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# Rt graphical representation

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Graphical representation

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### Rt graphical representation

1. 1. Graphical representation of data (Using Box-and-Whisker Diagram) Module Tutor: Rinchen Tshewang,
2. 2. To Start <ul><li>-What is median? What are other related positional values? </li></ul><ul><li>-Think individually what you know about the box plot. </li></ul><ul><li>-Share with your neighbour </li></ul><ul><li>-Group discussion </li></ul>
3. 3. BOX-AND-WHISKER PLOT / 5 NUMBER SUMMARY: <ul><li>They allow people to explore data and to draw informal conclusions when two or more variables are present. </li></ul><ul><li>It shows only certain statistics rather than all the data. </li></ul><ul><li>Five-number summary is another name for the visual representations of the box-and-whisker plot. </li></ul><ul><li>The five-number summary consists of the median, the quartiles, and the smallest and greatest values in the distribution. </li></ul><ul><li>Immediate visuals of a box-and-whisker plot are the center, the spread, and the overall range of distribution. </li></ul><ul><li>There are two types of box and whisker plot: </li></ul><ul><li>Traditional box and whisker plot </li></ul><ul><li>Modified version of the box and whisker plot. </li></ul>
4. 4. Traditional box and whisker OR The 5 Number Summary <ul><li>The five number summary is another name for the visual representation of the box and whisker plot. </li></ul><ul><li>The five number summary consist of : </li></ul><ul><ul><li>The median ( 2 nd quartile) </li></ul></ul><ul><ul><li>The 1 st quartile </li></ul></ul><ul><ul><li>The 3 rd quartile </li></ul></ul><ul><ul><li>The maximum value in a data set </li></ul></ul><ul><ul><li>The minimum value in a data set </li></ul></ul>
5. 5. Median drive = 85 yards Single middle value Review on the Median The median is the middle value of a set of data once the data has been ordered . Example 1 . Ugyen hits 11 balls at T/phu driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his/her drives. 85, 125, 130, 65, 100, 70, 75, 50, 140, 95, 70 50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 140 Ordered data
6. 6. Median drive = 90 yards Two middle values so take the mean. Review on The Median The median is the middle value of a set of data once the data has been ordered . Example 2 . Rinzin hit 12 balls at T/phu driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his/her drives. 85, 125, 130, 65, 100, 70, 75, 50, 140, 135, 95, 70 50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 135, 140 Ordered data
7. 7. Finding the median, quartiles and inter-quartile range. 12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Order the data Inter- Quartile Range = 9 - 5½ = 3½ Example 3 : Find the median and quartiles for the data below. Lower Quartile = 5½ Q 1 Upper Quartile = 9 Q 3 Median = 8 Q 2
8. 8. 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Finding the median, quartiles and inter-quartile range. 6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10 Order the data Inter- Quartile Range = 10 - 4 = 6 Example 4 : Find the median and quartiles for the data below. Upper Quartile = 10 Q 3 Lower Quartile = 4 Q 1 Median = 8 Q 2
9. 9. Lower Quartile Upper Quartile Lowest Value Highest Value <ul><ul><li>Note: plotting the median, lower quartile and upper quartile i.e. the box portion shows the range of middle 50% of the members with the median being the mid-point. </li></ul></ul>4 5 6 7 8 9 10 11 12 Median Box Whisker Whisker Anatomy of a Box and Whisker Diagram.
10. 10. Lower Quartile = 5½ Q 1 Upper Quartile = 9 Q 3 Median = 8 Q 2 4 5 6 7 8 9 10 11 12 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Example 5 : Draw a Box plot for the data below Drawing a Box Plot.
11. 11. Upper Quartile = 10 Q 3 Lower Quartile = 4 Q 1 Median = 8 Q 2 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Example 6: Draw a Box plot for the data below Drawing a Box Plot. 3 4 5 6 7 8 9 10 11 12 13 14 15
12. 12. Upper Quartile = 180 Q u Lower Quartile = 158 Q L Median = 171 Q 2 Question : Sonam recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data. Drawing a Box Plot. 137, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186 130 140 150 160 170 180 190 cm
13. 13. 2. The boys are taller on average. Question : The box plots for both boys and girls are shown below. Use the box plots to choose some correct statements comparing heights of boys and girls in the class. Justify your answers. Drawing a Box Plot. 130 140 150 160 170 180 190 Boys Girls cm 1. The girls are taller on average. 3. The girls show less variability in height. 4. The boys show less variability in height. 5. The smallest person is a girl 6. The tallest person is a boy
14. 14. Problem for the class to do: <ul><li>Suppose you caught 13 fish, during the after-math of the Paro Flood along the river side and you measured the length of the fish to be: (in cms) </li></ul><ul><li>12, 13,5,8,9,20,16,14,14,6,9,12,12 </li></ul><ul><li>Draw a box and whisker plot based on medians. </li></ul><ul><li>Assess step by step by step (peer assessment) as display the solution:- </li></ul><ul><li>Solution: </li></ul><ul><li>Step 1: Rewrite the data in order, from smallest length to largest: </li></ul><ul><li>5,6,8,9,9,12,12,12,13,14,14,16,20 </li></ul><ul><li>Step 2: Now find the median of all the numbers. Notice that since there are 13 numbers, the middle one will be the seventh number: </li></ul><ul><li>i.e. 12 </li></ul><ul><li>This must be the median (middle number) because there are six numbers on each side. </li></ul>
15. 15. <ul><li>Step 3: Is to find the lower quartile. This is the middle of the lower six numbers. The exact centre is half-way between 8 and 9 ... which would be 8.5 </li></ul><ul><li>Step 4: Now find the upper quartile. This is the middle of the upper six numbers. The exact centre is half-way between 14 and 14 ... which must be 14 </li></ul><ul><li>Now we are ready to start drawing the actual box and whisker diagram </li></ul><ul><li>Step 5: Draw an ordinary number line that extends far enough in both directions to include all the numbers in your data: locate the 5 number… </li></ul>5 10 15 20
16. 16. Final box and whisker plot:
17. 17. Short-comings of this plot: <ul><li>This method of display fails to show if the data does not have a near normal PDF. </li></ul><ul><li>For example: </li></ul><ul><li>Highly skewed and bimodal data are more difficult to discern using this data display method. The median and the traditional box-and-whisker diagram are often more representative when the data is bimodal. </li></ul>
18. 18. Homework: <ul><li>Investigate the Modified Box and whisker plot </li></ul><ul><li>Find out the difference between the two types of box and whisker plot </li></ul><ul><li>When and where should be use traditional and the modified box and whisker plot? </li></ul>
19. 19. <ul><li>The End </li></ul><ul><li>(Tashi Delek & Have a Great Day) </li></ul>