Instructions: 1. Answer all questions. 2. You must submit your answers as a PDF document. QUESTION 1 (a) Suppose a Statistics Honors student wants to investigate the performance of a sample of 30 STA1506 students for his research project. The student entered the datain Microsoft Excel in column Z with the label "STA1506 Assignment 3 marks", where the second row is the label and the data starts from row 3. Give the command for calculating the following statistics using the MS Excel formula. (i) Mean, x. (ii) Standard deviation, s. (iii) First quartile, Qi. (iv) Median. (v) Coefficient of variation. (b) Another student requested and obtained a sample of 52 STA1506 marks for the same investigations and the marks in percentages were 72 64 66 55 65 49 82 74 46 78 75 03 62 84 86 85 95 89 92 84 26 85 85 91 57 70 91 87 90 60 177 40 71 41 91 64 53 59 54 (1) (1) (1) (1) (1) 74 53 169 84 94 93 69 94 64 53 49 74 (i) Enter the data in Excel in columns A to M and name the MS Excel sheet "STA1506 Marks" and attach the spreadsheet. Among the data records, the student had some data entry errors: 169 is supposed to be 19 and 177 is supposed to be 77, and lastly, the missing record is 51. (4) (ii) Compute the mean, mode, median, range, standard deviation, coefficient of variation, lower quartile, upper quartile, IQR, and SIQR_ of the data using the formula bar and attach the spreadsheet. [Use the MS Excel formula] (18) (iii) Use the Excel analysis toolpak to obtain the descriptive statistics of the data and attach the spreadsheet with the output. (2) STA1506/104/0/2025 (iv) Now, on the same data, arrange from A1 to M4 in column A only starting at A1. Note that this data was previously arranged from A1 to M1, A2 to M2, and so on. Then use the Excel \"Data Analysis\" to obtain the descriptive statistics of the data and attach the spreadsheet with the output. (4) (v) From the results you obtained when evaluating (iv) and (iii), explain the difference between their sample sizes. Which is more representative of the STA1506 class marks among the two representations? (vi) From the answer you obtained in (iii), which column is more and less variable? (4) (4) (vii) Suppose the requirement to be accepted in the 2027 first-year Data Science degree in Statistical analysis is 85%, from the sample obtained; what percentage of students would qualify to get into the Data Science pilot degree in Statistical analysis, offered in UNISA for the 2027 academic year? What percentage do you think should be the accepted entrance percentage from the STA1506 course? (c) The following data is the cost of electricity in hundreds of rands during 2018 for a random sample of 50 two-bedroom apartments in Akasia, Pretoria. Cost of electricity (100Rs) 19.6 27.1 15.7 18.5 14.1 149 95 16.3 10.8 20.2 9 20.6 15 11.9 28.3 17.8 24.7 20.2 15.3 11.6 17.2 111 148 17.5 12.3 12.8 144 154 13 14.3 28.7 15.1 114 13.5 19.1 20.7 21.3 16.8 16.6 13.7 22.7 13 10.9 13.9 12.9 18.2 26.5 16.7 14.9 15.8 Using Microsoft Excel and outlining all steps taken: (4) (i) Construct a histogram of the data where the bin width is 2.0, the number of bins is 10, and a box whisker plot identifying the following values after the box whisker plot: Q1, Median, Mean, Q3, Maximum observation, and Minimum observation. Comment on the skewness of the data. Is there an outlier in the data? (ii) Around what amount does the monthly electricity cost seem to be concentrated? (Note: Ensure that all graphs are given titles, and the titles are centred.] (15) (2) [62]