CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 1. An Introduction to Analyzing Statistical Data

TABLE1.4:(continued)

Island or Volcano Number of Individuals Repatriated

Sierra Negra 286

Cerro Azul 357

Santa Cruz 210

Española 1293

San Cristóbal 55

Santiago 498

Pinzón 552

Pinta 0

Figure:Approximate Distribution of Giant Galapagos Tortoises in 2004 ("Estado Actual De Las Poblaciones de
Tortugas Terrestres Gigantes en las Islas Galápagos," Marquez, Wiedenfeld, Snell, Fritts, MacFarland, Tapia, y
Nanjoa,Scologia Aplicada, Vol. 3, Num. 1,2, pp. 98-11).

For this data, calculate each of the following:

(a) mode

(b) median

(c) mean

(d) a 10% trimmed mean

(e) midrange

(f) upper and lower quartiles

(g) The percentile for the number of Santiago tortoises reintroduced.

6. In the previous question, why is the answer to c significantly higher than the answer to b?

Review Answers

1. There is an outlier that is larger than most of the data. This outlier will “pull” the mean towards it while the
   median tends to stay in the center of the data, clustered somewhere between 45 and 52.


2. His mean for all four quarters would need to be at least 92.5 in order to receive the necessary grade. Multiply-
   ing 92.5 by 4, yields 370 as the necessary total. His existing grades total to 273. 370− 273 =97.


3. 10% of 300 is 30, therefore, we would remove 15 numbers from each end.


4. 270
   
   
   1. 
      
   
   
   2. 210
   
   
   3. 
      
      
      
      299. 2
      
      
      
      
   
   
   4. 222 (10% of 11 data points is really 1.1, so we decided to remove two points, or about 18%)
   
   
   5. 
      
      
      
      646. 5
           6.Q 1 : 0,Q 3 : 498
      
      
      
      
   
   
   6. 72.7%
   
   
   
   


5. There is one extreme point, 1293, which causes the mean to be greater than the median.