Frequency distribution:
The arrangement of data into groups or classes together with
the number of observations in each group or class is called frequency
distribution.
The number of observations falling (lying) in a particular
class is called frequency and is usually denoted by (f). Data presented in the form
of frequency distribution is also known as grouped data, while the data in
original form is called ungrouped data while constructing a grouped frequency
distribution. The following terms are associated with its construction. i.e.
class limits, class boundaries, class mark, or midpoint of a class, width of a
class or class interval size.
i.
Class limits:
The pair of number of a variable
which describe a class are called class limits. The smaller number is called
the lower class limit while the larger number is called the upper class limit.
The class limits are constructed in such a way that the upper limit of one
class do not coincide with the lower limit of next higher class. Thus there is
a gap between successive classes e.g. 10-19, 20-29, 30-39 etc.
ii.
Class boundaries:
When class are constructed in such a
way that the upper limit of one class coincides with the lower limit of next
higher class, then such limits are called class boundaries. Thus there will be
no gap between the successive classes. The class boundaries are exclusive.
E.g. 10-20, 20-30, 30-40, 40-50, etc hence 20
will be included in the class 20-30 instead of 10-20.
iii.
Midpoint of a class or class mark:
The midpoint of a class is obtained
by dividing the sum of upper and lower class limits/boundaries by 2. Since
individual identity of the observation is lost in grouping process, hence for
convenience of computation midpoint are compute, about midpoint of a class, we
assume that each value in a class is equal to its midpoint e.g. if frequency of
a class is 9 and its midpoint is 24, it means that all 9 values of a class are
equal to 24.
iv.
Width of a class or class interval size:
The different between successive
lower limits or between successive upper limits is called width of class or
class interval size. It may also be obtained by finding the difference between
successive midpoints. The width of a class is usually denoted by (h).
Construction of frequency distribution:
While constructing a grouped frequency distribution the following steps should be taken into consideration.
i. For convenience arrange the data in an array using stem and leaf display.
ii. Determine the largest and smallest number from an arrayed data in order
to find range i.e. the difference between largest and smallest number.
iii. Decide upon the number of classes. There is no hand and fast rule for
deciding the number of classes, but a reasonable number of classes between 5 to
20 may be included depending upon the size of the data. Sturges also suggested
a formula for deciding the number of classes i.e.
K
= 1+3.3 log N
iv. Tj find the class interval size (h) divide the range by the desired
number of classes e.g. if range of values is 87 and number of classes are 9,
then class interval size will be 87/ 9
= 9.67 or approximately 10. Similarly if
range is 43 and number of classes are 8, then class interval size will be 43/ 8 = 5.375 or 6 approximately (round off
to next higher integer).
v. Decide what should be the starting value of the first class. The starting
value is usually taken as the lowest value of the given data or less than that
which is a multiple of 2 5, 10, and such other figures. The upper limit is
obtained by adding the width of a class with the lower class limit. The remaining
class limits are determined similarly.
vi. Distribute the values in to appropriate classes either by listing actual
values In their proper classes or by using tally bars. The number of tallies is
then written infrequency column.
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