Activity 4MATH 250 Elements of StatisticsSummer 2016 DUE DATE: 06/29/2016 General Instructions: Please place your name above, then complete the following questions. NOTE: Read th feel for the activity before continuing. Make sure to save this Excel file often using the filename "yournameActi your answers to this activity by attaching your Excel file through the completion link in the Unit 2 Activity 4 ass Blackboard. Use the area to the near right in this Excel worksheet when calculating any statistics/parameters fro Overview: This activity has three major purposes. First, it is designed to show the importance of examining the data p calculations. Second, the activity should help you recognize the difference between a discrete random varia variable. Finally, the activity is designed to help you see how the statistical analysis differ for both types of d answering the questions below comes from the data collected in the Unit 1a Activity. The sample data set c course originally had a size of n = 184. However to make the set a bit more manageable for beginning stati values were selected. You may recognize your own data within this set if you were one of the randomly sele complied in the attached worksheet titled Original Data Set for Analysis...see the tab at the bottom of this do 1. The first step with analyzing data is to make sure the all data values were entered correctly and seem to be this is called cleaning the data. More formally one would also look for possible outliers using a process (l whether or not to include these data in further analysis. In general, a valid and well established argument s of any data from a data set; removal of any collected data should NOT be done arbitrarily or to skew the dat Analyze the data given in the ATTACHED worksheet (see this worksheet below as "Original Data Set for An discussed in the first unit, find the one outlier within the Height variable. You must show use of the 1.5IQR r an outlier exists, give the individual's ID# and data as your answer below to this question #1. FINALLY, cop designated region at the right (several columns over) on THIS sheet and then delete that one row of data fro data will NOT be used in any other calculations performed in answering questions in #2 and #3 below. You data in the region to the right when finished with this problem. 2. For this problem, focus only on the the Family Size variable in the data setyou are using the table row chosen in answering #1, correct? Defining the random variable X to be family size, complete 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,th them individually. X is a discrete random variable because the collection of values is finite or countable,th them individually. b. In the area to the right, create a probability distribution table showing the possible values of X 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 distri directly above. (Hint: the requirment is to use only the information in the table you produced data---see how to produce the mean from a probability distribution table via the Excel Guides equivalent text's method explained in Section 5-2.) MEAN : d. Determine the standard deviation of the random variable X, again using only the values within table. (You can check your answers by finding the population s.d. of the data on family size, B answered through use of only the probability distribution table built in part b--same hint applie St. Deviation : e. Applying the Range Rule of Thumb, decide if any of the included values of the random variab "unusual" and "outlier" are not the same thing.) Give a concluding statement below in regard f. Create a probability statement which is supported by the values in the probability distribution probability that a randomly selected member of this group comes from a family of size 2 or les 3. Now consider your cleaned data in reference to the foot length variable of the students. Notice that quantitative, continuous, ratio level in type. (This portion of the activity is Based on Workshop Statistics, Rossman, p a. In the area to the right, copy the foot length values (again take the cleaned data set of 100 valu from least to greatest. From this column of foot length values, create an appropriate frequency remember, we did such frequency charts back in Unit 1. For the next part b, you may choose t the same time. Finally 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 tab of the footlength values appear to be roughly normal? Explain your answer briefly. c. Compute the mean and standard deviation of the foot length values...not from the frequency ta above but as done in the first unit, assuming this is sample data of all stats students. Sample mean, xbar: Sample std. deviation, s: d. Determine the proportion of the students in this sample whose footlength is at most 24 cm. e. Suppose that the foot lengths in the population of all university students taking elementary st normal distribution (though our group did not) with the population mean = 25 cm and popul deviation = 2.7 cm . Under this assumption, determine the proportion of all students who ha most 24 cm. (HINT: this calculation is related to the concepts covered in text section 6-2 and NAME: ng questions. NOTE: Read the entire document below to get a ng the filename "yournameActivity4". Once complete, submit link in the Unit 2 Activity 4 assignment description in ng any statistics/parameters from data (except in part 1.) portance of examining the data prior to performing statistical between a discrete random variable and a continuous random analysis differ for both types of data. The data to be used in a Activity. The sample data set collected from the students of this e manageable