Question 1 [20 marks]: A cash management software used to forecast optimal cash demand at an ATM located in Newnham. Observing 20 transactions, the software reports the amount withdrawn of each transaction (A$) as follows: 195 80 150 50 70 120 50 160 70 20 100 50 20 100 70 100 190 50 20 120 (a) Determine the mean, mode, median and standard deviation of the above raw data. [4 marks] (b) Complete the following grouped data table and determine the mean of the grouped data of transactions. [4 marks] Amount withdrawn Number of transactions 0 & under 50 50 & under 100 100 & under 150 150 & under 200 (c) Is the mean found in part (b) similar to the mean found in part (a)? Explain why. [2 marks] (d) Using the following formula Median - Im + 2/2 -1 fm -F i - Im + ( 2 / 2 - F ) to determine the median of the grouped data. (6 marks] (e) Calculate the standard deviation based on the grouped data you have constructed in part (b). (4 marks]