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Univariate Data Review

Univariate Data Review. All data goes in L 1. Input the data into your calculator (Stat, Edit, Calc , 1-Var Stats) and find the 5-number summary. 1. a). 18, 20, 28.5, 38, 56. 62, 69, 77.5, 87, 99. b). c). 59, 61.5, 66, 69, 75. 2, 6, 8, 9, 10. All data goes in L 1.

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Univariate Data Review

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  1. Univariate Data Review

  2. All data goes in L1. Input the data into your calculator (Stat, Edit, Calc, 1-Var Stats) and find the 5-number summary. 1. a) 18, 20, 28.5, 38, 56 62, 69, 77.5, 87, 99 b) c) 59, 61.5, 66, 69, 75 2, 6, 8, 9, 10

  3. All data goes in L1. Find the requested statistics for the given sample data. Round answers to nearest tenth. 2. a) Mean = 145.4 Std. Dev. = 25.7 Range = 186 – 117 = 69 IQR = 170 - 123.5 = 46.5 Mean = 174.2 Std. Dev. = 27.2 Range = 208 – 115 = 93 IQR = 197 – 160.5 = 36.5 b) c) Mean = 161.9 Std. Dev. = 24.8 Range = 199 – 122 = 77 IQR = 179.5 – 136 = 43.5 Mean = 169.8 Std. Dev. = 27.8 Range = 199 – 123 = 76 IQR = 193.5 – 151 = 42.5

  4. Identify the data set as “unimodal” (one mode), “bimodal” (two modes), or “multi-modal” (more than two modes). Then identify the mode or modes. a) 3. There are 3 numbers that occur twice. Therefore, this data set is “multi-modal”. The modes are: 14, 15, & 17. Unimodal Mode = 280 b) c) Bimodal The modes are: 133 & 174 Unimodal Mode = 19

  5. All data goes in L1. Complete the frequency table for the given data. a) 4. b) c)

  6. Based on the given frequency table, find the relative frequency of the requested class. Round final answers to nearest hundredth. a) 5. Relative Frequency for the 150-200 class is: Relative Frequency for the 140-190 class is: Total = 269 b) c) Relative Frequency for the 100-125 class is: Relative Frequency for the 500-1000 class is:

  7. Find the cumulative relative frequency for the specified class., to the nearest hundredth. 550-560 class 150-175 class a) 6. 30 30+25=55 55+50=105 105+40=145 145+15=160 b) 300-400 class c) 180-200 class

  8. Based on the given cumulative frequencies, find the median class and estimate the median . a) 7. b) c)

  9. Put data in. Then, Stat, Calc, 1-var, L1, L2. Remember, you have to put in the “class marks” for x in L1. Find the mean and standard deviation of each of the following population frequency distributions, to the nearest tenth. a) 8. L1 L2 30 525 25 50 40 15 25 575 10 Mean = 540.1 Standard Deviation = 17.2 Mean = 142.7 Standard Deviation = 47.4 b) c) Mean = 172.5 Standard Deviation = 35.5 Mean = 454.6 Standard Deviation = 174.6

  10. Sketch as a normal distribution, then use the Empirical Rule to answer the question. Sketch as a normal distribution, then use the Empirical Rule to answer the question. Find the interval of the data that falls within one standard deviation of the mean. Normally distributed data with a mean of 112 and a standard deviation of 19.3. Find the interval of the data that falls within one standard deviation of the mean. Normally distributed data with a mean of 42 and a standard deviation of 4.7. 167.5 180 192.5 205 217.5 230 242.5 0.15% 0.15% 0.15% 34% 34% 34% 34% 0.15% 34% 34% 34% 34% 2.35% 2.35% 2.35% 2.35% 2.35% 2.35% 2.35% 2.35% 13.5% 13.5% 13.5% 13.5% 13.5% 13.5% 13.5% 13.5% 92.7 < x < 131.3 37.3< x < 46.7 55.4 92.7 37.3 78.6 131.3 46.7 43.8 73.4 32.6 112 67 42 54.1 27.9 32.2 90.2 150.6 51.4 169.9 101.8 56.1 Sketch as a normal distribution, then use the Empirical Rule to answer the question. Sketch as a normal distribution, then use the Empirical Rule to answer the question. Normally distributed data with a mean of 67 and a standard deviation of 11.6. Normally distributed data with a mean of 205 and a standard deviation of 12.5. Find the interval of the data that falls within two standard deviations of the mean. Find the interval of the data that falls within three standard deviations of the mean. 0.15% 0.15% 0.15% 0.15% 167.5 < x < 242.5 43.8 < x < 90.2

  11. Sketch as a normal distribution, then use the Empirical Rule to answer the question. Sketch as a normal distribution, then use the Empirical Rule to answer the question. Normally distributed data with a mean of 112 and a standard deviation of 19.3. Find the percent of data that falls above 73.4 . Find the percent of data that falls below 27.9 and above 56.1. Normally distributed data with a mean of 42 and a standard deviation of 4.7. 167.5 180 192.5 205 217.5 230 242.5 0.15% 0.15% 0.15% 34% 34% 34% 34% 0.15% 34% 34% 34% 34% 2.35% 2.35% 2.35% 2.35% 2.35% 2.35% 2.35% 2.35% 13.5% 13.5% 13.5% 13.5% 13.5% 13.5% 13.5% 13.5% 97.5% 0.3% 55.4 92.7 37.3 131.3 78.6 46.7 43.8 73.4 32.6 112 67 42 54.1 32.2 27.9 150.6 90.2 51.4 101.8 169.9 56.1 Sketch as a normal distribution, then use the Empirical Rule to answer the question. Sketch as a normal distribution, then use the Empirical Rule to answer the question. Normally distributed data with a mean of 67 and a standard deviation of 11.6. Normally distributed data with a mean of 205 and a standard deviation of 12.5. Find the percent of data that falls between 55.4 and 90.2. Find the percent of data that falls between 180 and 230. 0.15% 0.15% 0.15% 0.15% 95% 81.5%

