Please see the assignment attached. PART A: FREQUENCIES AND HISTOGRAMS Note: first read the posted textbook chapter (of Bluman) and watch the posted video; your solution should also cover the below mentioned steps: PROBLEM 1 (30 points) The (rounded) average price for a box of cookies obtained from different bakeries is listed below: 40 23 11 20 22 20 45 15 26 22 15 40 19 15 21 25 12 23 45 20 30 10 51 10 42 49 a. Construct a grouped frequency distribution and a cumulative frequency distribution with 5 classes. Note: give a brief explanation by specifying the covered steps. Grouped Frequency Distribution Step 1. Find Range: Step 2. Compute classes’ width (always round-up) Step 3. Create class boundaries Classes Class Boundaries Frequency Cumulative Frequency Distribution Step 1. Find Range: Step 2. Compute classes’ width: Step 3. Find the frequencies and the corresponding percentage Price Per Box Cumulative Frequency Percentage b. Use Excel to construct a Histogram. (Tools à Data Analysis à Histogram à for input range select the given values, for the bin range select the classes upper boundaries values à check Chart Output). PART B: DESCRIPTIVE STATISTICS (60 points) Note: Please round your results to 2 decimals; When the 3rd decimal is 5 or more you round up, otherwise you round down. For example: 0.398 I rounded to 0.40; 0.3923 is rounded to 0.39 For two of the below problems, COMPUTE ALL DESCRIPTIVE STATISTICS (WITHOUT using the excel’s tool “descriptive statistics”) – mean, median, mode, quartiles, range, inter-quartile range, variance, standard deviation, coefficient of variation. An example of solution is given in problem 1 solution. Remember two important things about typing in Excel: (1) to start typing, just click on the desired cell; (2) if what you type starts with “=”, it tells Excel to compute something instead of just displaying a value. When you want to enter a formula type “=” first. If you use an excel function, don’t type “=”; just click on the cell and next choose the excel function from the list of functions. For the rest of the problems COMPUTE ALL DESCRIPTIVE STATISTICS using the tool of your choice. If you use the excel tool “descriptive statistics” be sure you complete your solution by given the missing descriptive statistics (inter-quartiles, coefficient of variation). Double check the mode value(s). The excel tool gives only one mode value even if the set is multimode. Show the Excel output. For only one of the problems (of your choice) convert the data to Z-scores. You should always explain (comment, justify) the answers of your homework. Pay attention to the solution of problem 1 PROBLEM 1: #colds / year subjects 10; 8; 5; 2; 3; 3; 3; 6; 4; 2; 4; 5; 4; 4; 1; 0; 3; 5; For computations done by hand, data must be ordered. 0 1 2 2 3 3 3 3 4 Median 4 4 4 5 5 5 6 8 10 Q1 Q3 Sample mean = =72/18 = 4 colds Sample median = 4 colds (midpoint of data) Sample mode = 3 and 4 (the value that occurs most often; this is a bimodal data set) First Quartile (approximation) = 0.25 * N = 0.25 * 18 = 4.5; If the value is not an integer, we can round it up to the nearest integer 5 à value is 3 Third Quartile (approximation) = 0.75 * N = 0.75 * 18 = 13.5 à 14 à value is 5 Range = max – min – 0 = 10 IQR = Q3 – Q1 = 5 – 3 = 2 Variance = s 2 = = 96/17 = 5.64 colds squared Standard deviation = s = = 2.37 colds Coefficient of variation = CV = x 100% =2.37/4 *100% = 59.25% To convert to a Z-score: Zi = (Xi – mean)/s The 0 becomes (0 – 4) / 2.37 = -1.68; the 1 becomes (1 – 4) /2.37 = -1.27; the 2 becomes (2- 4)/2.37 = .84; and the 4 becomes a 0; etc. All values below the mean have negative Z scores and all values above the mean have positive Z scores. Below is the output from MS Excel using the descriptive tool. For your homework solution an output as the one below (for the excel solution) will be sufficient. Column1 Mean 4 Standard Error 0.560112 Median 4 Mode 3 Standard Deviation 2.376354 Sample Variance 5.647059 Kurtosis 1.497461 Skewness 0.887652 Range 10 Minimum 0 Maximum 10 Sum 72 Count 18 Quartiles are approximations. A more refined definition is the following: For Lower Quartile (25%): Sort all observations in ascending order Compute the position L1 = 0.25 * N, where N is the total number of observations. If L1 is already a whole number (integer), the lower quartile is midway (average) between the L1-th value and the next one. If L1 is not a whole number, change it by rounding up to the nearest integer. The value at that position is the lower quartile. For Upper Quartile(75%): Sort all observations in ascending order Compute the position L3 = 0.75 * N, where N is the total number of observations. If L3 is a whole number, the upper quartile is midway (average) between the L3-th value and the next one. If L3 is not a whole number, change it by rounding up to the nearest integer. The value at that position is the upper quartile. Please follow the above definitions in calculating the quartiles. Note: each of the following problems is 15 points. PROBLEM 2: average wait in minutes for subway Y: 25 4 5 5 5 6 12 17 10 10 13 8 15 16 PROBLEM 3: # employee absences 1 0 1 4 6 2 2 3 2 2 1 0 5 5 7 PROBLEM 4: Grades received in BUS310-01 course: 77 53 72 92 97 85 79 81 PROBLEM 5: Time to complete a specific job (in minutes) 10 14 12 11 12 8 8 7 6 5 9 4 5 