MATH 250 FALL 2014 FINAL

General Instructions:  Please place your name above, then complete the following questions.  NOTE:  Read the entire document below to get a feel for the activity before continuing. Make sure to save this Excel file often using the filename "yournameActivity4".  Once complete, submit your answers to this activity by attaching your Excel file through the completion link in the Unit 2 Activity 4 assignment description in Blackboard.  Use the area to the near right in this Excel worksheet when calculating any statistics/parameters from data.

Overview:

This activity has 3 major purposes.  First, it is designed to show the importance of examining the data prior to performing statistical calculations.  Second, the activity should help you recognize the difference between a discrete random variable and a continuous random variable.  Finally, the activity is designed to help you see how the statistical analysis differ for both types of data.  The data to be used in answering the questions below comes from the data collected in the Unit 1a Activity.  The sample data set collected from the students of this course orignally had a size of n = 148.  However to make the set a bit more managable for beginning statistics, a random collection of 76 values were selected.  You may recognize your own data within this set if you were one of the randomly selected indivdiuals.  This data is complied in the attached worksheet titled Original Data Set for Analysis...see the tab at the bottom of this document window.

1The first step with analyzing data is to make sure the all data values were entered correctly and seem to be reasonable/proper measurements—this is called cleaning the data.  More formally one would also look for possible outliers using a process (like the 1.5IQR rule) and decide whether or not to include these data in further analysis.  In general, a valid and well established argument should always be given for removal of any data from a data set; removal of any collected data should NOT be done arbitrarily or to skew the data to some desired viewpoint. Analyze the data given in the attached worksheet (see this below as "Orignial Data Set for Analysis").  Using the 1.5IQR rule discussed in the first unit, find the one outlier within the Foot Length variable.  You must show use of the 1.5IQR rule!  Once you demonstrate that an outlier exists, give the individual's number and data as your answer below to this question #1.  FINALLY, copy the entire data set to the designated region at the right (several columns over) on THIS sheet and then delete that one row of data from the copy so this indivdiual's data will NOTbe used in any other calculations performed in answering questions in #2 and #3 below.  You should be left with 75 rows of data in the region to the right when finished with this problem. 

Individual #:34Because the footspan of 8 is less than the value of Q1 - (1.5 * IQR), the value is an outlier.

2For this problem, focus only on the the Family Size variable in the data set—you are using the table in which you deleted the entire row chosen in answering #1, correct?  Defining the random variable X to be family size, complete the following: 

a.What makes X a discrete random variable and not a continuous one?

X is a discrete random variable because the collection of values is finite or countable,that is, it is possible to count them individually.

b.In the area to the right, create a probability distribution table showing the possible values of X, the frequency of each value, and the associated relative frequency values P(X) as determined by the collected data.

c.Determine the expected value (mean) of the random variable X using your probability distribution table created in part b. directly above.   (Hint: the requirment is to use only the information in the table you produced in part b., not to use the raw data---see how to produce the mean from a probability distribution table via the Excel Guides for Unit 2 or through the equivalent text's method explained in Section 5-2.)

d.Determine the standard deviation of the random variable X, again using only the values within your probability distribution table.  (You can check your answers by finding the population s.d. of the data on family size, BUT this problem needs to be answered through use of only the probability distribution table built in part b--same hint applies as given in part c.)

e.Applying the Range Rule of Thumb, decide if any of the included values of the random variable X are unusual  (recall that "unusual" and "outlier" are not the same thing.)  Give a concluding statement below in regard to your decision.

There are four unusual values. The value 7, presented twice, and the value 8, presented twice also. These values are unusual because they are more than two standard deviations away from the mean. 

f.Create a probability statement which is supported by the values in the probability distribution table.  (For example, “The probability that a randomly selected member of this group comes from a family of size 2 or less is ??%”).

3.Now consider your cleaned data in reference to the armspan variable of each class member.  Notice that this data category is quantitative, continuous, ratio level in type.  (This portion of the activity is Based on Workshop Statistics, Rossman, p. 66)

a.In the area to the right, copy the armspan values (again choose the cleaned data set of 75 values) and sort them in order from least to greatest. From this column of armspan values, create an appropriate frequency table with exactly 6 classes--remember, we did such frequency charts back in Unit 1.  Then extend your frequency table to include a relative frequency column.

b.Produce a histogram for your frequency table (if you did not do so as you constructed your table in part a).  Does the distribution of the armspan values appear to be roughly normal?  Explain your answer briefly.