for beginning statistics, a random collection of 101 ou were one of the randomly selected individuals. This data is ee the tab at the bottom of this document window. entered correctly and seem to be reasonable/proper measurements ossible outliers using a process (like the 1.5IQR rule) and decide and well established argument should always be given for removal done arbitrarily or to skew the data to some desired viewpoint. elow as "Original Data Set for Analysis"). Using the 1.5IQR rule ou must show use of the 1.5IQR rule! Once you demonstrate that o this question #1. FINALLY, copy the entire data set to the hen delete that one row of data from THE COPY so this individual's estions in #2 and #3 below. You should be left with 100 rows of ta setyou are using the table in which you deleted the entire e X to be family size, complete the following: us one? values is finite or countable,that is, it is possible to count showing the possible values of X, the frequency of each value, and by the collected data. X using your probability distribution table created in part b. mation in the table you produced in part b., not to use the raw bution table via the Excel Guides for Unit 2 or through the gain using only the values within your probability distribution n s.d. of the data on family size, BUT this problem needs to be e built in part b--same hint applies as given in part c.) uded values of the random variable X are unusual (recall that uding statement below in regard to your decision. es in the probability distribution table. (For example, \"The mes from a family of size 2 or less is ??%\"). ble of the students. Notice that this data category is ased on Workshop Statistics, Rossman, p. 66) e the cleaned data set of 100 values) and then sort them in order , create an appropriate frequency table with exactly five classes-the next part b, you may choose to produce the histogram graph at e a relative frequency column. do so as you constructed your table in part a). Does the distribution in your answer briefly. values...not from the frequency table as done in the discrete case ata of all stats students. se footlength is at most 24 cm. sity students taking elementary statistics do in fact follow a perfect lation mean = 25 cm and population standard proportion of all students who have a foot length measure of at s covered in text section 6-2 and 6-3!) MATH 250- Elements of Statistics Class Data, Spring 2016---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 Male Female Female Female Female Male Male Female Male Female Male Male Male Female Male Male Female Male Male Male Female Female Female Female Female Male Female Female Male Female Male Female Female Female Male Male Male Female Female Female Foot Length 24.5 25.5 23 25.5 24 25 31 24.5 21 23 25.5 27 27 22.5 27 24.5 31 26 29 24 28 26 24 26.5 24 27 25.5 24 24 25 24.5 27.5 20 20.5 24 21.5 32 25 25 23.5 27.5 27.5 27 23 23 22.5 Height 162.5 175.5 160 175 158 163 186 165 155 165 172 168 175.5 158 188.5 162.5 183 162.5 180.5 171 180.5 180.5 230 176 175 173 165.5 160 161.5 174 165 178 164 153 183 162.5 178 178 168.5 162.5 185.5 176.5 188 167 155 160.5 Age 27 31 30 29 25 22 30 18 27 24 37 28 26 32 22 46 26 47 50 27 36 36 38 21 28 31 20 47 24 22 29 48 43 9 22 31 37 34 23 35 31 29 37 20 28 27 Armspan 156.5 187 162 175 157 163 190 166 150.5 150 172 169 184.5 162.5 187 165 188 163 182 164 183 183 235 176.5 172.5 175 173.5 182.5 160 169 167.5 178 161.5 151.5 188 158 165 173.5 168 161.5 181 170.5 188 154 157.5 163 Number in Family 3 4 5 3 7 3 3 9 4 3 2 4 5 4 4 6 4 3 4 4 3 3 5 9 4 3 3 2 7 3 5 4 4 5 1 3 3 4 4 5 4 4 3 4 4 5 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 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 Male Female Male Male Female Female Female Female Female Female Female Female Female Female Male Male Female Female Male Female Female Female Female Female Female Female Female Female Female Female Male Male Male Male Male Female Male Male Female Female Female Female Female Male Female Female Female Female Male Male Male Female Female 27 28 28 26.5 25 24 23 25 23 22 23.5 21 24 23.5 28 25 24 24 28 24 25 24 25.5 25.5 25 26 25 26 26 24 25.5 29 27.9 29.5 29.5 25 25 25 24 24 24 25 24.5 28 25 23 23.5 25 19 30.5 26.5 24 24.5 173 177.5 180 178 171.5 168 164.5 170.5 168 160.5 165 157 161.5 157.5 173 172.5 171 162.5 183.5 173.5 170 175.5 170 175 165 173 170.5 176 176.5 170 181 177 185.5 198.5 183 172.5 180 172 160 165 160 157.5 161 185.5 162 165 162 167.5 190.5 188 175.5 167.5 170 34 41 33 32 21 14 23 25 22 32 30 21 24 22 39 20 26 21 23 27 25 30 33 37 36 18 25 26 41 20 29 25 21 25 38 27 33 33 20 21 24 37 22 28 44 20 27 33 28 22 28 29 35 173 175 189 172.5 168.5 168 166 174 160 162.5 157 158 160 160 160 161 162 158.5 183 167.5 190 170 170 170 172.5 173 174 177 178 178 179.5 187 190.5 190.5 187.5 172.5 183 182 158 164 155 152.5 154 188.5 166 141 164 160 191 190.5 174 170.5 170 3 3 3 2 3 4 4 2 4 6 5 3 7 2 6 4 5 4 5 5 5 3 4 5 4 4 2 6 9 5 9 3 3 7 4 3 1 6 4 4 4 3 5 4 4 6 4 5 5 3 9 2 8 100 101 Female Female 23.5 25.5 160 173.5 21 33 157.5 174.5 4 3 of Student Data Hair Color Blonde Black Brown Brown Brown Black Brown Brown Brown Black Black Black Brown Black Brown Brown Brown Brown Brown Blonde Black Brown Brown Brown Blonde Black Blonde Black Blonde Brown Brown Brown Blonde Brown Brown Blonde Brown Brown Brown Red Brown Brown Black Red Brown Brown Brown Brown Blonde Red Blonde Blonde Brown Blonde Brown Brown Brown Brown Blonde Brown Brown Black Brown Brown Brown Blonde Brown Blonde Brown Blonde Blonde Brown Blonde Brown Blonde Red Brown Brown Brown Brown Bald Red Brown Blonde Brown Blonde Blonde Blonde Brown Brown Brown Brown Brown Brown Black Brown Brown Red Brown Brown Blonde