Introduction to Statistics

This PERFORMANCE ASSESSMENT TASK is designed to assess the learner's ability to calculate the measures of central tendencies, plot the five-number summary, construct histogram for a set of data, calculate basic probability, and determine whether there is a positive, negative or no linear relationship between two variables.

Part I - Measures of Central tendency/ Histogram/ the Five-number Summary

A 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, 0, 30, 24, 28, 30, 35, 15, 15}

a.) Is this data set discrete or continuous? Explain your answer.

b.) Find the mean of hours worked outside the home for the sample data.

c.) Find the median, and describe why the median is sometimes preferable to the mean.

d.) Is there a mode? Why or why not?

f.) Determine the shape of the distribution of hours worked by comparing the mean and the median, as well as, by drawing a frequency histogram.

e.) Find the five-number summary of the hours worked outside of the home by the 25 Berkeley College students.

Part II- Basic Probability

Consider the experiment of tossing two fair dice, and observing the sum of the two dice.

a.) Make a list of all possible outcomes.

b.) What is the probability that the sum of the two dice equals 5?

c.) What is the probability that the sum of the two dice equals 12?

d.) What is the probability that the sum of the two dice greater than 2?

e.) What is the probability that the sum of the two dice is a multiple of 4?

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)

27.75

24.5

25.5

26

25

25.75

26.5

27

26.75

26.75

27.5

Head Circumference (inches)

17.5

17.1

17.1

17.3

16.9

17.6

17.3

17.5

17.3

17.5

17.5

a,) 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 a linear relation exist between height and head circumference? How would you describe the relationship and why?