Activity 4MATH 250 Elements of StatisticsFall 2017 DUE DATE: 10/10/2017 General Instructions: Please place your name above, then complete the following questi feel for the activity before continuing. Make sure to save this Excel file often using the file complete, submit your answers to this activity by attaching your Excel file through the com description in Blackboard. Use the area to the near right in this Excel worksheet when cal part 1.) Overview: This activity has three major purposes. First, it is designed to show the importance o calculations. Second, the activity should help you recognize the difference between variable. Finally, the activity is designed to help you see how the statistical analysis answering the questions below comes from the data collected in the Unit 1a Activity. course originally had a size of n = 211. However, to make the set a bit more manage data was selected. You may recognize your own data within this set if you were one compiled in the attached worksheet titled Original Data Set for Analysis...see the tab 1. The first step with analyzing data is to make sure the all data values were entered co this is called cleaning the data. In initial analysis of the student data, there were s measurements; much of this was cleaned already. More formally one would also loo rule) and decide whether or not to include these data in further analysis. In general, given for removal of any data from a data set; removal of any collected data should N desired viewpoint. Analyze the data given in the ATTACHED worksheet (see this wor the 1.5IQR rule discussed in the first unit (Lesson 4.4), find the one outlier within the rule! Once you demonstrate that an outlier exists, give the individual's ID# and data the entire data set to the designated region at the right (several columns over on this you copy over so this individual's data will NOT be used in any other calculations pe should be left with 74 rows of data in the region to the right when finished with this p For this problem, focus only on the Family Size variable in the data setyou 2. row chosen in answering #1; the table with 74 individuals' data left. Defining the following: For this problem, focus only on the Family Size variable in the data setyou row chosen in answering #1; the table with 74 individuals' data left. Defining the following: a. What makes X a discrete random variable and not a continuous one? b. In the area to the right, create a probability distribution table showing t the associated relative frequency values P(X) as determined by the co c. Determine the expected value (mean) of the random variable X using y above. (Hint: the requirement is to use only the information in the tab how to produce the mean from a probability distribution table via the E method explained in Section 7-3.) MEAN : d. Determine the standard deviation of the random variable X, again using table. (You can check your answers by finding the population s.d. of t answered through use of only the probability distribution table built in St. Deviation : e. Typically, any data outside of the 2 Sigma Rule (pg. 149) is considered random variable X are unusual. Give a concluding statement below in f. Create a probability statement which is supported by the values in the p probability that a randomly selected member of this group comes from 3. Now consider your cleaned data in reference to the Footlength variable of the quantitative, continuous, and ratio level in type. (This portion of the activity is Based o a. In the area to the right, copy the Footlength values (again take the clea least to greatest. From this column of Footlength values, create an appr we did such frequency charts back in Unit 1. For the next part, b, you time. Finally extend your frequency table to include a relative frequen b. Produce a histogram for your frequency table (if you did not do so as y of the Footlength values appear to be roughly normal? Explain your an c. Compute the mean and standard deviation of the Footlength values...n above but as done in the first unit, assuming this is sample data of all s Sample mean, xbar: Sample std. deviation, s: d. Determine the proportion of the students in this sample whose Footlen e. Suppose that the Footlengths in the population of all university studen normal distribution (though our group did not) with the population mea cm . Under this assumption, determine the proportion of all students w this calculation is related to the concepts covered in text section 8-4!) NAME: lete the following questions. NOTE: Read the entire document below to get a el file often using the filename "yournameActivity4(Fall 2017)". Once xcel file through the completion link in the Unit 2 Activity 4 assignment xcel worksheet when calculating any statistics/parameters from data (except in d to show the importance of examining the data prior to performing statistical ze the difference between a discrete random variable and a continuous random ow the statistical analysis differ for both types of data. The data to be used in cted in the Unit 1a Activity. The sample data set collected from the students of this the set a bit more manageable for beginning statistics, a collection of 75 individuals' hin this set if you were one of the randomly selected individuals. This data is t for Analysis...see the tab at the bottom of this document window. ata values were entered correctly and seem to be reasonable/proper measurements student data, there were several mismeasurments or incorrectly given ormally one would also look for possible outliers using a process (like the 1.5IQR rther analysis. In general, a valid