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Quartilesdecilesandpercentilescopy 180526143907

Nomndeni Sibiya
Nomndeni Sibiya

This video discusses how to calculate quartiles, deciles, and percentiles for discrete, simple, and grouped frequency distributions. It demonstrates calculating the third quartile, sixth decile, and 70th percentile for a discrete data set. For a grouped frequency distribution, it shows how to find the median, lower quartile, upper quartile, third decile, and 95th percentile. The key steps shown are arranging the data in ascending order, determining the cumulative frequency, and using formulas to calculate the values of interest based on the total sample size.

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SUMAN MATHEWS GRADE 11 MATH COLLEGE MATH
PREVIEW THIS VIDEO WOULD BE USEFUL FOR GRADE 11 STUDENTS STUDYING MATHEMATICS. IT WOULD ALSO BE USEFUL FOR STUDENTS AT THE COLLEGE LEVEL STUDYING STATISTICS. HERE WE SHOW HOW QUARTILES, DECILES AND PERCENTILES CAN BE CALCULATED . CALCULATION OF THE ABOVE IS DONE FOR DISCRETE, SIMPLE AND GROUPED FREQUENCY DISTRIBUTIONS
IF A GIVEN SET IS ARRANGED IN ASCENDING OR DESCENDING ORDER OF MAGNITUDE, MEDIAN DIVIDES THE SET INTO 2 EQUAL PARTS. QUARTILES DIVIDE THE SET INTO 4 QUARTERS. THERE ARE 3 QUARTILES 1, 2, 3 DECILES DIVIDE THE SET INTO 10 EQUAL PARTS. THERE ARE 9 DECILES, 1, 2,------9 PERCENTILES DIVIDE THE SET INTO 100 EQUAL PARTS. THERE ARE 99 PERCENTILES 1, 2, 99
1 = + 1 4 基瑞 FOR A DISCRETE DISTRIBUTION OR A SIMPLE FREQUENCY DISTRIBUTION 2 = + 1 2 基瑞 3 = 3 + 1 4 基瑞 =MEDIAN 倹 = (+1) ≠ 10 value = ( + 1) ≠ 100 ｐ
Question 1 Calculate the 3rd quartile, 6th decile and 70th percentile 28, 17, 12, 25,26, 19, 13, 27, 21,16 We first arrange in ascending order 12, 13, 16, 17, 19, 21, 25,26, 27, 28 3 = 3 11 4 ≠. Value = 8.25th value = 8≠ ｐ + 0.25 9≠ ｐ 8≠ ｐ = 26 + 0.25 27 26 = 26.25
6 = 6(11) 10 ≠ ｐ = 6.6≠ ｐ 6 = 6≠ ｐ + 0.6 7≠ ｐ 6≠ ｐ = 21 + 0.6 25 21 = 23.4 70 = 70 100 11 ≠ ｐ = 7.77≠ ｐ = 25 + .77 8≠ ｐ 7≠ ｐ = 25 + 0.77 26 25 = 25.77
Question 2 For the following frequency distribution , find 1, 3, 6, 45 18 15 19 18 20 25 21 27 22 40 23 25 24 19 25 16 26 8 27 7
18 15 19 18 20 25 21 27 22 40 23 25 24 19 25 16 26 8 27 7 We calculate the cumulative frequencycfcf 15 33 58 85 125 150 169 185 193 200
201 4 = 50.25 From the table, we look at the cf greater than 50.25 ie 58 Value of x corresponding to 58 is 20 1 = 20 3(201) 4 = 150.75 3 = 24 6 = 22 45 201 100 = 90.45 45 = 22 6 201 10 = 120.6
QUESTION 3 For the following table, find the median, lower quartile, upper quartile, 3rd decile, 95th percentile C I f 600-700 40 700-800 68 800-900 86 900-1000 120 1000-1100 90 1100-1200 40 1200-1300 26
For a grouped frequency distribution, we use n instead of n+1 1 = + ( 4 ) Where l = lower boundary of the class in which 1 cf = cumulative frequency of the class preceeding this class f = frequency of the class in which 1 = ゐ≠ ≠ ＄ｐ 2 = + ( 2 ) 3 = + ( 3 4 )
倹 = + ( 10 ) = + ( 100 )
C I f c f 600-700 40 40 700-800 68 108 800-900 86 194 900-1000 120 314 1000-1100 90 404 1100-1200 40 444 1200-1300 26 470 470 4 = 117.5 We take 800 -900 as the class in which 1 1 = 800 + ( 117.5 108 86 ) 100 = 811.04
2 = 470 2 = 235900 + (235 194 120 ) 100 = 934.17 3(470) 4 = 352.5 3 = 1000 + ( 352.5314 90 ) 100 =1042.78 3(470) 10 = 141
3 = 800 + 141 108 86 100 = 838.37 95(470) 100 = 446.5 95 = 1200 + 446.5 444 26 100 = 1209.62
FOR MORE VIDEOS ON STATISTICS, SUBSCRIBE TO MY PLAYLIST

