The number of employees absent from work at a large electronics manufacturing plant over aperiod of 106 days is given in the table below.
146 141 139 140 145 141 142 131 142 140 144 140
138 139 147 139 141 137 141 132 140 140 141 143
134 146 134 142 133 149 140 143 143 149 136 141
143 143 141 140 138 136 138 144 136 145 143 137
142 146 140 148 140 140 139 139 144 138 146 153
148 142 133 140 141 145 148 139 136 141 140 139
158 135 132 148 142 145 145 121 129 143 148 138
149 146 141 142 144 137 153 148 144 138 150 148
138 145 145 142 143 143 148 141 145 141
The company wants you to summarise the data and present it at the next board meeting in orderthat appropriate decisions can be made. Answer the following questions as a means to investigatethe best form of data presentation at the next board meeting. All graphs should be self explanatory.
(a) Construct a stem-and-leaf diagram. Don't round the data but be innovative in your choiceof a stem so that the diagram has between 5 and 10 stems.
(b) Construct three frequency distributions by using each of the following as the first class: "117 to less than 132", "119 to less than 126", and "120 to less than 122". Which frequency distribution provides the best summary? Explain your answer briefly. (Use a maximum of 100 words).
(c) Draw a histogram for the frequency distribution in Part (b) with the first class "119 to less than 126". On the same graph draw the frequency or percentage polygon.
(d) Draw an ogive or cumulative percentage polygon for the frequency distribution in Part (b) with the first class "119 to less than 126". The company wants to keep the plant operating each day and so is interested in the maximum number of staff absent on 95% of days. Use the ogive to determine the value of X where 95% of days have X (or fewer) staff absent. Describe briefly how you determined X or show your working on the ogive.
(e) When delivering the presentation at the board meeting, a board member asks why you didn't present the data in a Pareto diagram. How would you answer the question? (Use a maximum of 100 words).