1. 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

2. What is Statistics?

3. 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

6. 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

7. 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

8. What is
measure of tendency?

9. AIM Central tendency QOLB An Naas Dispersion tendency
MISSING
Dispersion tendency
MISSING
Dispersion tendency
MISSING

10. 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”?

11. 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.

12. Measure of central tendency
Mean
Population mean vs. sample mean
Example
N=4: 3,7,4,6

13. Computing the Mean from a Frequency DistributionX f 30 2 29 3 28 5 27 26

14. 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

15. 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

16. 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.

17. 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?

18. 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

19. 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

20. 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

21. Example

22. ∑K = 1 + 3,3 Log 80
=7.28~7
R=99-35=64
Ci=64/7=9.14 ~10

23. Finding Mean for grouped data
with
xk=midle value every classnilai tengah tiap kelas
fk =class frequencies

24. 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

25. MODUS
Is value or phenomenon that the most often appear, if the data is grouped than we have :