LearnStat MEASURES OF CENTRAL TENDENCY, Learning Statistics the Easy Way. Session on BUREAU OF LABOR AND EMPLOYMENT STATISTICS

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1 LearnStat t Learning Statistics the Easy Way Session on MEASURES OF CENTRAL TENDENCY, DISPERSION AND SKEWNESS

2 MEASURES OF CENTRAL TENDENCY, DISPERSION AND SKEWNESS OBJECTIVES At the end of the session, the participants should be able to: 1. Describe data using the common measures of central tendency; 2. Describe data in terms of their variability and skewness; and 3. Determine the most applicable measure of central tendency given different types of distribution. 2

3 OUTLINE 1. Measures of Central Tendency ٠Mean ٠Median ٠Mode 2. Measures of Dispersion 3. Skewness 4. Types of Distribution 3

4 Measures of Central Tendency n A. MEAN - commonly referred to as the average or arithmetic mean. - most widely used measure of central location. X = Sum of all values in the data set Total number of observations 4

5 Measures of Central Tendency Ages of 13 Job Applicants Example of mean computation Mean Age X = Applicant Age Number = 318/ = Total 318 5

6 Measures of Central Tendency n B. MEDIAN - the value of the middle item in a set of observations which has been arranged in an ascending or descending order of magnitude. - is the centermost value in a distribution. ib ti 6

7 Measures of Central Tendency Ages of 13 Job Applicants Example of finding the median (Number of observations is odd) 7 Applicant Age Number The median value is the middle most value in the data set. Median age = 25

8 Measures of Central Tendency Ages of 14 Job Applicants Example of finding the median (Number of observations is even) 8 Applicant Number Age The median value is the sum of the two middle most values in the data set divided by 2. Median age = = 25.5

9 Measures of Central Tendency n C. MODE - is the value in the data set that occurs most frequently. Example of finding the mode 9 Ages of 13 Job Applicants Applicant Number Age Mode = 25 is the value that occurs most frequently

10 Measures of Central Tendency n Advantages of the MEAN: takes into account all observations. can be used for further statistical calculations and mathematical manipulations. Disadvantages of the MEAN: easily affected by extreme values. cannot be computed if there are missing values due to omission or non-response. in grouped data with open-ended class intervals, the mean cannot be computed. 10

11 Measures of Central Tendency Advantages of the MEDIAN: not affected by extreme values. can be computed even for grouped data with open- ended class intervals. Disadvantages of the MEDIAN: Observations from dff different data sets have to be merged to obtain a new median, whether group or ungrouped data are involved. 11

12 Measures of Central Tendency Advantage of the MODE: can be easily identified through ocular inspection. Disadvantages of the MODE: does not possess the desired d algebraic property of the mean that allows further manipulations. like the median, observations from different data sets have to be merged to obtain a new mode, whether group or ungrouped data are involved. 12

13 MEASURES OF DISPERSION Let us take 5 sets of observations Set 1: Set 2: Set 3: Set 4: Set 5: x = 47 Questions remain unanswered even after getting the mean: How variable are the data sets? How do the values in each data set differ from each other? How are the values in each data set clustered or dispersed from each other? 13

14 Measures of Dispersion - group of analytical tools that describes the spread or variability of a data set. 14

15 Importance of the measures of dispersion supplements an average or a measure of central tendency compares one group of data with another indicates how representative the average is. 15

16 A measure of dispersion can be expressed in several ways: Measures of Dispersion Range Quartile Deviation Mean Absolute Deviation Variance/ Standard Deviation Based on the position of an observation in a distribution Measures the dispersion around an average Coefficient of variation Expressed in a relative value 16

17 SKEWNESS describes the degree to which the data deviates from symmetry. when the distribution of the data is not symmetrical, it is said to be asymmetrical or skewed. 17

18 Types of Distribution (in Relation to Mean, Median and Mode) Symmetrical/Normal Distribution Bell shaped distribution The mean, median and mode are all located at one point. Mean = Median = Mode 18

19 Positively Skewed Distribution Observations are mostly concentrated towards the smaller values and there are some extremely high values. Also called skewed to the right distribution No. of obser rvations Mode Median Mean Income Mode < Median < Mean 19

20 Negatively Skewed Distribution Observations are mostly concentrated towards the larger values and there are some extremely low values. No. of obser rvations Also called skewed to the left distribution. Mean Median Mode Age of BLES staff Mean < Median < Mode 20

21 Considerations to be made when using the three most common measures of central tendency: Distribution Level of Measurement Measure to Use Other Considerations Normal Interval or Mean When further statistical Ratio calculations or mathematical manipulations are needed When all observations are considered in the computation Skewed Ordinal Median When distribution has open-ended ended intervals Skewed Nominal Mode When interested in the most frequently occurring observation 21

22 Special Topic on Rounding Off Rules for Rounding off Numbers: If the first digit it to be dropped d is less than 5, round down. If the first digit to be dropped is greater than or equal to 5, round up.

23 Examples: Round off into a whole number: 186 Round off into a whole number: 185 Round off into a whole number: 185 Round off into one decimal place: 2.1 Round off into two decimal places: 2.07

24 More Examples: 1. Manual Computation 2010 labor productivity (at constant 2000 prices) = (GDP/Employed) 5,701,539M = 158, , M * = = Region VI-Employment growth rate ( ): Growth 2,974 Rate = = ( ) 100 2,883 * = x 100 = 3.156% = 3.2% *In LFS, figures are expressed in thousands.

25 2. Electronic Computation In Microsoft Excel, you can use the following syntax: =round(value to be rounded off, number of decimal place to be retained) The value to be rounded off can be a single number or a formula to obtain a single number. Example: Round off into two decimal places: =round( , 2) = labor productivity at constant 2000 prices: 5,701,539 round = 1,000,0 = 158,222 36,035

26 Labor Productivity Worksheet

27 Growth Rate Worksheet

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