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FDT

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Relative Freq. & Cumulative Frequency

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.

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Example:Suppose we are given a set of raw numerical data.These are the average monthly Kilowatt-hours utilized

by 32 households surveyed 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 152Source: 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)

NextFDT

Highest value

lowest value

Number of observations

Steps in Constructing a (FDT)

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 1: Find the range R.

R = highest value – lowest value

Solution:

R = 152 – 20

= 132

BackStep 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 2: Estimate the number of classes or intervals, k.

k = , where n = number of observations

Note: If the resulting value is fractional, then we

take the next higher integer.

Solution:

k =

= 6

BackStep 1

Step 3

Step 4

Step 5

Step 6

Step 7

n

32

Step 3: Estimate the class width c of each interval.

c =

Note: Round off the answer to the same number

of decimal places that the observations have.

Solution:

c =

= 22

BackStep 1

Step 2

Step 4

Step 5

Step 6

Step 7

k

R

6

132

Step 4:

Class Interval

20 – 41

42 – 63

64 – 85

86 – 107

108 – 129

130 – 151

152 - 173

List the lower and upper class limits of the first interval.

BackStep 1

Step 2

Step 3

Step 5

Step 6

Step 7

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 5:

BackStep 1

Step 2

Step 3

Step 4

Step 6

Step 7

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 Santiago

BackStep 1

Step 2

Step 3

Step 4

Step 5

Step 7

Step 7: Compute the class marks and class boundaries of each class intervals

Class mark = (lower class limit + class boundaries)/2

Lower 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 3.42 is accurate to the hundredth unit (or 0.01).

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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 Santiago

BackStep 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7:

20 – (1/2)(1.0) 41 + (1/2)(1.0)

Variations of the FDT include relative and cumulative frequencies.

For example, using data:

Relative Frequency = Frequency/

Total Frequency

Cumulative Frequency= It is the 'running total'

of frequencies.

End FDT

=1/32

=4/32

=1/32

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