13 14 10 9 10 12 10 PART A: FREQUENCIES AND HISTOGRAMS Note: first read the posted textbook chapter (of Bluman) and watch the posted video; your solution should also cover the below mentioned steps: PROBLEM 1 (30 points) The (rounded) average price for a box of cookies obtained from different bakeries is listed below: 40 23 11 20 22 20 45 15 26 22 15 40 19 15 21 25 12 23 45 20 30 10 51 10 42 49 a. Construct a grouped frequency distribution and a cumulative frequency distribution with 5 classes. Note: give a brief explanation by specifying the covered steps. Grouped Frequency Distribution Step 1. Find Range: Step 2. Compute classes’ width (always round-up) Step 3. Create class boundaries Classes Class Boundaries Frequency Cumulative Frequency Distribution Step 1. Find Range: Step 2. Compute classes’ width: Step 3. Find the frequencies and the corresponding percentage Price Per Box Cumulative Frequency Percentage b. Use Excel to construct a Histogram. (Tools à Data Analysis à Histogram à for input range select the given values, for the bin range select the classes upper boundaries values à check Chart Output). PART B: DESCRIPTIVE STATISTICS (60 points) Note: Please round your results to 2 decimals; When the 3rd decimal is 5 or more you round up, otherwise you round down. For example: 0.398 I rounded to 0.40; 0.3923 is rounded to 0.39 For two of the below problems, COMPUTE ALL DESCRIPTIVE STATISTICS (WITHOUT using the excel’s tool “descriptive statistics”) – mean, median, mode, quartiles, range, inter-quartile range, variance, standard deviation, coefficient of variation. An example of solution is given in problem 1 solution. Remember two important things about typing in Excel: (1) to start typing, just click on the desired cell; (2) if what you type starts with “=”, it tells Excel to compute something instead of just displaying a value. When you want to enter a formula type “=” first. If you use an excel function, don’t type “=”; just click on the cell and next choose the excel function from the list of functions. For the rest of the problems COMPUTE ALL DESCRIPTIVE STATISTICS using the tool of your choice. If you use the excel tool “descriptive statistics” be sure you complete your solution by given the missing descriptive statistics (inter-quartiles, coefficient of variation). Double check the mode value(s). The excel tool gives only one mode value even if the set is multimode. Show the Excel output. For only one of the problems (of your choice) convert the data to Z-scores. You should always explain (comment, justify) the answers of your homework. Pay attention to the solution of problem 1 PROBLEM 1: #colds / year subjects 10; 8; 5; 2; 3; 3; 3; 6; 4; 2; 4; 5; 4; 4; 1; 0; 3; 5; For computations done by hand, data must be ordered. 0 1 2 2 3 3 3 3 4 Median 4 4 4 5 5 5 6 8 10 Q1 Q3 Sample mean = =72/18 = 4 colds Sample median = 4 colds (midpoint of data) Sample mode = 3 and 4 (the value that occurs most often; this is a bimodal data set) First Quartile (approximation) = 0.25 * N = 0.25 * 18 = 4.5; If the value is not an integer, we can round it up to the nearest integer 5 à value is 3 Third Quartile (approximation) = 0.75 * N = 0.75 * 18 = 13.5 à 14 à value is 5 Range = max – min – 0 = 10 IQR = Q3 – Q1 = 5 – 3 = 2 Variance = s 2 = = 96/17 = 5.64 colds squared Standard deviation = s = = 2.37 colds Coefficient of variation = CV = x 100% =2.37/4 *100% = 59.25% To convert to a Z-score: Zi = (Xi – mean)/s The 0 becomes (0 – 4) / 2.37 = -1.68; the 1 becomes (1 – 4) /2.37 = -1.27; the 2 becomes (2- 4)/2.37 = .84; and the 4 becomes a 0; etc. All values below the mean have negative Z scores and all values above the mean have positive Z scores. Below is the output from MS Excel using the descriptive tool. For your homework solution an output as the one below (for the excel solution) will be sufficient. Column1 Mean 4 Standard Error 0.560112 Median 4 Mode 3 Standard Deviation 2.376354 Sample Variance 5.647059 Kurtosis 1.497461 Skewness 0.887652 Range 10 Minimum 0 Maximum 10 Sum 72 Count 18 Quartiles are approximations. A more refined definition is the following: For Lower Quartile (25%): Sort all observations in ascending order Compute the position L1 = 0.25 * N, where N is the total number of observations. If L1 is already a whole number (integer), the lower quartile is midway (average) between the L1-th value and the next one. If L1 is not a whole number, change it by rounding up to the nearest integer. The value at that position is the lower quartile. For Upper Quartile(75%): Sort all observations in ascending order Compute the position L3 = 0.75 * N, where N is the total number of observations. If L3 is a whole number, the upper quartile is midway (average) between the L3-th value and the next one. If L3 is not a whole number, change it by rounding up to the nearest integer. The value at that position is the upper quartile. Please follow the above definitions in calculating the quartiles. Note: each of the following problems is 15 points. PROBLEM 2: average wait in minutes for subway Y: 25 4 5 5 5 6 12 17 10 10 13 8 15 16 PROBLEM 3: # employee absences 1 0 1 4 6 2 2 3 2 2 1 0 5 5 7 PROBLEM 4: Grades received in BUS310-01 course: 77 53 72 92 97 85 79 81 PROBLEM 5: Time to complete a specific job (in minutes) 10 14 12 11 12 8 8 7 6 5 9 4 5 13 14 10 9 10 12 10