Measures of Central Tendency & Variability in Health Informatics

This content discusses various measures of central tendency (mean, mode, median) and explores the concept of nominal, ordinal, and interval/ratio-level data in health informatics. It emphasizes the importance of understanding these statistical measures for data analysis and interpretation in the field of healthcare.

• Central Tendency
• Variability
• Health Informatics
• Data Analysis
• Statistical Measures

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1. Central Tendency & Variability Heibatollah Baghi, Mastaneh Badii, and Farrokh Alemi Ph.D. HEALTH INFORMATICS PROGRAM HI.GMU.EDU

2. Mean MEASURESOF CENTRAL TENDENCY: MEAN X = X n Count of observations 23, 23, 24, 25, 25 ,25, 26, 26, 27, 28. 25.2 2 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

3. MEASURESOF CENTRAL TENDENCY: MODE Mode 20, 21, 21, 22, 22, 22, 22, 23, 23, 24 3 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

4. MEASURESOF CENTRAL TENDENCY: MEDIAN Median 21, 22, 22, 23, 24, 26, 26, 27, 28, 29 50% 50% 4 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

5. Median 22, 23, 23, 24, 25, 26, 27, 27, 28 50% 50% 5 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

6. Nominal, Ordinal, and (sometimes) Interval/Ratio-Level Data Ordinal-Level Data and Interval/Ratio-Level data (particularly when skewed) Mode Most frequently occurring value Median Exact center (when odd N) of rank-ordered data or average of two middle values (when even N) Mean Arithmetic average (Sum of Xs/N) Interval/Ratio-Level Data 6 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

7. COMPARISONOF MEASURESOF CENTRAL TENDENCY Nominal, Ordinal, and (sometimes) Interval/Ratio-Level Data Ordinal-Level Data and Interval/Ratio-Level data (particularly when skewed) Mode Most frequently occurring value Median Exact center (when odd N) of rank-ordered data or average of two middle values (when even N) Mean Arithmetic average (Sum of Xs/N) Interval/Ratio-Level Data 7 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

8. COMPARISONOF MEASURESOF CENTRAL TENDENCY Mode Most frequently occurring value Nominal, Ordinal, and (sometimes) Interval/Ratio-Level Data Ordinal-Level Data and Interval/Ratio-Level data (particularly when skewed) Median Exact center (when odd N) of rank-ordered data or average of two middle values (when even N) Mean Arithmetic average (Sum of Xs/N) Interval/Ratio-Level Data 8 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

9. COMPARISONOF MEASURESOF CENTRAL TENDENCYIN NORMAL DISTRIBUTION Frequency Normal 9 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

10. COMPARISONOF MEASURESOF CENTRAL TENDENCYIN BIMODAL DISTRIBUTION Frequency Bi-modal 10 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

11. Skewed to Left Frequency Negatively Skewed Outliers pull the mean away From the median 11 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

12. Skewed to Right Frequency Positively Skewed Outliers pull the mean away From the median 12 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

13. Frequency Uniform 13 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

14. Frequency Exponential 14 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

15. MEASURESOF VARIABILITYOR SCATTER Same Average Different Variability 15 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

16. MEASURESOF VARIABILITYOR SCATTER: RANGE Range Max 110, 120, 130, 140, 150, 160, 170, 180, 190 Min 16 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

17. MEASURESOF VARIABILITYOR SCATTER: SEMI INTER- QUARTILE RANGE Standard Quartile Range SQR = (Q3-Q1)/2 17 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

18. Sum Squares &Variance ss = (X - M)2 ss =n 2 s 1 18 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

19. Standard Deviation 2 ( X ) X = i S 1 n 19 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

20. 2 ( ) X = 2 SS X Sum of Squares n ss =n 2 s Variance ss 1 = s Standard Deviation 1 n 20 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

21. Data 110 120 130 140 150 150 160 170 180 190 Total X-M (X - M)2 CALCULATING STANDARD DEVIATION -40 1600 -30 900 -20 400 -10 100 0 0 0 0 10 100 20 400 30 900 40 1600 0 6000 (SS) 9 N-1 Sample Variance Standard Deviation 667 25.8 SS is the key to many statistics 21 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

22. Calculating formula Defining formula FORMULA VARIATIONS 2 ( ) X Sum of squares 2 ( X ) X = 2 SS X i = 2 s n 1 n ss Variance 2 ( X ) X =n 2 s i = 2 s ss 1 1 n Standard deviation 2 ( X ) X = i = S s 1 n 1 n 22 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

23. 23 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

24. STANDARDIZED SCORES: Z SCORES Standard Score Z = (x-m) / s 24 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

25. STANDARDIZED SCORES: Z SCORES Z = (x-m) / s Z = 140 110 / 10 = 3 25 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

26. Histogram 12 Expected Observed 10 Frequency 8 6 4 2 0 -1.71 -0.95 -0.18 0.59 1.36 More Bin 26 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY

27. Measures of Central Tendency & Variability Can Describe the Distribution of Data