Chapter I Measures of Central Tendency & Variability

1. Chapter IMeasures 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: 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

8. What is measure of tendency?

9. An Naas AIM Central tendency QOLB 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 • 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. The weighted mean Example • Group A: n=12 • Group B: n=8 • Weighted mean = 6.4

14. Computing the Mean from a Frequency Distribution

15. Estimating the Mean from a Grouped Frequency Distribution Example

16. 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

17. 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.

18. Sensitivity to Outliers Ex: 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?

19. 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?