Univariate Descriptive Statistics
Descriptive statistics vs. Inferential statistics  
You use descriptive statistics when you want to describe a sample  You use inferential statistics to make estimates about a population 
Descriptive statistics describe or summarize the data in a sample  Inferential statistics are estimates that describe or summarize the data in a population. 
Statistics  Parameters 
statistics summarize samples  parameters summarize populations 
you can calculate statistics directly  you can only estimate parameters 
you use Roman letters for statistics
(x, s, s^{2}) 
you use Greek letters for parameters
( ) 
X 
x  mean 
deviation score 

2 7 8 3 4 6 + 5 
2  5 = 7  5 = 8  5 = 3  5 = 4  5 = 6  5 = 5  5 = 
3 2 3 2 1 1 + 0 

35  0  
mean = 35 / 7 = 5 
x_{i}  d_{i}  d_{i}^{2} 
7 
2.625 
6.890625 
12  2.375  5.640625 
9  0.625  0.390625 
11  1.375  1.890625 
8  1.625  2.640625 
6  3.625  13.140625 
10  0.375  0.140625 
+ 14  4.375  + 19.140625 
77  49.875000 
so 7  9.625 = 2.625
x_{i}  x_{i}^{2}  
7 
49 

12  144  
9  81  
11  121  
8  64  
6  36  
10  100  
+ 14 
+ 196 

77  791  
77 × 77 = 5929  
5929 ÷ 8 = 741.125  
791  741.125 = 49.875  
variance = 49.875/7 = 7.125 = s^{2}  
std. dev. = square root of variance = 2.669269563 = s 
original method  computational form  
n = 8  n = 50  n = 8  n = 50  
additions  16  100  16  100 
subtractions  9  51  2  2 
multiplications  8  50  9  51 
divisions  2  2  2  2 
square roots  1  1  1  1 
total  36  204  30  156 