Chapter I Measures of Central Tendency Variability Curriculum

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

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

1. Population Is the set of all measurements of interest the investigator parameter 2. Sample Is 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

What is measure of tendency?

An Naas AIM Dispersion tendency MISSING Central tendency QOLB 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 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.

Measure of central tendency 1. Mean Population mean vs. sample mean – Example N=4: 3, 7, 4, 6

The weighted mean Example • Group A: n=12 • Group B: n=8 • Weighted mean = 6. 4

Computing the Mean from a Frequency Distribution X 30 29 28 27 26 f 2 3 5 3 2

Estimating the Mean from a Grouped Frequency Distribution Example Interval f Md. Pt 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 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.

Sensitivity to Outliers Ex: Incomes in Weissberg, Nova Scotia (population =5) Person Income (CAD) Sam Harvey 5, 467, 220 24, 780 Fred Jill Adrienne Mean 24, 100 19, 500 19, 400 1, 111, 000 In the above example, the mean is $1, 111, 000, the median is 24, 100. Which measure is better?

Mean : Sensitivity to Outliers Incomes in Weissberg, Nova Scotia (population =5) Person Sam Harvey Fred Jill Adrienne Mean Income (CAD) 5, 467, 220 24, 780 24, 100 19, 500 19, 400 1, 111, 000 In the above example, the mean is $1, 111, 000, the median is 24, 100. Which measure is better?