1. Sumukh Deshpande n Lecturer College of Applied Medical Sciences Statistics = Skills for life. BIOSTATISTICS (BST 211) Lecture 3

2. Displaying Data Diagrammatically

3. Basic Concepts  Frequency  Cumulative Frequency  Relative Frequency  Bar Charts  Histograms  Pie Charts  Stem-and-leaf Charts

4. What Can you see from a chart?  Shape of Distribution  Mode: uni or multimodal?  outliers  Is the data symmetrical?  Skewed to the right (+ve)  Skewed to the left (-ve)

5. Worked example  Birth weight of 46 babies in kg. Plot the data into a histogram and a pie chart

6. Histogram Frequency

7. What can you see in a histogram? Mode The distribution is NOT symmetrical Distribution skewed to the left (-vely skewed)

8. Multimodal Histogram  Example: 1, 2, 4, 4, 4, 7, 8, 8, 8, 9, 9  Mode: 4 and 8 XFrequency 11 21 43 71 83 92

9. Relative Frequency Freq of x divided by total frequencies

10. Relative Frequency Table Illustration WeightFreqRelFreq 1.811/46=0.022 2.011/46=0.022 2.211/46=0.022 2.422/46=0.043 2.644/46=0.087 2.844/46=0.087 3.066/46=0.130 3.21212/46=0.261 3.499/46=0.196 3.622/46=0.043 3.844/46=0.087 n = 46

11. Relative Frequency

12. Understanding Relative Freq chart Mode The distribution is NOT symmetrical Symmetry is easier to judge here The outlines of Relative Freq and histogram are similar.

13. Cumulative Frequency Freq of x plus sum of previous freq’s

14. Cumulative Frequency Table Illustration WeightFreqCumFreq 1.811 2.011+1=2 2.211+2=3 2.422+3=5 2.644+5=9 2.844+9=13 3.066+13=19 3.21212+19=31 3.499+31=40 3.622+40=42 3.844+42=46

15. Cumulative Frequency Cumulative Frequency Chart

16. What can you in a Cum Freq chart? Median & Quartiles http://www.bbc.co.uk/schools/gcsebitesize/mat hs/statistics/representingdata3hirev5.shtml Median: reading nb 23? Upper Quartile (Q3) nb 34.5? Lower Quartile (Q1) nb 11.5?

17. Pie Chart Circle is 360° and each frequency is represented by a suitable angle OR

18. Pie Chart Table Illustration WeightFreqAngle 1.811 X (360/46) = 7.8 2.011 X (360/46) = 7.8 2.211 X (360/46) = 7.8 2.422 X (360/46) = 15.7 2.644 X (360/46) = 31.3 2.844 X (360/46) = 31.3 3.066 X (360/46) = 47.0 3.21212 X (360/46) = 93.9 3.499 X (360/46) = 70.4 3.622 X (360/46) = 15.7 3.844 X (360/46) = 31.3 n = 46

19. Pie Chart

20. What can you spot in a pie chart? Illustrates Proportion of data in a sample or population

21. Horizontal Bar Chart Frequency

22. Stem and Leaf Chart XFrequency 1.82 2.01 2.21 2.42 2.64 2.84 3.06 3.212 3.49 3.62 3.84 1. 8 8 2.0 2. 2 2. 4 4 2. 6 6 6 6 2. 8 8 8 8 3. 0 0 0 0 0 0 3. 2 2 2 2 2 2 2 2 2 2 2 2 3. 4 4 4 4 4 4 4 4 4 3. 6 6 3. 8 8 8 8

23. Stem and Leaf Example 21112132212211324321 32432211431021432210 XFrequency 102 113 215 223 323 434 10 11 1 1 21 1 1 1 1 22 2 2 3 43 3 3

24. Comparison 1.8 8 2.0 2. 2 2. 4 4 2. 6 6 6 6 2. 8 8 8 8 3. 0 0 0 0 0 0 3. 2 2 2 2 2 2 2 2 2 2 2 2 3. 4 4 4 4 4 4 4 4 4 3. 6 6 3. 8 8 8 8

25. Conclusions  The same information can be presented in different format  Each type of chart can emphasise certain information  MS Excel can do all these charts and more  Download the Excel sheet for lecture 3 and practice in your own time