and well established argument should always be any collected data should NOT be done arbitrarily or to skew the data to some ED worksheet (see this worksheet below as "Original Data Set for Analysis"). Using d the one outlier within the Armspan variable. You must show use of the 1.5IQR e individual's ID# and data as your answer below to this question #1. FINALLY, copy veral columns over on this worksheet) making sure to delete that one row of data as any other calculations performed in answering questions in #2 and #3 below. You t when finished with this problem. ble in the data setyou should use the table in which you deleted the entire duals' data left. Defining the random variable X to be Family Size, complete d not a continuous one? istribution table showing the possible values of X, the frequency of each value, and X) as determined by the collected data. random variable X using your probability distribution table created in part b. directly the information in the table you produced in part b., not to use the raw data---see distribution table via the Excel Guides for Unit 2 or through the equivalent text's om variable X, again using only the values within your probability distribution ing the population s.d. of the data on family size, BUT this problem needs to be y distribution table built in part b--see Section 7-4.) ule (pg. 149) is considered "unusual." Decide if any of the included values of the luding statement below in regard to your decision. orted by the values in the probability distribution table. (For example, \"The of this group comes from a family of size 7 or more is ??%\"). ootlength variable of the students. Notice that this data is categorized as portion of the activity is Based on Workshop Statistics, Rossman, p. 66) values (again take the cleaned data set of 74 values) and then sort them in order from ngth values, create an appropriate frequency table with exactly 4 classes--remember, For the next part, b, you may choose to produce the histogram graph at the same include a relative frequency column. e (if you did not do so as you constructed your table in part a). Does the distribution y normal? Explain your answer briefly. f the Footlength values...not from the frequency table as done in the discrete case this is sample data of all stats students. his sample whose Footlength is at most 25 cm. ion of all university students taking elementary statistics do in fact follow a perfect ot) with the population mean = 25.2 cm and population standard deviation = 2.22 proportion of all students who have a Footlength measure of at most 25 cm. (HINT: vered in text section 8-4!) MATH 250- Elements Class Data, Fall 2017 Individual ID# ATH 250- Elements of Statistics lass Data, Fall 2017---CLEANED Student Data Gender Foot Length Height Age Armspan Number in Family Hair Color MATH 250- Elements of Statistics Class Data, Fall 2017---FIRST EXAMINATION of Student Data Individual ID# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Gender Female Male Female Male Female Female Female Female Male Female Female Female Female Female Female Male Female Female Male Male Female Female Male Male Male Female Male Male Female Female Female Female Female Male Female Female Female Male Male Female Female Female Female Female Female Female Foot Length 24.0 25.0 25.5 29.0 28.0 23.0 24.5 21.0 30.5 23.5 23.0 23.0 23.0 24.0 20.0 26.0 24.0 24.0 26.0 27.5 23.5 24.5 25.5 27.0 26.0 25.5 25.5 29.0 23.0 25.0 24.0 24.0 24.0 30.5 24.0 25.0 24.5 24.0 26.5 27.0 24.0 22.5 25.5 25.0 30.5 26.0 Height 160.0 172.5 170.5 185.0 174.5 168.0 157.0 152.0 187.5 157.5 165.0 166.0 152.5 165.0 163.0 178.0 162.5 164.5 184.0 183.5 161.5 157.5 179.5 175.0 185.0 170.0 186.0 180.0 148.0 172.5 167.5 168.0 159.0 185.5 164.0 166.0 164.0 179.0 177.0 170.0 170.0 161.0 171.5 158.0 176.5 158.0 Age 31 20 28 27 38 38 21 21 29 22 21 32 35 34 20 34 23 22 40 32 29 22 33 40 31 40 20 47 39 23 22 20 32 33 27 26 26 33 37 31 29 39 24 44 36 22 Armspan 159.0 177.5 174.0 192.5 183.0 168.0 153.0 151.0 190.0 160.0 163.0 160.0 160.0 165.0 153.0 175.5 170.5 160.5 169.0 183.0 157.5 150.0 184.5 175.0 179.0 169.0 188.0 180.0 150.0 170.5 162.5 169.0 157.0 193.5 168.5 169.0 165.0 160.0 180.0 166.0 155.0 165.5 142.0 167.0 198.0 160.0 Number in Family 3 2 4 3 5 3 4 8 5 5 2 3 6 6 4 2 4 5 3 2 5 3 6 4 3 5 4 7 5 6 3 3 8 4 5 3 3 3 6 6 5 4 3 2 1 3 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Female Female Female Male Female Male Female Male Female Female Female Male Male Female Female Female Female Female Male Female Female Male Male Female Female Male Female Female Male 23.5 25.0 27.0 27.0 26.0 28.5 23.0 28.0 23.5 25.5 23.5 24.0 21.0 25.0 22.0 24.0 26.0 25.5 28.0 22.0 24.0 26.0 26.0 24.0 26.5 31.0 26.0 23.0 28.0 152.5 182.0 167.5 180.0 178.0 178.0 165.0 183.0 170.5 170.0 170.0 160.0 137.5 169.5 151.5 159.0 162.5 170.0 181.0 154.0 180.0 178.5 178.0 162.5 165.0 178.0 176.0 160.0 177.0 21 24 27 37 26 31 31 27 22 27 42 46 22 22 34 40 21 28 27 23 31 35 37 31 48 21 21 23 38 152.5 177.0 167.0 173.0 175.0 185.5 167.0 193.0 172.0 170.0 150.0 165.0 131.5 164.5 156.5 161.5 162.5 165.5 182.5 142.0 178.0 186.0 176.5 162.5 169.0 152.0 160.5 150.0 184.0 2 4 4 4 4 5 2 3 5 3 3 4 3 8 4 7 4 6 4 3 4 6 3 4 2 5 3 2 3 Student Data Hair Color Red Blonde Brown Brown Brown Red Blonde Brown Black Blonde Red Brown Brown Blonde Blonde Black Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Red Brown Brown Blonde Brown Brown Black Brown Red Brown Blonde Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Black Brown Brown Brown Black Brown Blonde Brown Brown Black Brown Red Blonde Brown Brown Brown Blonde Brown Brown Brown Brown Black