Biostatisticslec3 for pharmacy studentss
- 1. Mathematics & Biostatistics Assistant Professor Aseel Hisham 2025 - 2024
- 2. Lecture 8 Biostatistics Mathematical presentation Assistant Professor Aseel Hisham 2024-2025
- 3. Methods of presentation of data 1-Mathematical or Numerical presentation 2-Tabular presentation. 3-Graphical presentation. 4-Pictorial presentation.
- 4. 1-Mathematical or Numerical presentation 1- Measures of central tendency:- A measure of central tendency is a measure which indicates where the middle of the data is. -The three most commonly used measures of central tendency are: The arithmetic mean, the Median, and the Mode. 2- Measures of dispersion :-
- 5. 1-Measures of central tendency 1-Arithmetic mean (Mean) (μ) It is the average of the data. Sum of all observations Number of observations 2-Median The observation which lies in the middle of the ordered observation. 3-Mode The value which occurs with the greatest frequency i.e. the most common value
- 6. 1-Arithmetic mean (Mean) (μ) -Mean of population =(x)/n -Mean of sample X¯ =(x)/n
- 7. Example Find the mean of ( 6, 8, 11, 5, 2, 9, 7,8) Solution 𝑿~ = σ𝒊=𝟏 𝒏 𝒙𝒊 𝒏 = 6 + 8 + 11 + 5 + 2 + 9 + 7+8 𝟖 = 𝟓𝟔 𝟖 = 7
- 8. Properties of the Mean 1- A single value. 2- Simple , easy to understand and to compute. 3-Affected by extreme values. 4- It take in consideration all values in the set (did not exclude any single value).
- 9. Example -Assume the values are 115, 110, 119, 117, 121 and 126. The mean = 118. -But assume that the values are 75, 75, 80, 80 and 280. The mean = 118, a value that is not representative of the set of data as a whole.
- 10. The Median
- 13. The Mode -It is the value which occurs most frequently. -Example: For the same random sample, the value 28 is repeated two times, so it is the mode
- 14. Properties of the Mode: • Sometimes, it is not unique. • - It may be used for describing qualitative data. • -It is not affected by extreme values. • -If all values are different there is no mode. • -Sometimes, there are more than one mode. • -Data distribution with one mode is called “unimodal”. • -When a distribution has two “modes,” it is called bimodal. • -If a distribution has more than 2 “modes,” it is called multimodal. • -The mode is not a very useful measure of central tendency. • -It is insensitive to large changes in the data set. • -The mode it is used for quantitative and qualitative data.
- 15. Relations Between the Measures of Central Tendency • In symmetrical distributions, the median and mean are equal. • For normal distributions, mean = median = mode. • In positively skewed distributions, the mean is greater than the median. • In negatively skewed distributions, the mean is smaller than the median.
- 16. 2-Measures of dispersion A measure of dispersion conveys information regarding the amount of variability present in a set of data. • Note: 1. If all the values are the same → There is no dispersion . 2. If all the values are different → There is a dispersion:- a). If the values close to each other →The amount of Dispersion small. b).If the values are widely scattered → The Dispersion is greater.
- 17. 2-Measures of dispersion Measures of non central locations 1-Range(R). 2-Variance(S2). 3-Standard deviation(SD). 4-Standard error(SE). 5-Coefficient of variation(C.V).
- 18. 1.The Range (R)
- 19. Properties of the Range • Simple to calculate. • Easy to understand . • It neglect all values in the center and depend on the extreme value. • It is not passed on all observation. • It is not amenable for further mathematic treatment. • Should be used in conjunction with other measures of variability.
- 20. 2.The Variance(S2) -Population Variance (sigma squared) 𝟐 = σ(𝒙 − μ) 𝟐 𝒏 -Sample Variance 𝑺𝟐 = 𝒏 σ 𝒙𝟐 − ( σ 𝒙) 𝟐 𝒏 − 𝟏
- 21. Properties of Variance •Variance can never be a negative value. •All observation are considered. •The problem with the variance is the squared unit.
- 23. 3-Standard deviation (SD) • The standard deviation measured the variability between observation in the sample or the population or from the mean of the sample or that population. • The unite is not squared . • SD is the most widely used measure of desperation.
- 24. 4-Standard error (SE) • A measure of variability among means of samples selected from certain population. • It measures the variability of dispersion of the sample mean from population mean. • It is used to estimate the population mean, and to estimate differences between populations means. • SE=SD/ 𝒏
- 25. 5.The Coefficient of Variation (C.V)
- 26. Properties of the Coefficient of Variation (C.V) • It has no unit. • It is used to compare dispersion in two sets of data especially when the units are different. • It measures relative rather than absolute variation. • It takes in consideration all values in the set.