Problem 2 [12 points]: Consider the descriptive statistics of 15 data points x., x;, ..., x]; as follow: 2= 15, s2 =32. Qo=11. 01 = 14. Q: =04= 17 (a) [4 points] Calculate the values of lm, 23:19:;- + 1)2 and the IQR. (b) [4 points] If we transform the original data x.- to the new data y; as follows: yi=23xi for i=1,2,3.....15 What are the sample mean, median, range and sample variance of 311. 31;, , 3115? (c) [4 points] Suppose that two new data points Jr\"5 = 23 x1, = 18 is added to the original data set. What are the (5) sample mean and (ii) median and (iii) sample variance of the 17 data points x1,x2, ...,x15.xu