Background of Data In this exam, you will at some analysis on a Technology company employee and their experience, education and their annual salary. In addition, the company examines various departments and their relationship with the employee proles. The data is based on the records from 2003 to 2010. You are required to examine the outputs covering different areas of the analysis and provide the insight report for the company to understand its departmental roles and their driving capacity towards the iture expansion in the country. Question 1 (18 marks} The table below consist of employ-recs1 annual salary by their age group. Annual Salary Number of employees Cumulative number Cumulative '56 of Employee lS'OD] aged 40 and over of employees aged 40 and over 10 22 31 14 S 110-130 130-150 8 150-170 2 Grand Total (a). From the above table with employees' annual salaries given in groups, state some of the problems when computing the mean salaryr of the employees who are aged 40 and above years age. In this case what is the approximations would you require to make? (2 marks] (b). Next we want to evaluate the median annual salary. In this case, What is the definition of the median?ii. Based on the table above, describe how you would calculate the median annual salary of the employees aged 40 and over years. (2 marks] iii. Using the above method you have described in the previous question, give the median estimate for the median for the employees aged 40 and above years old. (1 mark) (c). The employees who are aged 40 and over years have annual mean salary of about $79,885. If the median you found in part (b) is approximated to $76,000, what does this tell us about the shape of the distribution of the data set? Give some intuition for why this shape? (3 marks)(d). Given the sample standard deviation of employees who are 40'!) and above years of age is estimated to $383564? i. Illustrate with the formula how this standard deviation is calculated 'om the mean and the data values. (2 marks) ii. Describe in words the above formulaic. how the standard deviation is calculated from the mean and the data values, and how it meamres the spread of the data. {3 marks] ili. Other measure of the spread/dispersion of the data include the interquartile range (IQR), range and coefficient of variation (CV). Explain how the range and IQR are calculated. Why the standard deviation (SD) is generally a better measure of spread/dispersion than the range and even IQR. (2 marks)iv. When the data is normally,r (or approximately normally] distributed, we often use the empirical rule to construct a condence interval. For example, based on 12 standard deviations either side of the mean, this range usually covers 95% of the. For our data with a mean of $79,885, standard deviation of $38,956 salary of the employees aged 40' and over years old and the median you estimated earlier ($?6,000], explain what would be a problem about this approach? (2 marks]