  12. Sketch as a normal distribution, then use the Empirical Rule to answer the question. Sketch as a normal distribution, then use the Empirical Rule to answer the question. Find the standard deviation. Normally distributed data with a mean of 66 and that 99.7% of the data falls between 25.5 and 106.5. Find the standard deviation. Normally distributed data with a mean of 79 and that 95% of the data falls between 60.6 and 97.4. 0.15% 0.15% 0.15% 34% 34% 34% 34% 0.15% 34% 34% 34% 34% 2.35% 2.35% 2.35% 2.35% 2.35% 2.35% 2.35% 2.35% 13.5% 13.5% 13.5% 13.5% 13.5% 13.5% 13.5% 13.5% 13.5 9.2 51.4 60.6 69.8 79 88.2 97.4 106.6 Sketch as a normal distribution, then use the Empirical Rule to answer the question. Sketch as a normal distribution, then use the Empirical Rule to answer the question. Normally distributed data with a mean of 185 and that 68% of the data falls between 161 and 209. Normally distributed data with a mean of 85 and that 2.5% of the data falls above 109. Find the standard deviation. Find the standard deviation. 25.5 39 52.5 66 79.5 93 106.5 0.15% 0.15% 0.15% 0.15% 12 24 113 137 161 185 209 233 257 49 61 73 85 97 109 121

  13. A set of data is normally distributed, with a mean of 230 and a standard deviation of 15. Find the z-value associated with the specified x-value by using the formula above, to the nearest hundredth. x = 200 x = 240 x = 195 x = 185

  14. Determine what % of the data falls below the specified z-score by referring to the z-table, to the nearest hundredth of a percent. z = 1.67 z = -1.33 0.0918 = 9.18% 0.9525 = 95.25% z = 0.67 z = -3.33 0.0004 = 0.04% 0.7486 = 74.86%

  15. Determine what % of the data falls abovethe specified z-score by referring to the z-table, to the nearest hundredth of a percent. z = 1.60 z = -1.67 1 – 0.0475 = 0.9525 = 95.25% 1 - 0.9452 = 0.0548 = 5.48% z = -1.97 z = 1.38 1 – .9162 = 0.0838 = 8.38% 1 - .0244 = 0.9756 = 97.56%

  16. Determine what % of the data falls between the specified x-values. Round final answer to the nearest hundredth of a percent. Mean of 230 and standard deviation of 15. x = 240 and x = 255. Mean of 230 and standard deviation of 15. x = 180 and x = 185. .0013 - .0004 = 0.09% 0.9525 – 0.7486 = 0.2039 = 20.39% Mean of 230 and standard deviation of 15. x = 240 and x = 260. Mean of 230 and standard deviation of 15. x = 195 and x = 205. .9772 - .7486 = 22.86% .04750 - .0099 = 3.76%

  17. Determine how many values from the given data set would be expected to fall in the given region. Remember, you must first find the % of data expected to be in that region. Data set with 300 pieces of data, a mean of 400 and standard deviation of 12.5. How many values are expected to fall below 370? Data set with 750 pieces of data, a mean of 134, and a standard deviation of 11.6. How many values are expected to fall below 140? 0.0082 or 0.82% 0.6985 or 69.85% Data set with 1050 pieces of data, a mean of 600, and a standard deviation of 112. How many values are expected to fall below 750? Data set with 2500 pieces of data, a mean of 175, and a standard deviation of 22. How many values are expected to fall below 167? 0.9099 or 90.99% 0.3594 or 35.94%

  18. Determine how many values from the given data set would be expected to fall in the given region. Remember, you must first find the % of data expected to be in that region. Data set with 1300 pieces of data, a mean of 400 and standard deviation of 12.5. How many values are expected to fall above 370? Data set with 50 pieces of data, a mean of 134, and a standard deviation of 11.6. How many values are expected to fall above 140? 1 - 0.0082 = 0.9918 or 99.18% 1 - 0.6985 = 0.3015 or 30.15% Data set with 100 pieces of data, a mean of 600, and a standard deviation of 112. How many values are expected to fall above 750? Data set with 500 pieces of data, a mean of 175, and a standard deviation of 22. How many values are expected to fall above 167? 1 - 0.9099 = 0.0901 or 9.01% 1 - 0.3594 = 0.6406 or 64.06%

  19. Determine how many values from the given data set would be expected to fall in the given region. Remember, you must first find the % of data expected to be in that region. Data set with 350 pieces of data, a mean of 134, and a standard deviation of 11.6. How many values are expected to fall between 140 and 160? Data set with 1900 pieces of data, a mean of 400 and standard deviation of 12.5. How many values are expected to fall between 370 and 405? 0.9875 - 0.6985 = 0.289 or 28.9% 0.6554 - 0.0082 = 0.6472 or 64.72% Data set with 1100 pieces of data, a mean of 600, and a standard deviation of 112. How many values are expected to fall between 750 and 590? Data set with 5500 pieces of data, a mean of 175, and a standard deviation of 22. How many values are expected to fall between 167 and 170? 0.4090 - 0.3594 = 0.0496 or 4.96% 0.9099 – 0.4641 = 0.4458 or 44.58%

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