Question 4 [(2 + 4 + 4) + (2 + 2 + 4+ 2) = 20 marks] (a). A survey of all the 113 firms in a small state was carried out to find the number of people employed at each of the sectors. The results are shown in the following table. Number of 1 - 10 11-20 21-30 31 -40 41 -50 Employees Frequency 35 34 14 12 18 ( Find the mean. (mi) Calculate the standard deviation. (mii) Find the median. [Verify your answer by MICROSOFT EXCEL and attach the printowl (b). The Connect Internet service officer takes a sample of 30 subscribers to find out the number of hours they spent 'on-line' in the last month. Here are the results: 9 14 15 16 17 18 21 23 24 24 27 28 3.3 36 37 39 39 401 41 43 44 45 47 48 53 57 59 63 () Construct a stem-and-leaf plot for the raw data. (1i) Explain why it is likely that the underlying population of all users may have a symmetric distribution? Give two reasons. (mii) Construct a frequency distribution for these data, using 5 classes. (iv) Construct a histogram and a frequency polygon for the cumulative frequency distribution. [Verify your answer by MICROSOFT EXCEL and attach the printow]