In a graduate probability course, 7 students are enrolled. After midterm, the marks (out of 100) are: 62,82,74,76,86,92, 90. (a) Find the five-summary statistics by hand, namely, find min, Q1, median, Q3 and Max with details. (b) Find the standard deviation of the midterm result in this class with details. (c) If an undergraduate also enroll in this course, but ended up with a low mark, say lower than 40, taking his/her mark into account, how would this low mark will affect the mean and the standard deviation? Will it Increase or decrease the mean and standard deviation you found in part (a), (b)

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.