stat 1080 “elementary probability and statistics” by dr. afrah bossly [email protected]
TRANSCRIPT
LECTURE 1
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 thecalculation 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 uponinformation contained in a sample.
Variable: Variable is a characteristic of interest concerning the
individual elements of a population or a sample.Note That:
A variable is often represented by a letter such as X, Y or Z.
The value of a variable for one particular element from the sample or population is called an Observation.
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. Discretevariables usually result from counting.
( ii )A continuous variable is a quantitative variable that can assume any numerical valueover an interval or over several intervals.
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.
Variable
Quantitative Qualitative
Continuous Discrete
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 sampleof 50 pregnant Saudi women.
Identify the variable, the population, the sample size and whether the variable isquantitative 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 isquantitative or qualitative; and if quantitative, whether the variable is discrete orcontinuous.
Solution: Variable: "hemoglobin level"
Population: all people who have a certain diseaseSample size: 75 peopleThe values of variable: numbersThe type of variable: QuantitativeThe variable is a continuous quantitative.
Organizing the dataSuppose 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 using1 -Frequency distributions.
2 -Frequency graphs.3 -Compute some statistical measures.
Qualitative Variablesimple frequency distribution, frequency bar and pie char can be made for a qualitativevariable 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 currentlyfollowing. For a sample, suppose we obtain:
Diet only Insulin and diet Nothing Diet onlyDiet only Diet only Insulin and diet Diet onlyDiet only Insulin and diet Insulin and dieta) prepare a simple frequency distribution for this datab) construct a frequency bar charc) construct a frequency pie char
Solution:The population: All a diabetic personsSample size: 11 peopleVariable: treatment that a diabetic person is currently followingType of variable: qualitative
)a)Frequency distribution
Table 1.1
The relative frequency of a category is obtained by dividing the frequency for a category by thesum of all the frequencies.
Percentage Relative frequency frequency Treatment
9.1%54.5%36.4%
1/11=0.0916/11=0.5454/11=0.364
164
NothingDiet only
Insulin and diet
100 1 n=11 Total
=Relative frequencyThe sum of the relative frequencies will always equal one.
The percentage for a category is obtained by multiplying the relative frequency for that categoryby 100.
Percentage=100 × Relative FrequencyThe sum of the percentages for all the categories will always equal 100percent.
nfrequancy /
Bar Graph: Bar chart is a graph composed of bars whose
heights are the frequencies of the differentcategories.
( b )Frequency Bar Char
Frequency
7654321
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 followsAngle size =relative frequency x360
Frequency Pie CharTable 1.2
Angle Relative frequency frequency Treatment
0.091x360=32.760.545x360=196.2
0.364x360=131.04
1/11=0.091 6/11=0.545 4/11=0.364
164
NothingDiet only
Insulin and diet
360 1 n=11 Total