What is class boundary in frequency distribution?

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.

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