Form 5 Chapter 7 Measures of Dispresion For Grouped Data.pptx

math form 5 kssm

1. MEASURES OF DISPERSION FOR GROUPED DATA 7.1 DISPERSION 7.2 MEASURES OF DISPERSION

2. HOW TO CONSTRUCT HISTOGRAM, FREQUENCY POLYGON AND OGIVE

3. We can observe the dispersion for a grouped data by constructing histogram and frequency polygon . Prior to that, you need to know the class interval, lower limit, upper limit, midpoint, lower boundary, upper boundary and cumulative frequency that can be obtained from a frequency table.

4. CLASS INTERVAL, LOWER LIMIT, UPPER LIMIT, MIDPOINT, LOWER BOUNDARY, AND UPPER BOUNDARY CAN BE OBTAINED FROM A FREQUENCY TABLE

5. CUMMULATIVE FREQUENCY The cumulative frequency of a class interval is the sum of the frequency of the class and the total frequency of the classes before it. This gives an ascending cumulative frequency

6. What is histogram? Histogram is a graphical representation in which the data is grouped into ranges by using contiguous bars. Aims to be easier to understand, analyse and present for a grouped data set.

7. STEPS IN CONSTRUCTING HISTOGRAM HISTOGRAM Find the lower boundary and upper boundary of each class interval. Choose an appropriate scale on the vertical axis. Represent the frequencies on the vertical axis and the class boundaries on the horizontal axis. Draw bars that represent each class where the width is equal to the size of the class and the height is proportionate to the frequency.

8. What is frequency polygon Frequency polygon is a graph that displays a grouped data by using straight line that connect midpoints of the classes which lie at the upper end of each bar in a histogram

9. Steps to construct a frequency polygon Mark the midpoints of each class on top of each bar. Mark the midpoints before the first class and after the last class with zero frequency. Draw straight lines by connecting the adjacent midpoints.

10. Steps to construct a frequency polygon without constructing a histogram Add one class interval before the first class and after the last class with zero frequency . Find the midpoint of each class interval. Use a suitable scale on the vertical axis for the frequencies. Label the horizontal axis with the midpoint of each classes. Mark the midpoint with the corresponding frequency. Connect each midpoint with a straight line.

11. FREQUENCY POLYGON

12. A distribution is symmetric if the shape and size of the distribution are almost the same when divided into two parts, left and right. The shape of distribution is skewed if one tail of the histogram is longer than the other tail. DISTRIBUTION SHAPES OF DATA

13. State the distribution shape of the histogram for the two events. (b) Which event has a wider dispersion of the time taken? Give your reason. (c) Between backstroke and freestyle, in which event did the swimmers perform better?

14. FREQUENCY POLYGON FROM A HISTOGRAM WITHOUT HISTOGRAM Mark the midpoints of each class on top of each bar Mark the midpoints before the 𿿿first class and after the last class with zero frequency. Draw straight lines by connecting the adjacent midpoints Add one class interval before the first class and after the last class with zero frequency Find the midpoint of each class interval Choose an appropriate scale on the vertical axis. Represent the frequencies on the vertical axis and the midpoints on the horizontal axis Mark the midpoint with the corresponding frequency Connect each midpoint with a straight line

15. STEP IN CONSTRUCTING OGIVE Add one class before the first class with zero frequency. Find the upper boundary and the cumulative frequency for each class. Choose an appropriate scale on the vertical axis to represent the cumulative frequencies and the horizontal axis to represent the upper boundaries. Plot the cumulative frequency with the corresponding upper boundary. Draw a smooth curve passing through all the points. OGIVE

16. TYPES X-AXIS Y-AXIS HISTOGRAM (HTK) H (histogram) T ( titik tengah /median) K (kekerapan/frequency) FREQUENCY POLYGON (FTK) F (frequency polygon) T (titik tengah/median) K (kekerapan/frequency) OGIVE (OSALO) O (ogive) SA (sempadan atas/ upper boundary) LO ( longgokan / cummulative frequency) HOT TIPS ! USEFUL IN CONSTRUCTING GRAPHS :

17. EXAMPLE OF HISTOGRAM AND FREQUENCY POLYGON

18. EXAMPLE OF OGIVE

19. FIRST QUARTILE, MEDIAN, THIRD QUARTILE FROM AN OGIVE

20. PERCENTILE -WE CAN ANALYSE A LARGE DATA MORE EASILY AND EFFECTIVELY WHEN WE DIVIDE THE DATA INTO SMALL PARTS WHICH IS KNOWN AS PERCENTILE. A PERCENTILE IS A VALUE THAT DIVIDES A SET OF DATA INTO 100 EQUAL PARTS AND IS REPRESENTED BY P1 , P2 , P3 , …, P99

21. PERCENTILE -WE CAN ANALYSE A LARGE DATA MORE EASILY AND EFFECTIVELY WHEN WE DIVIDE THE DATA INTO SMALL PARTS WHICH IS KNOWN AS PERCENTILE. A PERCENTILE IS A VALUE THAT DIVIDES A SET OF DATA INTO 100 EQUAL PARTS AND IS REPRESENTED BY P1 , P2 , P3 , …, P99

22. 7.2 MEASURES OF DISPERSION (GROUPED DATA)

23. RANGE AND INTERQUARTILE RANGE

24. VARIANCE AND STANDARD DEVIATION

25. How to construct and interpret a box plot for a set of grouped data?

26. HOW TO COMPARE AND INTERPRET TWO OR MORE SETS OF GROUPED DATA BASED ON MEASURES OF DISPERSION?

27. QUESTION TIME