 # Stat 1080 “Elementary Probability and Statistics” By Dr. AFRAH BOSSLY

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Stat 1080 “Elementary Probability and Statistics” By Dr. AFRAH BOSSLY Afr_bossly@yahoo.com

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 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 : 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. Discrete variables usually result from counting. (ii) A continuous variable is a quantitative variable that can assume any numerical value over 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 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.

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

(a)Frequency distribution Table 1.1 The relative frequency of a category is obtained by dividing the frequency for a category by the sum of all the frequencies. PercentageRelative frequencyfrequencyTreatment 9.1% 54.5% 36.4% 1/11=0.091 6/11=0.545 4/11=0.364 164164 Nothing Diet only Insulin and diet 1001n=11Total

=Relative frequency 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

Frequency 7 6 5 4 3 2 1 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 AngleRelative frequencyfrequencyTreatment 0.091x360=32.76 0.545x360=196.2 0.364x360=131.04 1/11=0.091 6/11=0.545 4/11=0.364 164164 Nothing Diet only Insulin and diet 3601n=11Total

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