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Quartilesdecilesandpercentilescopy 180526143907

  • 1. SUMAN MATHEWS GRADE 11 MATH COLLEGE MATH
  • 2. PREVIEW THIS VIDEO WOULD BE USEFUL FOR GRADE 11 STUDENTS STUDYING MATHEMATICS. IT WOULD ALSO BE USEFUL FOR STUDENTS AT THE COLLEGE LEVEL STUDYING STATISTICS. HERE WE SHOW HOW QUARTILES, DECILES AND PERCENTILES CAN BE CALCULATED . CALCULATION OF THE ABOVE IS DONE FOR DISCRETE, SIMPLE AND GROUPED FREQUENCY DISTRIBUTIONS
  • 3. IF A GIVEN SET IS ARRANGED IN ASCENDING OR DESCENDING ORDER OF MAGNITUDE, MEDIAN DIVIDES THE SET INTO 2 EQUAL PARTS. QUARTILES DIVIDE THE SET INTO 4 QUARTERS. THERE ARE 3 QUARTILES 1, 2, 3 DECILES DIVIDE THE SET INTO 10 EQUAL PARTS. THERE ARE 9 DECILES, 1, 2,------9 PERCENTILES DIVIDE THE SET INTO 100 EQUAL PARTS. THERE ARE 99 PERCENTILES 1, 2, 99
  • 4. 1 = + 1 4 基瑞 FOR A DISCRETE DISTRIBUTION OR A SIMPLE FREQUENCY DISTRIBUTION 2 = + 1 2 基瑞 3 = 3 + 1 4 基瑞 =MEDIAN 倹 = (+1) ≠ 10 value = ( + 1) ≠ 100 ｐ
  • 5. Question 1 Calculate the 3rd quartile, 6th decile and 70th percentile 28, 17, 12, 25,26, 19, 13, 27, 21,16 We first arrange in ascending order 12, 13, 16, 17, 19, 21, 25,26, 27, 28 3 = 3 11 4 ≠. Value = 8.25th value = 8≠ ｐ + 0.25 9≠ ｐ 8≠ ｐ = 26 + 0.25 27 26 = 26.25
  • 6. 6 = 6(11) 10 ≠ ｐ = 6.6≠ ｐ 6 = 6≠ ｐ + 0.6 7≠ ｐ 6≠ ｐ = 21 + 0.6 25 21 = 23.4 70 = 70 100 11 ≠ ｐ = 7.77≠ ｐ = 25 + .77 8≠ ｐ 7≠ ｐ = 25 + 0.77 26 25 = 25.77
  • 7. Question 2 For the following frequency distribution , find 1, 3, 6, 45 18 15 19 18 20 25 21 27 22 40 23 25 24 19 25 16 26 8 27 7
  • 8. 18 15 19 18 20 25 21 27 22 40 23 25 24 19 25 16 26 8 27 7 We calculate the cumulative frequencycfcf 15 33 58 85 125 150 169 185 193 200
  • 9. 201 4 = 50.25 From the table, we look at the cf greater than 50.25 ie 58 Value of x corresponding to 58 is 20 1 = 20 3(201) 4 = 150.75 3 = 24 6 = 22 45 201 100 = 90.45 45 = 22 6 201 10 = 120.6
  • 10. QUESTION 3 For the following table, find the median, lower quartile, upper quartile, 3rd decile, 95th percentile C I f 600-700 40 700-800 68 800-900 86 900-1000 120 1000-1100 90 1100-1200 40 1200-1300 26
  • 11. For a grouped frequency distribution, we use n instead of n+1 1 = + ( 4 ) Where l = lower boundary of the class in which 1 cf = cumulative frequency of the class preceeding this class f = frequency of the class in which 1 = ゐ≠ ≠ ＄ｐ 2 = + ( 2 ) 3 = + ( 3 4 )
  • 12. 倹 = + ( 10 ) = + ( 100 )
  • 13. C I f c f 600-700 40 40 700-800 68 108 800-900 86 194 900-1000 120 314 1000-1100 90 404 1100-1200 40 444 1200-1300 26 470 470 4 = 117.5 We take 800 -900 as the class in which 1 1 = 800 + ( 117.5 108 86 ) 100 = 811.04
  • 14. 2 = 470 2 = 235900 + (235 194 120 ) 100 = 934.17 3(470) 4 = 352.5 3 = 1000 + ( 352.5314 90 ) 100 =1042.78 3(470) 10 = 141
  • 15. 3 = 800 + 141 108 86 100 = 838.37 95(470) 100 = 446.5 95 = 1200 + 446.5 444 26 100 = 1209.62
  • 16. FOR MORE VIDEOS ON STATISTICS, SUBSCRIBE TO MY PLAYLIST