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

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LECTURE 1 Some Definitions

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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.

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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.

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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.

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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.

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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.

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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.

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Variable Quantitative Qualitative Continuous Discrete

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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.

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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

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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.

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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.

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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.

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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.

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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

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Solution: The population: All a diabetic persons Sample size: 11 people Variable: treatment that a diabetic person is currently following Type of variable: qualitative

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(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

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=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.

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Bar Graph: Bar chart is a graph composed of bars whose heights are the frequencies of the different categories. (b) Frequency Bar Char

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Frequency 7 6 5 4 3 2 1 Nothing Diet only Insulin and diet Treatment

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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

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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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