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frequency distribution table

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frequency distribution table

  1. 1. FDT Relative Freq. &Cumulative Frequency Shut DownStart
  2. 2. Frequency Distribution Table (FDT)• It is a grouping of all the (numerical) observations into intervals or classes together with a count of the number of observations that fall in each interval or class.End Next
  3. 3. Example:Suppose we are given a set of raw numerical data. These are the average monthly Kilowatt-hours of Households in Barangay Santiago. 20 25 30 36 38 40 40 42 45 48 50 53 56 58 60 64 66 68 70 72 74 80 88 90 96 100 120 130 135 140 150 152 Source: Elementary Statistical manual The following may be used as a guide in constructing an FDT (note that if there is an existing set of class intervals for the specific data, then steps 1 to __ will not apply)FDT Next
  4. 4. Steps in Constructing a (FDT)Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7
  5. 5. Step 1: Find the range R. R = highest value – lowest value Solution: R = 152 – 20 = 132Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Back
  6. 6. Step 2: Estimate the number of classes or intervals, k.k = n , where n = number of observations Note: If the resulting value is fractional, then we take the next higher integer. Solution: k = 32 =6Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Back
  7. 7. Step 3: Estimate the class width c of each interval.c = R/k Note: Round off the answer to the same number of decimal places that the observations have. Solution: c = 132/6 = 22Step 1 Step 2 Step 4 Step 5 Step 6 Step 7 Back
  8. 8. Step 4: List the lower and upper class limits of the first interval. Class Interval 20 – 41 42 – 63 64 – 85 86 – 107 108 – 129 130 – 151 152 - 173 Step 1 Step 2 Step 3 Step 5 Step 6 Step 7 Back
  9. 9. Step 5:List all the succeeding lower and upper class limits by adding the class with c to the lower limit of the first class interval. The upper class limit of the first interval should be the number before the lower class interval of the second interval. The highest class should contain the largest observation. Note: Class limits must have the same number of decimal places as the raw data. Step 1 Step 2 Step 3 Step 4 Step 6 Step 7 Back
  10. 10. Step 6:• From the data, tally the observations according to the interval which it belongs to. Summarize the tallies in a column for the frequencies. Class Interval Tally Frequency 20 – 41 IIII-II 7 42 – 63 IIII-IIII 8 64 – 85 IIII-II 7 86 – 107 IIII 4 108 – 129 I 1 130 – 151 IIII 4 152 - 173 I 1 Average Monthly Kilowatt-hours of Households in Barangay SantiagoStep 1 Step 2 Step 3 Step 4 Step 5 Step 7 Back
  11. 11. Step 7: Compute the class marks and class boundariesof each class intervalsClass mark = (lower class limit + class boundaries)/2Lower class boundary = lower class limit – ½(unit of accuracy)Upper class boundary = upper class limit + ½(unit of accuracy)Note: The number 2.5 is accurate to the tenth unit (or 0.1) while 3.42is accurate to the hundredth unit (or 0.01). Next
  12. 12. Step 7: Class Interval Tally Frequency Class boundary 20 – 41 IIII-II 7 19.5 – 41.5 42 – 63 IIII-IIII 8 41.5 – 63.5 64 – 85 IIII-II 7 63.5 – 85.5 86 – 107 IIII 4 85.5 – 107.5 108 – 129 I 1 107.5 – 129.5 130 – 151 IIII 4 129.5 – 151.5 152 - 173 I 1 151.5 – 173.5 Average Monthly Kilowatt-hours of Households in Barangay SantiagoStep 1 Step 2 Step 3 Step 4 Step 5 Step 6 Back
  13. 13. Variations of the FDT include relative and cumulative frequencies.For example, using data: Class Interval Relative Cumulative Frequency Frequency Relative Frequency 20 – 41 7 0.21875 7 = Frequency/ Total Frequency 42 – 63 8 0.25 15 64 – 85 7 0.21875 22 Cumulative Frequency 86 – 107 4 0.125 26 = It is the running total 108 – 129 1 0.03125 27 of frequencies. 130 – 151 4 0.125 31 152 - 173 1 0.03125 32 End FDT

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