Chapter I Measures of Central Tendency & Variability
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Transcript of Chapter I Measures of Central Tendency & Variability
Chapter IChapter IMeasures of Central TendencyMeasures of Central Tendency
& Variability& 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
Descriptive Inferential
Statistics
What is Statistics?
• 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
Mean
Median
Mode
Measures ofCentral Tendency
Variance
Standard Deviation
Range
Deviation
Mean Deviation
Sum of SquaredDeviation
Measure ofVariability
FrequencyDistribution tables
FrequencyDistribution Polygon
Histogram
Bar Graph
GraphicDisplays
DescriptiveStatistics
z-scores
Single Samplet statistic
Independentt statistic
Dependentt statistic
Estimation
PearsonCorrelation
Phi-coefficient
Linear Regression
Correlation &Regression
Test forGoodness of Fit
Test forIndependence
Chi-Square
InferentialStatistics
1. PopulationIs the set of all measurements of interest the
investigator parameter
2.SampleIs a subset of measurements selected from
the population of interest statistic
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: 50 – 80 derajat C, Hot 80 – 110 C, Very Hot: 110 – 140 C b. Ratio Data Can be applied with mathematic operations
Example : height, weight
An Naas
Dispersion tendency
MISSING
AIM
Central tendencyCentral tendencyQOLBQOLB
Dispersion tendency
MISSING
Dispersion tendency
MISSING
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”?
Measure of central tendency
• Central tendencyCentral tendency– A statistical measure that identifies A statistical measure that identifies
a single score as representative for a single score as representative for an entire distribution. an entire distribution.
– The goal of central tendency is to The goal of central tendency is to find the single score that is most find the single score that is most typical or most representative of typical or most representative of the entire group.the entire group.
Measure of central tendencyMeasure of central tendency1.1. MeanMeanPopulation mean vs. sample mean
– Example
N=4: 3,7,4,6
N
X
54
20
n
Xx
n
Xx
Computing the Mean from a Frequency Distribution
X f
30 2
29 3
28 5
27 3
26 2
1
1
K
i iiN
ii
X fX
f
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
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
Calculating the MedianCalculating 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 :Note :The mean is “sensitive to outliers,” while the median is not.The mean is “sensitive to outliers,” while the median is not.
Sensitivity to OutliersEx: 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 In the above example, the mean is $1,111,000, the median is 24,100.24,100.Which measure is better?Which measure is better?
Mean : Sensitivity to OutliersMean : 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
04/19/23
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
04/19/23
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
Example
∑K = 1 + 3,3 Log 80 =7.28~7
R=99-35=64
Ci=64/7=9.14 ~10
Finding Mean for grouped dataFinding Mean for grouped data
with
xk=midle value every classnilai tengah tiap kelas
fk =class frequencies
withTb : lb med interval class,i: class intervalN : amount of the observationfseb : cum freq before med class
med
seb2
1
medf
fNi
Tb
Finding Med For grouped dataFinding Med For grouped data
MODUS
Is value or phenomenon that the most often appear, if the data is grouped than we have :