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STATISTICS MATH 30-6 Probability and Statistics

L1 Statistics

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Page 1: L1 Statistics

STATISTICS

MATH 30-6Probability and Statistics

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OBJECTIVES

The students at the end of the lesson are expected to: • Define statistics and its fields• Differentiate the fields of statistics and relate to its

significance• Determine the scientific procedures of data

collection• Classify the types of data and relate to real life

situations the category of data to be used.• Practice the various techniques of data gathering and

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Statistics

• a scientific method of collection, presentation, analysis and interpretation of data for the purpose of drawing valid conclusions and reasonable decisions.

• Fields of Statistics– Descriptive Statistics– Inferential Statistics

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Descriptive Statistics• This method is concerned to the collection and

description of a set of data to yield meaningful information.

• Descriptive statistics provides information only about collected data and does not draw inferences or conclusions about a larger set of data.

• Examples:– In 2010, there have been reported 3 deaths and 80

firecracker related incidents.– 25% of the miners of Asbestos in Canada developed lung

related disease.

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Inferential Statistics• composed of those methods concerned with the

analysis of a smaller group of data leading to predictions or inferences about the larger set of data

• Statistics that deals in giving a generalization about the whole from an analysis of the part of the group.

• Examples:– Study shows that decreasing smoking by 3 sticks a day

would lengthen the life by 5 years.– AGB Nielsen states that 36% of the household prefers to

watch Saksi

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Population and Sample

• Population– Totality of all observations from which the data is

acquired– All of the possible events should be considered– Variable that describes population is known as PARAMETER

• Sample– Small group taken from the population.– A group heterogeneous as possible taken from the

large group to represent the population.– Variable that describes population is known as STATISTIC

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Variables• The parameters being studied in statistics.• Qualitative Variables– Also known as Categorical Data which are commonly

answered by non numeric data usually qualitative in form. – Examples: preferences, gender, civil status and location

• Quantitative Variables– Also known as Numerical Data are information and

observations that are countable or measurable quantities. – Examples: scores, force, moment, weight, voltage, current,

power, tensile strength and grades

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Dependent Vs Independent Variable

When two variables are correlated or being compared to the effect of one to the other, variables can be:

Independent Variablea naturally occurring phenomena that can be altered by increasing or decreasing its magnitude.

Dependent Variablea variable that is observed upon application of the changes applied to the independent variable.

Controlled Variablea variable that is kept constant to check for the external effects of the dependent to the independent variable.

Extraneous Variablevariables that would have minimal effect to the result of the independent variable to the independent variable.

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Scales of Measurement

• Nominal– Assigning numerical to categorical data

• Ordinal Data– Assigning rank to the levels of data.

• Interval– Assigning a constant difference between numeric data

• Ratio– Assigning continuous range of data over a range.

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Nominal Data

• Nominal Data are commonly categorical data assigned to numbers. In this data type, counting the number of times a certain data would fall on the category would only be the applicable measurement. Example of which is assigning 1 for males and 2 for females. Data that can be categorized as nominal data include course, civil status, color, preference.

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Ordinal Data

• Ordinal Data are quantities where the numbers are used to designate the rank order of the data. In this data type, the correlation or the effect of the ranking of one variable to another can be measured. However, the range for each rank is not constant. Examples of quantities that use this level of measurement are the results of a race, ranking of a beauty pageant, and level of hardness of a material in the Moh’s scale.

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Interval Data• Interval Data is a data type where the range

between the numeric values is constant. In this data type addition and subtraction of values can be performed, however, multiplication and division is not appropriate. Examples for this type of measurement are the year, and temperature in Celsius and Fahrenheit scales. In the year 2009, one year can be added to become 2010, however multiplying the year by two as in 2009 x 2 is meaningless. Multiplication and division can only be done in the difference between intervals.

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Ratio Data

• Ratio Data are the widely used data in science and engineering. Length, mass, angles, charge, and energy are some of the quantities that uses in this data type. Almost all of the basic mathematical operations can be performed in this data type. One significant characteristic of this data type is the presence of a non arbitrary zero point.

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Categories of Quantitative Data

• Discrete Data– Countable quantities. Data that has finite equal intervals.– Data that has been measured by digital measuring device that

tends to have exact values.– Example: Number of individuals, Months oh the year

• Continuous Data– Measurable quantities. Data that has infinite values between

intervals.– Data that has been measured by analog devices and has infinite

values based on interpolations– Example: Height, Weight, Ratio of persons

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Sampling • Process of taking the sample from the population• The two general classifications are the non-probability

sampling and probability sampling. • Non Probability Sampling• This type of sampling technique has certain or

individual that has no chance of being selected of being a sample.

• Probability Sampling The probability sampling eliminates the biases against

certain event that has no chance to be selected by listing all the possible events and taking a chance that they be selected to be part of the sample.

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Non Probability Sampling• Convenience Sampling is a sampling technique based primarily on the availability

of the respondents. The usual respondents of this type of data gathering procedure are those housemates without work, friends of the one conducting the research. Individuals with personal differences with the one conducting the survey tend to be not part of the data being gathered.

• Quota Sampling is a type of sampling technique where there is a desired number of sample and the respondents were taken as they volunteered themselves as to become part of the experiment. In this type of sampling, individuals who lack time filling up forms and those who are hesitant to answer such surveys are usually eliminated in this type of sampling. Phone call survey where the first 100 callers are taken is an example of this type of sampling.

• Purposive Sampling is a type of sampling where the sample is obtained based on a certain premise. If for example, the study is about pregnant women, the male population would have zero chance of being selected as part of the survey.

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Probability Sampling

• Simple Random Sampling• Systematic Sampling• Stratified Sampling• Cluster Sampling

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Simple Random Sampling• Simple Random Sampling is performed by

arranging the population according to a certain rule, each element being numbered and a sample is taken by various randomizing principles. A table of random numbers, random number generator in computers and calculators, and lottery are some examples of the randomizing events. Each event in the population has equal chance of being selected as part of the sample.

• Example: Lottery, placing every name in a drop box and selecting a name. A random number generator.

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Systematic Sampling

• Systematic Sampling is done by arranging the population in accordance to a certain order and the sample will be taken by dividing the population into equal groups and obtaining the kth element in each group.

• Example: Getting the temperature of the patient every 4 hours.

• Getting the blood platelet count every 12 hours• Getting the voltage of the signal every constant

interval and converting to signal

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Stratified Sampling• Stratified Sampling is a technique done by grouping the

population into strata, a subpopulation with generally homogeneous or similar characteristics. After dividing the population into several strata, a random sampling is performed in each stratum proportional to the size of each stratum relative to the population.

• Example: – Choosing a respondent according to a predetermined

grouping. 10 Respondents from Class A, 20 from Class B, 50 from Class C etc.

– Parliamentary election of selecting a representative that belongs to the same group.

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Cluster Sampling• Cluster Sampling is a techniques done by

identifying groups called clusters, a subpopulation with elements as heterogeneous or diverse characteristics as possible. These clusters must be similar to each other with respect to the parameter being examined. A cluster or clusters will be selected as sample. This type of sampling technique is preferred since it will be saving time and money to go to various clusters.

• Example: Selection of a certain region

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REFERENCES

• http://en.wikipedia.org/wiki/Statistics• http://writing.colostate.edu/guides/research/

stats/index.cfm