frequency distribution table

FDT
Relative Freq. &
Cumulative Frequency

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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

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

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

Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Back

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

=6


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
= 22

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 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 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

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).

Next

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 Santiago


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

frequency distribution table

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frequency distribution table