Data Management Project
Answers to Questions from Student Handout 

1.	On spreadsheet

2.	a)  Stem and Leaf
Stem 	Leaf	
0	8	
1	0, 2, 2, 3, 5	
2	0, 1, 2, 3, 4, 5, 6, 8	
3	1, 1, 2, 2, 2, 3, 3, 4, 5, 6, 6, 8, 9	
4	1, 2, 2, 3, 5, 5, 6, 6, 8, 9	
5	0, 1, 5, 5, 6, 6, 7, 7	
6	0, 1, 5 	
7	7	
8		
9	2	

b)  Box-and-Whisker Plot

     8                     26.5      37          49.75				          92

										
         10	 20	   30        40         50        60        70        80         90

3.	A single number to represent the typical height of a five-year-old fir tree from Dale’s field would be 38.8.

4.	Using the mean = 38.8 and standard deviation = 17.6, we know the values for the bell curve range from –14 cm to 91.6 cm.  
•	68% of the data would be between 21.2 cm and 56. 4 cm
•	95% of the data would be between 3.6 cm and 74 cm
•	99.7% of the data would be between –14 cm and 91.6 cm

Using this information:
•	I would not be confident about the measurement of the 92 cm tree. 
•	I would be confident about the measurement of the 8 cm tree.
•	I would also be confident about the measurement of the 77 cm tree.
•	I would also be confident about the measurement of the 40 cm tree. 

5.	Repeat of question 3 – For the changed data, a single number representing the typical height of a five-year-old fir tree from Dale’s field would be 37.96 (cm).

Repeat of question 4 - For the changed data, using the mean = 37.96 and standard deviation = 15.88, we know the values for the bell curve range from –9.68 cm to 85.6 cm.  
•	68% of the data would be between 22.08 cm and 53.84 cm
•	95% of the data would be between 6.2 cm and 69.72 cm
•	99.7% of the data would be between –9.68 cm and 85.6 cm

Using this information:
•	There is no measurement for 92 cm in the new data; however, I would not be confident if there was a tree that measured 92 cm. 
•	I would be confident about the measurement of the 8 cm tree.
•	I would be confident about the measurement of the 77 cm tree.
•	I would be confident about the measurement of the 40 cm tree. 

6.	For the original data: mean = 38.8, median = 37, mode = 32
For the changed data: mean = 37.96, median = 37, mode = 32

There was no change to the median and mode, which would be expected because we only changed one number and it was greater then the median originally and when we changed it was still greater then the median. The mode didn’t not change because we the number we added and deleted was not part of this calculation. 

The mean was the only number that changed because the new number was a smaller value. This means the sum of all 50 numbers would be less, and therefore the average would be lower. 

7.	Original Standard Deviation = 17. 6
 	New Standard Deviation = 15.88

The standard deviation dropped by almost 2 points, which makes sense, since the range of the number also decreased. Since we have a lower range, we will have a smaller standard deviation. 

8.	Answered in question 4. The normal curve would have to be completed by hand and passed in separately. 

Part B

9.  On spreadsheet

10.	On spreadsheet, the line of best fit must be drawn on the chart after the document has printed.

11.	The slope is 9.45 and the y-intercept is 24.21

12.	The equation of the line of best fit, according to the LINEST equation is: 

13.	The predicted height of a tree 4.5 years old is 66.75 cm 
The predicted height of a tree 10 years old is 118.74 cm
The predicted height of a tree 7 years old is 90.38 cm
The predicted height of a tree 120 years old is 1158.50 cm
The predicted height of a tree 1000 years old is 9476.60 cm

14.	The predictions in question 13 are reasonable for some of the answers but not all of the answers. 
The predicted heights for a tree at 4.5 years, 7 years and 10 years make sense, according to our data. 
The predicted heights for a tree 120 years and 1000 years old fit the formula but do not make sense in a real life situation. Trees would not continue growing at a constant rate as they get older. As trees continue to grow and age, they tend to develop additional width, not just height. Another problem with the prediction is that fir trees generally do not live to be 120 and certainly would not survive for 1000 years.