HW3Descriptive2hertribm

1 ENED 3061 Probability & Statistics HW 3: Descriptive Statistics 2 - p. Spring 2023, Murphy due by 8:00am on Thursday February 2 Note: This is an individual assignment. The work you submit must be your own. Your submission of work for this assignment indicates your affirmation of the CEAS Honor Code statement, which is provided verbatim below. https://ceas.uc.edu/about/info-current-students/academic-action-criteria.html College of Engineering and Applied Science Honor Code As students of the University of Cincinnati's College of Engineering and Applied Science, we honor the high standards required by our future profession. We pledge to uphold those high standards by practicing integrity within our classrooms, our communities, and our careers. We believe in honest representation of individual work and in fair advancement of academic position; therefore, we refuse to partake in actions at the expense of our academic integrity. We expect academic integrity from our peers who share the responsibilities of this code. Our commitment to this pledge entitles us to trust from our peers, our instructors, and our institution. We maintain the right and share the responsibility to report any unfair advantage with anonymity and without retribution. I hereby affirm that this is my own work in accordance with the Honor Code of the University of Cincinnati College of Engineering and Applied Science.

2 ENED 3061 Probability & Statistics HW 3: Descriptive Statistics 2 - p. Spring 2023, Murphy due by 8:00am on Thursday February 2 Some of the work needs to be done by hand. You may include pictures of your hand-written work (make sure it's legible and well organized) or you may type your work and answers. (1) Show and/or explain enough work that we can tell what you did. For full credit, you must fill in all of the cells. ´ x = ∑ i = 1 n x i n = 159 + 170 + 173 + 175 + 177.8 + 178 + 180.3 + 182.9 + 187 + 188 + 195.6 11 = 178.7818 s 2 = ∑ i = 1 n ( x i −´ x ) 2 n − 1 = 972.382 11 − 1 = 97.2382 I used the equations in the headers of the table to calculate the deviations from the mean ( x i −´ x = x i − 178.7818 ) and squared those values to get the deviation squared I summed my x i −´ x values to get the sum of deviations. Because I rounded my values to 4 decimal places, that is why my sum of deviations is not zero. (a) By hand (using a calculator), complete the table below to calculate the mean and standard deviation for the given data set. x i = Height ( cm ) x i −´ x (deviation from the mean) x ( ¿¿ i −´ x ) 2 ¿ (deviation squared) 159 -19.7818 391.3203 170 -8.7818 77.1203 173 -5.7818 33.4294 175 -3.7818 14.3021 177.8 -0.9818 0.9640 178 -0.7818 0.6112 180.3 1.5182 2.3040 182.9 4.1182 16.9594 187 8.2182 67.5385 188 9.2182 84.9749 195.6 16.8182 282.8512 (b) Why does "sum of deviations" work out to be 0 (or close to 0)? The sum of deviations is the sum of x i values minus the sum of the ´ x ´ x

3 ENED 3061 Probability & Statistics HW 3: Descriptive Statistics 2 - p. Spring 2023, Murphy due by 8:00am on Thursday February 2 mean ´ x = ¿ 178.7818 sum of deviations = -0.0003 sum of (deviations) 2 = 972.382 variance s 2 = 97.2382 standard deviation s = 9.8609 (2) Show and/or explain enough work that we can tell what you did. A data set has the following 25 values for one of the variables (same data set that was used for HW 2: Descriptive Statistics 1): 19 7 71 71 84 10 80 91 19 27 30 82 21 98 64 26 78 50 24 61 93 39 16 99 29 Complete the follow items. Include screenshots of your Minitab results. (a) Use Minitab to construct a histogram of the data. Include a screenshot of your Minitab output. (b) Use Minitab to calculate the mean ´ x and the standard deviation s. Include a screenshot of your Minitab output.