Stat 1080 “Elementary Probability and Statistics” By Dr. AFRAH BOSSLY [email protected].

Stat 1080

“Elementary Probability and Statistics”

By Dr. AFRAH [email protected]

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