QUESTION 2 (30 MARKS) NECESSARY CALCULATION STEPS TO PRODUCE THE RESULTS SHOULD BE PROVIDED A psychologist did an experiment of mental health issue in 2020, and collected 20 participants' information. Below are the scores of 20 participants' mental health. 21 46 47 55 35 59 38 41 67 45 25 22 55 26 55 63 40 96 43 78 (a) Find the following values of descriptive statistics for the above data set: (i) Find the mean (1 mark), median (1 mark), mode (1 mark). (j) Compute the standard deviation (2 marks). [Please show your steps of calculation] (ii) Find the five-number summary and interquartile range (IQR) of the data set [Please show your steps of calculation] (12 marks). (b) Describe the skewness of the distribution of the data set with reason (4 marks). When the psychologist compared the data in 2019, it is found that the average score is 50. After your investigation, you find the coefficient of skewness of the 2019 data set is -1.2. Based on the above figure, comment the overall performance of people's mental health (4 marks). (c) One news report wants to write a news article about the mental health status in Hong Kong. To present the central tendency of this issue, which value will you use to present, median or mean (2 mark)? Please illustrate your point of view (3 marks). Please correct your final answers to 2 decimal places whenever appropriate