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# Fdt

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### Fdt

1. 2. FDT Shut Down Relative Freq. & Cumulative Frequency Start
2. 3. Frequency Distribution Table (FDT) <ul><li>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. </li></ul>Next End
3. 4. Example: Suppose we are given a set of raw numerical data. <ul><li>These are the average monthly Kilowatt-hours utilized by 32 households surveyed in Barangay Santiago. </li></ul>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) Highest value lowest value Number of observations 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 Next FDT
4. 5. Steps in Constructing a (FDT) Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7
5. 6. Step 1: Find the range R. <ul><ul><li>R = highest value – lowest value </li></ul></ul><ul><ul><ul><li>Solution: </li></ul></ul></ul><ul><ul><ul><li>R = 152 – 20 </li></ul></ul></ul><ul><ul><ul><li> = 132 </li></ul></ul></ul>Back Step 2 Step 3 Step 4 Step 5 Step 6 Step 7
6. 7. Step 2: Estimate the number of classes or intervals , k. <ul><li>k = , where n = number of observations </li></ul><ul><ul><li>Note: If the resulting value is fractional, then we take the next higher integer . </li></ul></ul><ul><ul><ul><li>Solution: </li></ul></ul></ul><ul><ul><ul><ul><ul><li>k = </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li> = 6 </li></ul></ul></ul></ul></ul>Back Step 1 Step 3 Step 4 Step 5 Step 6 Step 7
7. 8. Step 3: Estimate the class width c of each interval. <ul><li>c = </li></ul><ul><ul><li>Note: Round off the answer to the same number of decimal places that the observations have. </li></ul></ul><ul><ul><ul><li>Solution: </li></ul></ul></ul><ul><ul><ul><ul><ul><li>c = </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>= 22 </li></ul></ul></ul></ul></ul>Back Step 1 Step 2 Step 4 Step 5 Step 6 Step 7
8. 9. 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 Back Step 1 Step 2 Step 3 Step 5 Step 6 Step 7
9. 10. <ul><li>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. </li></ul><ul><ul><li>Note: Class limits must have the same number of decimal places as the raw data. </li></ul></ul>Step 5: Back Step 1 Step 2 Step 3 Step 4 Step 6 Step 7
10. 11. Step 6: <ul><li>From the data, tally the observations according to the interval which it belongs to. Summarize the tallies in a column for the frequencies. </li></ul>Average Monthly Kilowatt-hours of Households in Barangay Santiago 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 Back Step 1 Step 2 Step 3 Step 4 Step 5 Step 7
11. 12. Step 7: Compute the class marks and class boundaries of each class intervals <ul><li>Class mark = (lower class limit + class boundaries)/2 </li></ul><ul><li>Lower class boundary = lower class limit – ½( unit of accuracy ) </li></ul><ul><li>Upper class boundary = upper class limit + ½( unit of accuracy ) </li></ul><ul><li>Note: The number 2.5 is accurate to the tenth unit (or 0.1) while 3.42 is accurate to the hundredth unit (or 0.01). </li></ul>Next
12. 13. Average Monthly Kilowatt-hours of Households in Barangay Santiago 20 – (1/2)(1.0) 41 + (1/2)(1.0) 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 Back Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7:
13. 14. Variations of the FDT include relative and cumulative frequencies. <ul><li>For example, using data: </li></ul>Relative Frequency = Frequency/ Total Frequency Cumulative Frequency = It is the 'running total' of frequencies. =1/32 =4/32 =1/32 + + + End FDT