Part I – Measures of Central tendency/Relative Frequency/ the Five-number SummaryA random sample of 25 Berkeley College students was asked, “How many hours per week typically do you work outside the home?” Their responses were as follows: {0, 0, 15, 20, 30, 40, 30, 20, 35, 35, 28, 15, 20, 25, 25, 30, 5, 10, 30, 24, 28, 30, 35, 15, 15}a. Find the mean, the median and the mode of hours worked outside the home for the sample data. Show all your work to justify your answer.b. Use the above data to complete the following table summarizing the number of hours worked outside the home. Express the relative frequency as a percent.ClassTallyFrequencyRelative Frequency (0 -10)(11-20)(21 – 30)(31- 40)Totalc. Find the five-number summary of the hours worked outside of the home by the 25 Berkeley College students. Part II- Basic ProbabilityConsider the experiment of tossing two fair dice, and observing the sum of the two dice.a. Make a list of all possible outcomes.

2b. What is the probability that the sum of the two dice equals 5? State specifically what outcomes show a sum of two dice equals 5.c. What is the probability that the sum of the two dice equals 14? State specifically what outcomes show a sum of two dice equals 14.d. What is the probability that the sum of the two dice greater than 9? State specifically what outcomes show a sum of two dice greater than 9.e. What is the probability that the sum of the two dice is less than 2? State specifically, if any, what outcomes show a sum of two dice is less than 2. Part III- Linear Relationship Scenario: A pediatrician wants to determine the relation that may exist between a child’s height and head circumference. She randomly selects eleven 3-year old children from her practice, measures their heights and head circumference, and obtains the data shown below:Height (inches)Head Circumference (inches)27.7517.524.517.125.517.12617.32516.925.7517.626.517.32717.526.7517.326.7517.527.517.5a. If the pediatrician wants to use height to predict head circumference, determine which variable is the explanatory variable and which is response variable.b. Draw a scatter diagram of the data.c. Draw the best fit line on the scatter diagram.d. Does this scatter diagram show a positive, negative, or no relationship between a child’s height and the head circumference?