Biostatistics Lectures PDF

Lectures of Biostatistics Prepared By: Assoc. Prof. M A Alawady Department of Mathematics Faculty of Science Zagazig University 2022 2 3 4 5 6 7 8 Median for Grouped Data 9 10 11 12 13 Mode...

Lectures of Biostatistics Prepared By: Assoc. Prof. M A Alawady Department of Mathematics Faculty of Science Zagazig University 2022 2 3 4 5 6 7 8 Median for Grouped Data 9 10 11 12 13 Mode for Grouped Data 14 15 16 17  Descriptive Statistics Measures of Dispersion key words: Descriptive Statistic, measure of dispersion, range,variance, coefficient of variation. 19  Descriptive Statistics - 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: 3.If the values close to each other →The amount of Dispersion small. b) If the values are widely scattered → The Dispersion is greater. 20  ** Measures of Dispersion are : 1.Range (R). 2. Variance. 3. Standard deviation. 4.Coefficient of variation (C.V). 21 1.THE RANGE (R): Range =Largest value- Smallest value = 𝑥(𝑛) − 𝑥(1) Note: Range concern only onto two values Example : 43,66,61,64,65,38,59,57,57,50. Find Range? Range=66-38=28 22  2.The Variance: It measure dispersion relative to the scatter of the values a bout there mean. a) Sample Variance ( 𝑆 2 ) : σ 𝑛 2 (𝑥 − 𝑥) lj 𝑆2 = 𝑖=1 𝑖 ,where 𝑥lj is the sample mean 𝑛−1 Example: Refer to previous Example Find Sample Variance of ages , 𝑥lj = 56 Solution: S2= [(43-56) 2 +(66-56) 2+…..+(50-56) 2 ]/ 10 = 900/10 = 90 23  𝜎 2 b)Population Variance ( ) : σ𝑁 2 (𝑥 𝑖=1 𝑖 − 𝜇) 𝜎2 = 𝑁 where 𝜇 is Population mean 3.The Standard Deviation: is the square root of variance= 𝑉𝑎𝑟𝑖𝑛𝑐𝑒 a) Sample Standard Deviation = S = 𝑆 2 b) Population Standard Deviation = σ = 𝜎 2 24 25 26 27 4.The Coefficient of Variation (C.V): Is a measure use to compare the dispersion in two sets of data which is independent of the unit of the measurement. 𝑆 𝐶. 𝑉 = 𝑋ሜ (100) where S: Sample standard deviation. 𝑋ሜ : Sample mean. 28  Example: Suppose two samples of human males yield the following data: Sampe1 Sample2 Age 25-year-olds 11year-olds Mean weight 145 pound 80 pound Standard deviation 10 pound 10 pound 29  We wish to know which is more variable. Solution: c.v (Sample1)= (10/145)*100= 6.9 c.v (Sample2)= (10/80)*100= 12.5 Then age of 11-years old(sample2) is more variation 30