The table below consist of employees' annual salary by their age group. Annual Salary ($'000) Cumulative...

       

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The table below consist of employees' annual salary by their age group. Annual Salary ($'000) Cumulative number of employees 10-30 30-50 50-70 70-90 90-110 110-130 130-150 150-170 Grand Total (a). Number of employees aged 40 and over 6 10 22 31 14 8 00 8 2 101 6 16 38 69 83 91 99 101 Cumulative % of Employee aged 40 and Over 5.94% 15.84% 37.62% 68.32% 82.18% 90.10% 98.02% 100.00% From the above table with employees' annual salaries given in groups, state some of the problems when computing the mean salary of the employees who are aged 40 and above years age. In this case what is the approximations would you require to make? (b). Next we want to evaluate the median annual salary. In this case, What is the definition of the median? i. 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 400 and above years of age is estimated to $38,956.47: i. Illustrate with the formula how this standard deviation is calculated from the mean and the data values. (2 marks) iii. 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 (or approximately normally) distributed, we often use the empirical rule to construct a confidence interval. For example, based on ±2 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 ($76,000), explain what would be a problem about this approach? (2 marks) The table below consist of employees' annual salary by their age group. Annual Salary ($'000) Cumulative number of employees 10-30 30-50 50-70 70-90 90-110 110-130 130-150 150-170 Grand Total (a). Number of employees aged 40 and over 6 10 22 31 14 8 00 8 2 101 6 16 38 69 83 91 99 101 Cumulative % of Employee aged 40 and Over 5.94% 15.84% 37.62% 68.32% 82.18% 90.10% 98.02% 100.00% From the above table with employees' annual salaries given in groups, state some of the problems when computing the mean salary of the employees who are aged 40 and above years age. In this case what is the approximations would you require to make? (b). Next we want to evaluate the median annual salary. In this case, What is the definition of the median? i. 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 400 and above years of age is estimated to $38,956.47: i. Illustrate with the formula how this standard deviation is calculated from the mean and the data values. (2 marks) iii. 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 (or approximately normally) distributed, we often use the empirical rule to construct a confidence interval. For example, based on ±2 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 ($76,000), explain what would be a problem about this approach? (2 marks)