M2 Problem Set

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Jan 9, 2024

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M2: Problem Set Question 1 0/0pts The following tutorial video demonstrates how to insert a table. You will need to be able to do this to complete the following question. The students in a statistics class have the following majors: Sociology English Biology Education Education History Human Services Accouning Computer Science English Education Computer Science Education Biology English History Human Services Biology Human Services History English Sociology Biology History Education Computer Science Education Accounting English Accounting Education History a) Make a frequency distribution for this data. b) Make a relative frequency distribution for this data. Include relative percentages on this table. a.) Major Frequency Sociology 2 English 5 Biology 4 Education 7 History 5 Human Services 3 Accounting 3 Computer Services 3 Total 32 b.) Major Calculation Relative Relative Frequency Percentage Sociology 2/32 = .0625 6.25 % English 5/32 = 156 156 % Biology 4132 = 125 125 % Education 732 = 219 219% History 5/32 = 156 15.6 % Human Services 3/32 = 0938 9.38 % Accounting 3/32 = .0938 9.38 % Computer Services 3/32 = .0938 9.38 %

The following tutorial video demonstrates how to insert an equation into your answer. This is important to be able to do to complete the following questions. [ Question 2 Opts Consider the following set of data (32.40,52,23,39) a) Find the mean of this sample. b) Find the median. ©) Find the mode of this set. Edit View insert Format Tools Table 120t Paragraph B I VY A-2vT O E G Eg i Question 2 Consider the following set of data: {32, 40, 52, 23, 39} a) Find the mean of this sample. b) Find the median. ¢) Find the mode of this set. 0/0pts

a.) b) In order to find the median, we must first put the numbers in ascending order: 23, 32, 39, 40, 52. The median is the middle number, so the median is 39. c) No number is represented in the set more than once, so there is No Mode.

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Question 3 0/0pts Consider the following set of data: {21,32,21,15,80,84,90,78} a) Find the mean of this sample. b) Find the median. c) Find the mode of this set. There are eight points, so n=8. a) The sample mean is given by: 21+32+21+15+80+84+90+78 ¥= +32+21+ ; +84+90+ = 52625, = b) In order to find the median, we must first put the numbers in ascending order: 15, 21, 21, 32, 78, 80, 84, 90. Notice that there are two “middle” numbers, 32 and 78. The median is the average of these two numbers. Median = (32+78)/2 = 55. c) The number that occurs most is 21. So, the mode is 21.

Question 4 0/0pts Consider the following data: 323 412 380 401 280 301 317 440 297 371 353 394 427 399 375 438 329 309 361 340 a) Find the 60th and 70th percentile of this data. b) Find the quartiles for this data.

There are a total of twenty numbers, so n= 20. In order to find the percentiles, we must put the numbers in ascending order: 280297 301 309 317 323 329 340 353 361 371 375 380 394 399 401 412 427 433 440 a) For the 60th percentile: e (%) n= (%) 20=12. Therefore, the 60th percentile index for this data set is the 12th observation. In the list above, the 12th observation is 375. For the 70th percentile: ._ (P _ (70 _ i=(s)n= (m)zo =14 Therefore, the 70th percentile index for this data set is the 14th observation. In the list above, the 14th observation is 394. b) In order to find the quartiles, first find the median, M, of the data (note that this median is also Q,): _361+371 _ = ———— =366 Next, separate the data into two halves, those values below the median and those values above the median: Bottom half: 280 297 301 309 317 323 329 340 353 361 Top half: 371 375 380 394 399 401 412 427 433 440 Find the median of the bottom half, which is Q;: = 317+323 .0 2 Find the median of the top half, which is Qg: _399+401 _ s=—3 400 In summary Qg = 320 Q; = 366 Q3 = 400.

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Question 5 Consider the following data: {17, 14, 20, 18, 11} a) Find the sample mean of this data. b) Find the range of this data. ¢) Find the sample standard deviation of this data. d) Find the coefficient of variation. 0/0pts

There are five points, so n=5. {17, 14, 20, 18, 11} a) The sample mean is given by: _ Tx 17+14+20+18+11 = = - b) The range is the largest value minus the smallest value: Range=20-11=9 ¢) In order to find the sample standard deviation, we must first find the sample variance: - T(x-%)? _ (17 -16)% + (14— 16)% + (20 - 16)* + (18 - 16)* + (11 - 16)° -1 5-1 =125 The standard deviation is given by: s=s2=V12.5=3.53 d) The coefficient of variation is given by: Coof ficient of Variation < Standard Deviation =~ 353 o o = +100 = +100 =22, oef ficient of Variation o i

Question 6 0/0pts Given a data point x, what does the z-score tell us about x? Your Answer: Z-score tells researchers how many standard deviations x is from the mean of the data set. Solution. Given a data point x, the z-score tells us how many standard deviations x is from the mean.

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Question 7 0/0pts ‘ Suppose that you have a set of data that has a mean of 34 and a standard deviation of 6. a) Is the point 28 above, below, or the same as the mean. How many standard deviations is 28 from the mean. b) Is the point 46 above, below, or the same as the mean. How many standard deviations is 46 from the mean. c) Is the point 43 above, below, or the same as the mean. How many standard deviations is 43 from the mean. d) Is the point 20 above, below, or the same as the mean. How many standard deviations is 20 from the mean. a) The data point 28 is below the mean. Now use the z-score to determine how many standard deviations 28 is below the mean. We are told that the mean is 34 and the standard deviation is 6. So, the z-score is given by: The z-score is -1, so the data point 28 is 1 standard deviation below the mean (the negative sign indicates that the point is below the mean). b) The data point 46 is above the mean. Now use the z-score to determine how many standard deviations 46 is above the mean. We are told that the mean is 34 and the standard deviation is 6. So, the z-score is given by: The z-score is 2, so the data point 46 is 2 standard deviation above the mean (the positive sign indicates that the point is above the mean). ¢) The data point 43 is above the mean. Now use the z-score to determine how many standard deviations 43 is above the mean. We are told that the mean is 34 and the standard deviation is 6. So, the z-score is given by: The z-score is 1.5, so the data point 43 is 1.5 standard deviation above the mean (the positive sign indicates that the point is above the mean). d) The data point 20 is below the mean. Now use the z-score to determine how many standard deviations 20 is below the mean. We are told that the mean is 34 and the standard deviation is 6. So, the z-score is given by: The z-score is -2.333, so the data point 20 is 2.333 standard deviation below the mean (the negative sign indicates that the point is below the mean).

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