largest, using the Minitab directions below. Write down the raw scores on lines #1, #20, and #40. Compute the corresponding z-scores by using the formula. Round to two decimal places. Line # x value z - score Value in table 4 1 Low value (L) = 20 Middle Value (M) = 40 High Value (H) = (1 point) 4. Using the mean and standard deviation from #1 above, and using the formula , find the data value x that goes with the following z-scores. Use x z and . s x z - score z 2.50 z 3.20 z0 x value 1 MATH 131 LAB 6 8/11 z 0.5 For the rest of the lab, you will make the assumption that your data is approximately normally distributed. For some students this is a reasonable assumption; for others, it is not. If you have any questions about this, please see your instructor. Each problem from 5 - 10 is worth 1 point. 5. a) Sketch a normal curve with your value for x as . b) Locate your low x value (L) and your high x value (H) on the x axis. c) Shade the area between x = L and x = H. d) Use the values from the tables in #3 to find the shaded area. e) Find P(L < x H). _______________________________________ 3 MATH 131 LAB 6 8/11 9 a) Sketch a normal curve using your value for . b) Shade the area where the lowest 10% of your values would be. c) What is the z - score for this area. ___________________ d) Using the method from #4 above, find the value x. e) Use this information to fill in the blanks. The first blank should be your name for x. "10% of all _________________________ in my population are below ____________." 10 a) Sketch a normal curve using your value for . b) Shade the area where the top 5% of your values would be. c) What is the z - score for this area. ___________________ d) Using the method from #4 above, find the value x. e) Use this information to fill in the blanks. The first blank should be your name for x. "5% of all _________________________ in my population are above ____________." Minitab Directions to sort your list of data values: Data Sort select V3 4 MATH 131 LAB 6 8/11 by column (c3 if that is the location of V3) Store in column of current worksheet (pick a column that is empty.) OK 5