Download statistics - Daytona State College

STATISTICS
Frequency Distribution
Statistics is essentially the process of learning from data. The goal of statistics is to make correct
statements or inferences about a population based on a sample.
Terminology utilized in Statistics includes the following symbols:

Denotes the addition of a set of values
x
is the variable usually used to represent the individual data values
n
represents the number of values in a sample
N
represents the number of values in a population
x
x
u
x
n
n
is the mean of a set of sample values
is the mean of a all values in a population
f 
is the frequency of occurrence of a given data variable range (ie 60 to 69)
f x
is the product of the frequency of occurrence and the midpoint of the range
x
 x f
f
denotes the mean of the frequency distribution
Finding Mean from a Frequency Distribution
The following chart identifies data resulting from measuring the nicotine level of 40 smokers.
Nicotine Level Range
0-99
100-199
200-299
300-399
400-499
Totals
Frequency (f)
Range
Midpoint (x)
49.5
149.5
249.5
349.5
449.5
11
12
14
1
2
 x  40
x
 x f
f

f x
544.5
1794.0
3493.0
349.5
899.0
 f  x  7080.0
7080
 177.0 Mean Distribution
40
The Academic Support Center at Daytona State College (Math 63 pg 1 of 2)
Finding the Standard Distribution from a Frequency Distribution
s

Nicotine
Level
Range
0-99
100-199
200-299
300-399
400-499
Totals
s
s
   f  x  = Standard Deviation
n  f  x2  

2
nn  1
Frequency
(f)
11
12
14
1
2
 x  40
Range
Midpoint
(x)
49.5
149.5
249.5
349.5
449.5
   f  x  =
n  f  x2  
nn  1
2
 f  x
f  x2
544.5
1794.0
3493.0
349.5
899.0
  f  x  7080

 f  x 
2
  7080  =
40 1692910 
4039
2
26952.75
268203.00
871503.50
122150.25
404100.50
 1692910
67716400  50126400
1560
67716400  50126400 17590000
=
= 11275.641  106.18681  106.2
1560
1560
The Academic Support Center at Daytona State College (Math 63 pg 2 of 2)