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Chapter I Measures of Central Tendency & Variability
Curriculum Objective: The students will determine the measures of central tendency and variability Apply these tendencies to solving problems Analyze these measure in the case
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What is Statistics?
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Descriptive Statistics
Describe the characteristic of the data such as ; mean, median, std dev, variansi etc Inferential Statistics Make an inferences about the population, characteristics from information contained in a sample drawn from this population Such as : prediction, estimation, take the decision
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1. Population Is the set of all measurements of interest the investigator parameter Sample Is a subset of measurements selected from the population of interest statistic
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Data Scale Qualitative Data a. Nominal
Example: gender, date birth same level b. Ordinal Example : taste, grade score(difference level) Quantitative Data a. Interval Data have a range Example : Hot enough: – 80 derajat C, Hot 80 – 110 C, Very Hot: 110 – 140 C b. Ratio Data Can be applied with mathematic operations Example : height, weight
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What is measure of tendency?
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AIM Central tendency QOLB An Naas Dispersion tendency
MISSING Dispersion tendency MISSING Dispersion tendency MISSING
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Statistic Ilustration
Imagine you were a statistician, confronted with a set of numbers like 1,2,7,9,11 Consider a notion of “location” or “central tendency – the “best measure” is a single number that, in some sense, is “as close as possible to all the numbers.” What is the “best measure of central tendency”?
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Measure of central tendency
A statistical measure that identifies a single score as representative for an entire distribution. The goal of central tendency is to find the single score that is most typical or most representative of the entire group.
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Measure of central tendency
Mean Population mean vs. sample mean Example N=4: 3,7,4,6
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Computing the Mean from a Frequency Distribution
X f 30 2 29 3 28 5 27 26
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Estimating the Mean from a Grouped Frequency Distribution
Example Interval f MdPt Sum 81-90 7 85.5 598.5 71-80 11 75.5 830.5 61-70 4 65.5 262.0 51-60 3 55.5 166.5 25 1857.5
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2. Median The score that divides a distribution exactly in half.
Exactly 50 percent of the individuals in a distribution have scores at or below the median. The median is often used as a measure of central tendency when the number of scores is relatively small, when the data have been obtained by rank-order measurement, or when a mean score is not appropriate. Therefore, it is not sensitive to outliers
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Calculating the Median
Order the numbers from highest to lowest If the number of numbers is odd, choose the middle value If the number of numbers is even, choose the average of the two middle values. odd: 3, 5, 8, 10, 11 median=8 even: 3, 3, 4, 5, 7, 8 median=(4+5)/2=4.5 Note : The mean is “sensitive to outliers,” while the median is not.
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Sensitivity to Outliers
Ex: Incomes in Weissberg, Nova Scotia (population =5) Person Income (CAD) Sam 5,467,220 Harvey 24,780 Fred 24,100 Jill 19,500 Adrienne 19,400 Mean 1,111,000 In the above example, the mean is $1,111,000, the median is 24,100. Which measure is better?
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Mean : Sensitivity to Outliers
Incomes in Weissberg, Nova Scotia (population =5) In the above example, the mean is $1,111,000, the median is 24,100. Which measure is better? Person Income (CAD) Sam 5,467,220 Harvey 24,780 Fred 24,100 Jill 19,500 Adrienne 19,400 Mean 1,111,000
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FREQUENCIES DISTRIBUTION :
It used to organized sistematically data in many group without reduce the data information If there are a lot of data then its will be divide on many of class but if the there are little data then we need’nt to devide it 4/4/2019
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Steps to make freq. distr
Decide the amount of the class (∑K) that will taken from N data Decide the range Decide Class Interval ∑K = 1 + 3,3 Log N Range (R) = The biggest obs-the smallest obs Ci = R / ∑K 4/4/2019
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Example
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∑K = 1 + 3,3 Log 80 =7.28~7 R=99-35=64 Ci=64/7=9.14 ~10
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Finding Mean for grouped data
with xk=midle value every classnilai tengah tiap kelas fk =class frequencies
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Finding Med For grouped data
with Tb : lb med interval class, i: class interval N : amount of the observation fseb : cum freq before med class
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MODUS Is value or phenomenon that the most often appear, if the data is grouped than we have :
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