

Practice Problems (Answers)
Homework
 Descriptive
 Serves to organize, summarize, and describe data.
 Inferential
 Serves to make inferences or generalizations about a total set of individuals or events on the basis of data from a smaller group.
Note population and sample are relative terms. While this class might be a sample from the population of all students at the college, all students at the college could be a sample from the population of all students at public universities in the USA.
In light of these later definitions, we can now be more precise in our definitions of the two functions of statistics:
Population  Sample  

Freshman  40%  Freshman  40%  
Sophomore  30%  Sophomore  30%  
Junior  20%  Junior  20%  
Senior  10%  Senior  10% 
Are a set of procedures for assigning numbers to things. Note that the act of measurement discretizes (rounds off) a continuous variable because one can never measure a continuous variable exactly. Ex. I am 5'8" tall. However, if you measured me, I would probably be something like 5'8.21332. . . . inches tall.
There are four scales of measurement that you should be familiar with. The first two are sometimes called nonparametric because they have nothing resembling a zero point.
Number  Unit of meas.  1/2 Unit of meas.  Exact Limits  

Lower  Upper  
33  32.5  33.5  
33.3  33.25  33.35  
33.33  33.325  33.335  
33.333  33.3325  33.3335 
Rule  Exs. 
Unit of meas. 
1/2 Unit 
Remain decim. frac. 
Exs. Rounded 


1.  If remaining decimal fraction is less (<) than 1/2 unit of measurement, drop it. 

2.  If remaining decimal fraction is greater (>) than 1/2 unit of measurement, increase the preceding digit by 1. 

3.  If remaining decimal fraction equals (=) 1/2 unit of measurement, increase preceding digit by 1 if it is odd & drop it if it is even. Hence, this is called the "Odd/Even Rule". 
7.25 
7.2 
Exs. 
Unit of meas. 
1/2 Unit 
Remaining decim. frac. 
Rounded 
Rule used 

Always up  Our rules  

Number  Rounded  Number  Rounded  
3.5  4  3.5  4  
4.5  5  4.5  4  
5.5  6  5.5  6  
6.5  7  6.5  6  
20  22  sums  20  20 
Consider:
Subject  X 

1  X_{1}=3 
2  X_{2}=8 
3  X_{3}=10 
4  X_{4}=13 
5  X_{5}=17 
Subject  X  X^{2} 

1  3  9 
2  5  25 
3  6  36 
∑X = 14  ∑X^{2} = 70  
(∑X)^{2} = 196 

Note: ∑X^{2} ≠ (∑X)^{2} 
Subj. X c cX Y (X+Y) 1 3 2 6 1 4 2 5 2 10 4 9 3 6 2 12 7 13 N=3 ∑X=14 ∑c=6 ∑cX=28 ∑Y=12 ∑(X+Y)=26