Problem 1: Student Survey Data Load the MASS library using the command library(MASS) and consider the dataset survey. a. We want to find the mean height of students in the dataset. However, by using the mean command, we obtain: mean (survey$Height) ## [1] NA Explain why this is happening. How can we compute the mean height? b. Find the median heights of male students and of female students. c. Compute the mean pulse rate for male students under 20. d. Suppose we want to extract the data of students who are taller than 190 cm. Try to execute the command: survey [survey$Height > 190, ] What happens? How can we extract the desired data? e. Extract a dataset showing only pulse rate, exercising frequency, and age of students who are less than 17 or more than 40 years old. f. The ages are recorded as numeric values representing a number of years. Modify the data frame so that the age is measured using an integer number of months (for example, 20.167 years should be converted to 242 months). g. What is the percentage of left handers who do not clap with their left hand on top? h. Create a histogram showing the distribution of students' heights and use a QQ plot to compare it a standard normal sample. (These two plots should appear side by side in the same figure). Are students' heights close or far from being normally distributed? i. Create a box plot showing pulse rates (y-axis) for students with different exercising frequency (x-axis). What do you observe? j. Consider the following variables: span of writing hand, span of non-writing hand, pulse rate, height, and age. Are there any pairs of variable in this set that exhibit a linear dependence relation?