# Summarizing, Presenting, and Analyzing Data

Document Sample

```					Summarizing and
Presenting Data
Statistics
The scientific study of
numerical data based
upon variation in nature.
Some Definitions
•   Observations
•   Datum/Data
•   Variable
•   Statistical Population
•   Sample
Descriptive Statistics
• Statistics of Location
– Average (Mean)
– Median
– Mode
• Statistics of Dispersion
– Range
– Standard Deviation
Calculating an Average

n
X   Xi n
i 1
Calculating an Average
i      Xi

1       2
2       3
3       5
4       8
5     10
n

∑Xi= X1 + X2 + X3 + X4 + X5
i=1

= 2 + 3 + 5 + 8 + 10
= 28
Calculating an Average
i      Xi

1       2
2       3
3       5
4       8
5     10
n

X = (∑Xi)/n = (X1 + X2 + X3 + X4 + X5)/n
i=1

= (2 + 3 + 5 + 8 + 10)/5
= 28/5 = 5.6
Calculating a
Standard Deviation

 n                  
           
2
S.D.   X  Xi       n  1 
i 1                
Calculating a
Standard Deviation
           n    
2 
                     
 n            
 Xi 

i 1 
                        n  1
2
S.D.   Xi                 
i 1             n 
                     
                     
Calculating a
Standard Deviation
2
n
  ( Xi )
i=1
Calculating a
Standard Deviation
Calculating a
Standard Deviation
Xi   (Xi)2
2      4
3      9
5     25
8     64
10    100
28    202

= 2 02
Calculating a
Standard Deviation
Calculating a
Standard Deviation
22
28
S.D. =
(( 2 0 2   5         )
(   5    1   )
Calculating a
Standard Deviation
Calculating a
Standard Deviation

=
((202        )
15 6.8

( 4)
Calculating a
Standard Deviation
Calculating a
Standard Deviation

=     11.3     =   3.36
Presenting Tables
TABLE I
The Effects of High Fat Versus Low Fat
Diets on Rat Weights and Lengths
AVERAGE          AVERAGE
DIET     WEIGHT           LENGTH
TYPE       (g)              (cm)
high fat   545.5             55.3
low fat    346.7             53.2
Graphing Data
Presenting Graphs
10
9
8
7
6
frequency

5
4
3
2
1
0
8    9 10 11 12 13 14 15 16
number of seeds per pod
Figure 1.               Frequency histogram of number of seeds
per pod for koa haole, Leucaena
leucocephala, seed pods.
Presenting Graphs
5

weight (g)   4

3

2
10   11     12     13   14   15
length (cm)
Figure 2.               Weight-length relationships of koa
haole, Leucaena leucocephala, seed
pods.
Rules for Tables and Figures
• Each figure or table must be
identified by a figure or table
reference number
• Each figure or table must have a
clear descriptive title. If the figure or
table refers to biological specimens,
then the scientific names of these
specimens are generally referred to
in the title
Rules for Tables and Figures
should clear identify the variable and
its units of measure
• In figures such as graphs, the axes
should be clearly labeled and the
units of measure indicated
• In figures, such as diagrams or
maps, the pertinent features should
be clearly labeled
Rules for Tables and Figures
• Do not cram figures and graphs into
a small space on a sheet of paper;
try to fill up a whole sheet of paper
• A general rule of thumb is that each
figure/table should be able to stand
alone without forcing the reader to