**Frequency distribution :**

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.

**Solution :**

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.

**Solution :**

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.

**Solution :**

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.

Thus,
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".

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.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**