7A-GROUPEDDATA_INTRODUCTION eeeeeee.pptx

Education

1. MEASURES OF POSITION FOR GROUPED DATA

2. FORMULAS: QUARTILE = LB + [ ( kN /4) – cfb ] i f Qk DECILE = LB + [ ( kN /10) – cfb ] i f D k PERCENTILE = LB + [ ( kN /100) – cfb ] i f P k

3. where: LB = lower boundary of the kth class N = total frequency c fb = cumulative frequency before or below f k = frequency of the kth class i = size of class interval k = nth position of the class

4. How to solve for position of the class: QUARTILE = kN / 4 where k = 1, 2, 3 DECILE = kN / 10 where k = 1,2,3,…9 PERCENTILE = kN / 100 where k = 1,2,3,…99

5. To solve for the range: Range = highest score – lowest score To solve for class size: Class size = Range / class interval Remember: class interval is set as 10 Remember: Class size always make it to a nearest odd number.

6. Example: Scores of 50 students in Mathematics Quiz 43 32 24 38 36 47 41 30 27 21 37 44 48 25 27 31 43 29 30 35 48 26 28 33 41 45 28 32 46 44 34 38 32 48 49 25 34 27 34 33 48 21 18 19 20 21 22

7. Solve : a. Range b. Class size c. Make a frequency distribution table

8. Make a frequency distribution table Class scores interval Tally Frequency Midpoint Lower Boundary Upper Boundary Less than Cumulative Frequency Greater than Cumulative Frequency

9. Class score Interval Tally Frequency Lower Boundary Less than cumulative frequency

10. Solution: Range = 49 – 18 = 31 Class size = 31 / 10 = 3.1 round off to nearest odd number = 3 Start the class interval with the lowest score e.g. 18 – 20, 21 – 23, 24 – 26, …. until reach the highest score.

11. Midpoint = middle class size. e.g. (18 + 20) / 2 = 19 Lower Boundary = subtract 0.5 from the lower class size. e.g. 18 – 0.5 = 17.5 Upper Boundary = add 0.5 from the upper class size. e.g. 20 + 0.5 = 20.5