Statistics Detective Goal: Review concepts from the statistics and probability segment.
Goal: Investigate real-world data and interpret key features.
Goal: Utilize technology to adapt or build and use mathematical formulas that include cell referencing to answer real-world questions and interpret results

Instructions: I selected a person by random number generator and built clues from there. Use these clues in order to identify the "odd person out" in our class data set (download and open the file classdata.xlsx). To mark off eliminated people on the computer, be sure that up at the very top of the screen View/Ribbon is checked (View is on the very top menu between Edit and Insert, not on the lower menu) and that you can see the paint can under Home. You can then use the fill-in feature to eliminate suspects by clicking on the row number and then the paint can. Once someone violates one clue, they are out of the running. In this way, your document will show suspects eliminated using the clues as painted rows, where each color represents a different clue.
The suspect...

1. supports the statement that says that the average person is better able to remember real words than nonsense words.
   Eliminate people who contradict the clue and remember nonsense words at least as well as real words. Choose a color for this clue and highlight any eliminated rows in that color. You'll eliminate 6 people.
   
   
2. has a golden mean of (1+sqrt(5))/2 ~ 1.618, within a .200 margin of error, embedded in the forearm to hand ratio.
   -What are lower and upper boundaries for the interval rounded to 3 decimal places (Hint: use 1.618 and the margin of error)?
   lower boundary: _______________   upper boundary: _______________
   -Which column letter represents forearm? _______________                        hand? _______________
   -If we wanted to look at the ratio of columns J/I in Excel for person 2, we would use the Excel cell referencing command =J2/I2. Using Excel cell referencing, what is the Excel formula for forearm/hand for the first person in row 2 (don't forget the equal sign and use the columns you listed above rather than J and I)?
   
   _______________ Type this into K2 and hit return. Go back to that box, go to the bottom right until you see the symbol change to a black plus, click and fill down the column for the forearm to hand ratios. Here is the fill down helper video, if you need help.
   -Eliminate those remaining who contradict the statement and have a ratio outside the interval since the suspect is within. Choose a clue 2 color and highlight any new eliminations in Excel. Eliminate anyone who hasn't already been eliminated that is less than the lower boundary or greater than the upper boundary. You'll eliminate 32 new people from consideration.
   
   
3. falls within the middle 50% of the class on the boxplot of the distance from home.
   -First, as a review, compute in Excel the 5-number summary in some empty boxes, using the following commands, and then roughly sketch the boxplot by-hand by creating a reasonable scale for the axis. Be sure that your commands match these:
   Excel work:                                                                                By-hand sketch:
   Q₄ or maximum: =quartile(b2:b54,4) _______________
   Q₃: =quartile(b2:b54,3) _______________
   Q₂ or median: =quartile(b2:b54,2) _______________
   Q₁: =quartile(b2:b54,1) _______________
   Q₀ or minimum: =quartile(b2:b54,0) _______________
   
   -Now eliminate rows who contradict the statement and who fall strictly outside the box borders - i.e.
   eliminate those who are strictly below Q₁ or strictly above Q₃. Choose a different color and highlight any new eliminations in Excel. You'll have eliminated 6 new people. Also verify that you have 9 people remaining at this point. If not, check your clues and compare with others.
   
4. hits the 3rd quartile "on the head" for the number of competitors of the family bathroom.
   
   -Which column does the clue apply to? _______________
   
   -Use Excel cell referencing. What is the Excel command for Q₃? (don't forget the equal sign) _______________
   
   -After you execute the command in Excel in a blank box, what is Q₃ of that column: ______
   -Next, eliminate those who are different than Q₃
   -You should have eliminated 7 people and have 2 people remaining at this point. Write down the number of each row that is left.
   
   _______         _______
   
   
5. has a y-value within 12cm of the best fit line for "does armspan predict height."
   -Use Excel to create the scatterplot and best fit line, like we did a couple weeks ago (you can review #3 in that lab for the instructions)
   
   y=_____________________________
   -Compute the predicted line value of height by plugging in the armspan (the x value) of ONLY your remaining suspects into the equation of the line to solve for the y value height. Show work. Also write down the actual height of each person from Excel.
   
   Predicted height y=_____________________________ = ______________. Actual height=_______
   
   Predicted height y=_____________________________ = ______________. Actual height=_______
   
   -Compare the predicted line height value with the actual height and eliminate the person whose difference is greater than 12cm
   
   -Which row is left as the "winner" _______
   -Does the "winner" drag the line up or down? I.e. is their actual height value above (drags up) or below (drags down) the predicted line value?
   
   -Circle one:             up             down             exactly on the line
   
   Notice that the closest to the line isn't actually the closest to Leonardo da Vinci's prediction because of all the class mismeasurements!
6. Verify your responses with your neighbors and ask me any questions. I'm not collecting this lab but I will check over items as I make my way around. Next, work on reviewing material for the exam tomorrow or completing any ASULearn items in this segment. I'll come around to help!