Frequency distribution I :
A frequency distribution may be defined as a tabular
representation of statistical data, usually in an ascending order, relating to a measurable characteristic according to individual value or a group of values of the characteristic under study.
For the construction of a frequency-distribution of a variable, we need to go through the following steps.
Step 1 :
Find the largest and smallest observations and obtain the difference between them, known as Range, in case of a continuous variable.
Step 2 :
Form a number of classes depending on the number of isolated values assumed by a discrete variable. In case of a continuous variable, find the number of class intervals using the relation,
No. of class Interval X class length ≅ Range.
Step 3 :
Present the class or class interval in a table known as frequency-distribution table.
Step 4 :
Apply ‘tally mark’ i.e. a stroke against the occurrence of a particulars value in a class or class interval.
Step 5 :
Count the tally marks and present these numbers in the next column, known as frequency column, and finally check whether the total of all these class frequencies tally with the total number of observations.
Example 1 :
Following are the records of babies born in an hospital in San francisco during a week (B denoting Boy and G for Girl) :
Construct a frequency-distribution according to gender.
In order to construct a frequency-distribution of babies in accordance with their gender, we count the number of male births and that of female births and present this information in the following table.
Example 2 :
A review of the first 30 pages of a statistics book reveals the following printing mistakes :
Make a frequency-distribution of printing mistakes.
Since x, the printing mistakes, is a discrete variable, x can assume seven values 0, 1, 2, 3, 4, 5 and 6. Thus we have 7 classes, each class comprising a single value.
Frequency-distribution of the number of printing mistakes of the first 30 pages of a book
Example 3 :
Following are the weights in kgs. of 36 students of an university.
Construct a frequency-distribution of weights, taking class length as 5.
We have, Range = Maximum weight – minimum weight
= 73 – 44
= 29 kgs
No. of class interval × class length ≅ Range
No. of class interval × 5 ≅ 29
No. of class interval ≅ 29 / 5
No. of class interval ≅ 6
(We always take the next integer as the number of class intervals so as to include both the minimum and maximum values).
Frequency-distribution of weights of 36 Students
In case, the characteristic under consideration is an attribute, say nationality, then the tabulation is made by allotting numerical figures to the different classes the attribute may belong like, in this illustration, counting the number of American, Indian, British, French, German and so on.
The qualitative characteristic is divided into a number of categories or classes which are mutually exclusive and exhaustive and the figures against all these classes are recorded.
The figure corresponding to a particular class, signifying the number of times or how frequently a particular class occurs is known as the frequency of that class.
the number of Americans, as found from the given data, signifies the
frequency of the Americans. So frequency distribution is a statistical
table that distributes the total frequency to a number of classes.
When tabulation is done in respect of a discrete random variable, it is known as Discrete or Un grouped or simple Frequency Distribution and in case the characteristic under consideration is a continuous variable, such a classification is termed as Grouped Frequency- distribution.
In case of a grouped frequency-distribution, tabulation is done not against a single value as in the case of an attribute or a discrete random variable but against a group of values.
The distribution of the number of car accidents in Newyork during 12 months of the year 2005 is an example of a un grouped frequency-distribution and the distribution of heights of the students of St. Xavier’s College for the year 2004 is an example of a grouped frequency-distribution.
After having gone through the stuff given above, we hope that the students would have understood "Frequency distribution I".
Apart from the stuff given above, if you want to know more about "Frequency-distribution", please click here
Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Different forms equations of straight lines
MATH FOR KIDS
HCF and LCM word problems
Word problems on quadratic equations
Word problems on comparing rates
Ratio and proportion word problems
Converting repeating decimals in to fractions