Mathematics 10 - Quarter 4 Week 1-4 (Quartiles, Deciles and Percentiles).pptx

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1. y x L 1 L 2 ( x 1 , y 1 ) x 1 y 1 MATHEMATICS 10       1

2. Session 2nd Session 5th Session 3r d Session 1st Session 4 th Mathematics 10 – Quarter 4 Week 1-4 Tchr. James Luck M. Valenzuela 2

3. If you will be ranked together with the people living with you at home given the following situations, what would it be?   Order of birth from youngest to eldest Weight in kilograms from lightest to heaviest Your height in feet from shortest to tallest 3

4. STATISTICS 4

5. 5 QUARTILES (Q 1 , Q 2 , Q 3 ) The quartiles are points that divide a ranked data into four equal parts. Each set of data has 3 quartiles. First Quartile or Q 1 , 25% of the scores are smaller in value than Q 1 and 75% of the scores are higher in value. It is sometimes called the lower quartile. Second Quartile or Q 2 is above 50% and at the same time below 50% of the scores which means that it is the median of the scores. Third Quartile or Q 3 , 75% of the scores are smaller in value than Q 3 and 25% of the scores are higher in value. It is sometimes called the upper quartile. Lowest Score Q 1 Q 2 Q 3 Highest Score Interquartile range is the difference of the upper quartile and the lower quartile. 25% 25% 25% 25%

6. 6 Example 1: Quartiles (Ungrouped Data) A = {15, 23, 19, 37, 25, 39, 43}. Find the upper and lower quartile and the median

7. 7 B = {48, 39, 57, 32, 28, 63, 51, 54, 36}. Find the median , Q 1 and Q 3 and the interquartile range

8. 8 Daily Wages in Peso Frequency 426-450 3 401-425 12 376-400 9 351-375 8 326-350 5 301-325 3   N = 40 Using the table, find: Q 1 , Q 2 and Q 3

9. 9 Daily Wages in Peso Frequency 426-450 3 401-425 12 376-400 9 351-375 8 326-350 5 301-325 3   N = 40 Using the table, find: Q 1 , Q 2 and Q 3

10. 10 Daily Wages in Peso Frequency 426-450 3 401-425 12 376-400 9 351-375 8 326-350 5 301-325 3   N = 40 Using the table, find: Q 1 , Q 2 and Q 3

11. Deciles and Percentiles (Ungrouped data)

12. 59 79 90 45 56 86 83 84 73 78 73 87 51 95 93 81 92 76 77 79 98 71 65 71 71 78 40 91 64 69 75 89 73 75 96 91 78 87 59 65 61 48 83 96 89 73 67 66 69 99 The scores of 50 students in the last Math Exam are given below. Find: a ) 5 th and 8 th Decile and b ) 30 th and 90 th Percentile. Step 1. Arrange the data in increasing order ( counting starts from column 1 to column 10 ) 40 59 65 71 73 77 79 86 90 95 45 59 66 71 73 78 81 87 91 96 48 61 67 71 75 78 83 87 91 96 51 64 69 73 75 78 83 89 92 98 56 65 69 73 76 79 84 89 93 99 n = 50

13. Step 1. Arrange the data in increasing order ( counting starts from column 1 to column 10 ) 40 59 65 71 73 77 79 86 90 95 45 59 66 71 73 78 81 87 91 96 48 61 67 71 75 78 83 87 91 96 51 64 69 73 75 78 83 89 92 98 56 65 69 73 76 79 84 89 93 99 n = 50 a. 5 th Decile and 8 th Decile

14. Step 1. Arrange the data in increasing order ( counting starts from column 1 to column 10 ) 40 59 65 71 73 77 79 86 90 95 45 59 66 71 73 78 81 87 91 96 48 61 67 71 75 78 83 87 91 96 51 64 69 73 75 78 83 89 92 98 56 65 69 73 76 79 84 89 93 99 n = 50 b. 30 th Percentile and 90 th Percentile

15. Deciles and Percentiles (Grouped data)

16. Class Interval f 134 – 139 10 128-133 9 122-127 8 116-121 1 110-115 5 104-109 2 98-103 9 92-97 5 86-91 1   N = 50 Use the frequency distribution to calculate D 8 and P 85 + where = Total frequency = cumulative frequency before the 8 = frequency of the = size or gaps of the class interval  

17. Class Interval f 134 – 139 10 128-133 9 122-127 8 116-121 1 110-115 5 104-109 2 98-103 9 92-97 5 86-91 1   N = 50 Use the frequency distribution to calculate D 8 and P 85 +  

18. Class Interval f 134 – 139 10 128-133 9 122-127 8 116-121 1 110-115 5 104-109 2 98-103 9 92-97 5 86-91 1   N = 50 Use the frequency distribution to calculate D 8 and P 85 +  

19. Class Interval f 134 – 139 10 128-133 9 122-127 8 116-121 1 110-115 5 104-109 2 98-103 9 92-97 5 86-91 1   N = 50 Use the frequency distribution to calculate D 8 and P 85 +  

20. Class Interval f 134 – 139 10 128-133 9 122-127 8 116-121 1 110-115 5 104-109 2 98-103 9 92-97 5 86-91 1   N = 50 Use the frequency distribution to calculate D 8 and P 85 +  

21. Class Interval f 134 – 139 10 128-133 9 122-127 8 116-121 1 110-115 5 104-109 2 98-103 9 92-97 5 86-91 1   N = 50 Use the frequency distribution to calculate D 8 and P 85 + where = Total frequency = cumulative frequency before the = frequency of the = size or gaps of the class interval  

22. Class Interval f 134 – 139 10 128-133 9 122-127 8 116-121 1 110-115 5 104-109 2 98-103 9 92-97 5 86-91 1   N = 50 Use the frequency distribution to calculate D 8 and P 85 +  

23. Class Interval f 134 – 139 10 128-133 9 122-127 8 116-121 1 110-115 5 104-109 2 98-103 9 92-97 5 86-91 1   N = 50 Use the frequency distribution to calculate D 8 and P 85 +  

24. Class Interval f 134 – 139 10 128-133 9 122-127 8 116-121 1 110-115 5 104-109 2 98-103 9 92-97 5 86-91 1   N = 50 Use the frequency distribution to calculate D 8 and P 85 +  

25. Class Interval f 134 – 139 10 128-133 9 122-127 8 116-121 1 110-115 5 104-109 2 98-103 9 92-97 5 86-91 1   N = 50 Use the frequency distribution to calculate D 8 and P 85 +