# Frequency Tables, Construct a Frequency Distribution

An important branch of mathematics that deals with gathering, organizing, estimating and interpreting the vast numerical data for a survey or a research, is known as statistics. There may be one or more numbers of statistical data that are used more than once. The number of times a particular data item is utilized, is known as its frequency.

When the distribution of frequencies is listed in a table OR tabular presentation of frequency distribution, known as frequency table. It is used to list out one or more variables taken in a sample. Each sample contains an individual frequency and each frequency is distributed with an interval between each frequency. It is also of two types that is univariate and joint. Frequency distribution can be defined as a summary presentation of the number of observations of an attribute or values of a variable arranged according to their magnitudes either individually in the case of discrete series or in a range or class interval in the case of both discrete and continuing series.

**Frequency Table**

Frequency Distribution Table is a way to organize data. A frequency distribution table is an organized tabulation of the number of individual events located in each category. It contains at least two columns, one for the score categories (X) and another for the frequencies (f). Below we have explained briefly for you to understand the concept of frequency table better and workout frequency table example:

**Solved Example**

**Question: **Here is the list of marks obtained for the students in the examination. Find the number of students who got more than 85 marks, More than 95, Less than 80 more than 76.

Score (X) | Frequency (f) |

Below 75 | 4 |

76 – 80 | 14 |

81 – 85 | 2 |

86 – 90 | 8 |

91 – 95 | 5 |

96 – 100 | 1 |

**Solution:**

**From the table we can conclude that:**

Students who got more than 85 = 8 + 5 + 1 = 14

Students who got more than 95 = 1

Students who got less than 80 more than 76 = 14.

**Construction of Frequency Distribution**

The following steps are involved in the construction of a frequency distribution.

(1) Find the range of the data: The range is the difference between the largest and the smallest values.

(2) Decide the approximate number of classes in which the data are to be grouped. There are no hard and first rules for number of classes. In most cases we have 5 to 20 classes. H.A. Sturges provides a formula for determining the approximation number of classes.

K=1+3.322logN

where K= Number of classes

and logN = Logarithm of the total number of observations.

Example: If the total number of observations is 50, the number of classes would be

K=1+3.322logN

K=1+3.322log50

K=1+3.322(1.69897)

K=1+5.644

K=6.644

7 classes, approximately.

(3) Determine the approximate class interval size: The size of class interval is obtained by dividing the range of data by the number of classes and is denoted by h class interval size

h = Range Number of Classes

In the case of fractional results, the next higher whole number is taken as the size of the class interval.

(4) Decide the starting point: The lower class limit or class boundary should cover the smallest value in the raw data. It is a multiple of class intervals.

Example: 0,5,10,15,20, etc. are commonly used.

(5) Determine the remaining class limits (boundary): When the lowest class boundary has been decided, by adding the class interval size to the lower class boundary you can compute the upper class boundary. The remaining lower and upper class limits may be determined by adding the class interval size repeatedly till the largest value of the data is observed in the class.

(6) Distribute the data into respective classes: All the observations are divided into respective classes by using the tally bar (tally mark) method, which is suitable for tabulating the observations into respective classes. The number of tally bars is counted to get the frequency against each class. The frequency of all the classes is noted to get the grouped data or frequency distribution of the data. The total of the frequency columns must be equal to the number of observations.

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