‫‪Stat 1060‬‬
‫احصاء حيوي‬
Chapter 1
Basic statistics and statistical data classification
Some Definitions
Statistics:
Statistics is a discipline of study dealing with the collection, analysis,
interpretation, and presentation of data.
Descriptive statistics:
Descriptive statistics is organizing and summarize information by using the
graphs, charts, tables and the calculation of various statistical measures to the
set of data.
Population:
Population is the collection of individuals, items, or data under consideration
in a statistical study.
Population size:
Population size is the number of elements in the population, denoted by N.
Parameter:
Parameter is a numerical quantity measuring some aspect of a population of
scores.
Sample:
Sample is any part of a population.
Sample size:
Sample size is the number of elements in the sample, denoted by n.
Statistic:
Statistic is a numerical quantity measuring some aspect of a sample of scores.
Inferential statistics:
Statistical inference is the techniques for reaching conclusions about a
population based upon information contained in a sample
Variable:
Variable is a characteristic of interest concerning the individual elements of a
population or a sample.
Note That:
1- A variable is often represented by a letter such as X, Y or Z.
2- The value of a variable for one particular element from the sample or
population is called an Observation.
3- A data set consists of the observations of a variable for the elements of a
sample.
Quantitative variable
Quantitative variable is determined when the description of the
characteristic of interest results in a numerical value.
(i)
A discrete variable is a quantitative variable whose values are
countable. Discrete variables usually result from counting.
Examples:
*Number of patients admitted to a hospital in one day (x=1,2,…)
* Number of pain killer tablets (x= 0.5,1,1.5,2 ,2.5,…)
Note: Discrete values can take either integer values or decimal values with
gaps between the values.
(ii)
A continuous variable is a quantitative variable that can assume any
numerical value over an interval or over several intervals.
Examples:
*Level of chemical in drinking water
*height (140<x<190)
*blood sugar level of a person.
Qualitative variable
Qualitative variable is determined when the description of the characteristic
of interest results in a non-numerical value.
A qualitative variable may be classified into two or more categories.
Raw Data:
Information obtained by observing values of a variable is called raw data.
Example 1:
Suppose that we measure whether or not one regularly takes a vitamin for a
sample of 50 pregnant Saudi women.
Identify the variable, the population, the sample size and whether the variable
is quantitative or qualitative; and if quantitative, whether the variable is
discrete or continuous.
Solution:
Variable: "whether or not one regularly takes a vitamin"
Population: all pregnant Saudi women
Sample size: 50 women
The values of variable: Yes and No
The type of variable: Qualitative
Example 2:
Suppose that we measure the hemoglobin level in g/dl for a sample of 75
people who have a certain disease.
Identify the variable, the population, the sample size and whether the variable
is quantitative or qualitative; and if quantitative, whether the variable is
discrete or continuous.
Solution:
Variable: "hemoglobin level"
Population: all people who have a certain disease
Sample size: 75 people
The values of variable: numbers
The type of variable: Quantitative
The variable is a continuous quantitative
Exercise: for more exercises and details about graphs
http://onlinestatbook.com/chapter2/graphing_qualitativ
e.html
Organizing the data
Suppose we have a population and variable of interest and we collect
information on a sample of size n, so we try to organize the sample data by
using:
1- Frequency distributions.
2- Frequency graphs.
3- Compute some statistical measures.
Qualitative Variable
Simple frequency distribution, frequency bar and pie char can be made for a
qualitative variable as discrete quantitative variable.
A frequency distribution:
For qualitative data lists all categories and the number of elements that belong
to each of the categories.
Example 3: Suppose that we measure the type of treatment that a
diabetic person is currently
Following. For a sample, suppose we obtain:
Diet only Insulin and diet nothing
Diet only Diet only
Diet only
Insulin and diet Diet only
Diet only Insulin and diet
Insulin and diet
a) Prepare a simple frequency distribution for this data
b) Construct a frequency bar char
c) Construct a frequency pie char
Solution:
The population: All a diabetic persons
Sample size: 11 people
Variable: treatment that a diabetic person is currently following
Type of variable: qualitative
Frequency distribution
Table 1.1
Treatment
frequency
Relative
frequency
Percentage
Nothing
Diet only
Insulin and
diet
1
6
4
1/11=0.091
6/11=0.545
4/11=0.364
9.1%
54.5%
36.4%
Total
n=11
1
100
The relative frequency of a category is obtained by dividing the frequency for a
category by the sum of all the frequencies.
Relative frequency=frequency/n
The sum of the relative frequencies will always equal one.
The percentage for a category is obtained by multiplying the relative frequency
for that category by 100.
Percentage=100 × Relative Frequency
The sum of the percentages for all the categories will always equal 100percent
Bar Graph:
Bar chart is a graph composed of bars whose heights are the frequencies of
the different categories.
(b) Frequency Bar Char
Chart Title
7
6
frequnce
5
4
3
2
1
0
Nothing
Diet only
Insulin and diet
treatment
Pie Chart:
Pie chart is also used to graphically display qualitative data.
To construct a pie chart, a circle is divided into portions that represent the
relative frequencies or percentages belonging to different categories.
We compute the angle size as follows
Angle size =relative frequency x360
Frequency Pie Char
Table 1.2
Discrete Quantitative Data
A simple frequency distribution, frequency bar char can be used to organize
the discrete quantitative variable.
Example 1:
Suppose that we are interest in the number of children that a Saudi Women
has and we take a sample of 16 women and obtain the following data on the
number of children:
3 5 2 4 0 1 3 5 2 3 2 3 3 2 4 1
a) Prepare a simple frequency distribution for this data
b) Construct a frequency bar char
Solution:
the population: All Saudi women, sample size: 16 women, variable: number of
Children that a Saudi woman has, Type of variable: discrete quantitative.
(a)Frequency distribution
Number of
children
Frequency
Relative
frequency
Percentage
0
1
2
3
4
5
1
2
4
5
2
2
1/16=0.0625
2/16=0.125
0.25
0.3125
0.125
0.125
6.25%
12.5%
25%
31.25%
12.5%
12.5%
Total
n=16
1
100
b) Frequency Bar Chart
Displaying Group Frequencey Distrbution :