Practical Exercise Biostatistics

Muhammad Afzal Senior Research Officer

Community Medicine Department

For the following data set calculate

1) Range 2) Mean3) Median4) Mode5) Standard deviation 6) Quartiles (Q1, Q2, Q3)

14241315112213201619

1. Range:

Range: Maximum value – Minimum Value

Range = 13

2. Mean: Mean: Sum of all values / n

Mean = 167 / 10 = 16.70

3. Median:

Median: (if No. of values Even, n = 10) Arrange All values in Ascending order then (n+1)/2 th Value 11 / 2 = 5.5 th value = 15+16/2 = 15.50 11, 13, 13, 14, 15, 16, 19, 20, 22, 24

3. Median:

Median: (if No. of values Odd, n = 11) Arrange All values in Ascending order then (n+1)/2 th Value 12 / 2 = 6 th value 11, 13, 13, 14, 15, 16, 19, 20, 22, 24, 31

4. Mode:

Mode: Most Frequently Occurring value

11, 13, 13, 14, 15, 16, 13, 20, 22, 24 Mode = 13

4. Mode:

Mode: (2nd case) Most Frequently Occurring value

11, 13, 13, 14, 15, 16, 16, 20, 22, 24 Mode = ????

5. Standard Deviation:

Standard Deviation:

SD=

Steps to calculate SD:

10

1. Calculate mean of all observations2. Calculate difference between each individual

measurement and mean3. Square all these differences4. Take sum of all squared differences5. Divide this sum by number of measurements6. Finally take the square root of value

x x-mean (x-mean)**214 -2.7 7.2924 7.3 53.2913 -3.7 13.6915 -1.7 2.8911 -5.7 32.4922 5.3 28.0913 -3.7 13.6920 3.3 10.8916 -0.7 0.4919 2.3 5.29167 168.1

So,

SD = Sqr ( 168.10 / 10 ) = Sqr ( 16.81) SD = 4.10

6. Quartiles: (Q1, Q2, Q3)

Q1 = n+1/4

Q2= n+1/2  Q3= 3(n+1)/4

11, 13, 13, 14, 15, 16, 19, 20, 22, 24, 31

Q1 = n+1/4 = 3rd Value

Q2= n+1/2 = 6th Value   Q3= 3(n+1)/4 = 9th Value

11, 13, 13, 14, 15, 16, 19, 20, 22, 24, 31

Exercise 2: For the following data set calculate

Mean Median Standard deviation and Quartiles (i.e. Q1, Q2, Q3) 

13 21 13 15 16 11 19 13 16