Frequency Distribution frequency distribution Arrangement of data or objects into different classes with their frequencies is known as...
Frequency Distribution
frequency distribution Arrangement of data or objects into different classes with their frequencies is
known as frequency distribution, If data of continuous variable is arranged into
different classes with their frequencies, is known as continuous frequency
distribution, If data of discrete variable is arranged into different classes with
their frequencies, is known as discrete frequency distribution or discontinuous
frequency distribution.
 |
| Statistics Frequency Distribution what is Class limits and Class boundaries Class interval |
For example,
Weight:55 - 59
Frequency:5
Frequency is the number of values falling in a class, It is denoted by f
Relative frequency of any class is the ratio of its frequency and total frequency.
Frequency distribution may be constructed both for discrete and continuous
variables. Discrete frequency distribution can be converted back to original
values but for continuous variable it is not possible. To convert the raw data of
continuous variable into a
frequency distribution following five steps are taken into account:
(i) Find range which is the difference of highest and smallest values of given data
(ii) Decide the number of classes depending upon the total number of
observations. Very small number of classes loses proper importance of
many observations and large number of classes makes the computations
tiresome. The number of classes between 5 and 20 is most suitable. The
commonly used formula for obtaining the number of classes is:
Another formula not frequently used for obtaining the number of classes is:
Number of classes 1 + 3.3 log(n). Where "n" is the total number of
observations. There is a disadvantage with this formula that it gives large
number of classes for small number of observations and small number of
classes for large number of values.
For example, number of classes 1 + 3.3
log(4) 3 if there are four observations and five if n 10 and 11 classes if
number values is 1000.
Range
(iii) Minimum size of class interval
No. of classes
The word minimum is used because in some situations the calculated size of
class interval does not occupy all the observation, so it becomes necessary to
increase it,
(iv) Write the class limits taking minimum value of raw data as the lower limit of
first class. Lower limit of second class is obtained by adding the class interval in
the lower limit of first class. Upper limit of first class is obtained by subtracting 1
from lower limit of second class if the data is in whole numbers; subtract o A or
0.01 etc if there are one or two digits after decimal
(v) Put the values in the respective classes with thr help of tally marks.
if the data is discrete write unrepeated values of variable in a column. Count the
number of repetitions of each observation and write it against the corresponding
observation in the frequency column.
A continuous frequency distribution is known as open end distribution if lower
limit of 1st class or upper limit of last or both are not given as shown below.
OPEN END FREQUENCY DISTRIBUTION
Weight:60 - 64
Frequency:25
Concept of Class limits and Class boundaries
The values of a variable that define end points of various classes and are
included in each class are called class limits. More over the upper and lower
limits of two consecutive classes are dissimilar. It is also called inclusive
classification, The lower value of each class is called lower class limit and larger
value is called upper class limit. In the following table concept of class limits and
Lower class' limit f 1st class
Lower class limit of 2M class
If the variable is continuous and measurements are made nearest to the whole
numbers difference between upper limit of 1st class and lower limit of 2nd class
is taken equal to 1, if up to one decimal place then 0.1, if up to two decimal
places then 0.01 and so on.
A similar concept of class limits is class boundaries, which are values of a
variable that define end points of various classes and either lower or upper limit
(usually upper limit), is not included in each class. More over the upper and
lower limits, of two consecutive classes are similar. It is also called exclusive
classification.
Class Interval
It is the difference between two consecutive lower or upper class limits or
between two successive mid points. in case of class boundaries there are two
ways to calculate it: (i) By finding the difference between two consecutive lower
or upper class boundaries (ii) Subtracting the lower class boundary from upper
class boundary of a class. Class interval is denoted by "h" Size of class interval
is different if calculated from class limits, mid points or from class boundaries.
Class Mark (X)
Class mark denoted by (X) is the average of upper and lower class limit of a
class or upper and lower class boundary of a class. Calculation of class marks
is necessary because no measure can be made from classes directly.
Construction of Cumulative Frequency Distribution And
Cumulative Relative Frequency Distribution
Sum of frequencies of a frequency distribution from first class up to and
including the specified class is known as cumulative frequency Cumulative
frequency distribution is the arrangement of data into classes with their
cumulative frequencies. Another similar concept is cumulative relative frequency
distribution in which against each class ratio o/ cumulative frequency of that class and total
frequency is given, The method of construction of cumulative frequencies and
cumulative relative frequencies is explained in the following table with an
example: weight and frequency.
No comments