ICSE Class 7 Maths Chapter 33 Collection and Tabulation of Data

Unit 6 - Statistics

Chapter 33: Collection And Tabulation Of Data

(Including Graphs And Arithmetic Mean)

33.1 Basic Treatment

Statistics is the science which deals with the collection, classification and interpretation of available information and data.

For Example

Mohit visits 20 families of a locality to collect informations about the families with less than 4 members, with 4 members and with more than 4 members. He then summarises the information collected as shown below:

33.2 Data

The set of numerical facts collected (as shown above), in order to reveal useful informations, is called data.

Whatever be the method of collecting the data, once the data is collected, it must be arranged in a systematic way (form).

The arrangement of data in a systematic form, usually in a table (tabular) form, is called tabulation.

e.g., consider the following tabulation:

The above table represents the result of a particular examination of a primary school.

33.3 Raw Data And An Arrayed Data

Suppose the marks (in a test) of 30 children of a class are as follows:

12 22 14 16 28 30 20 26 14 22

25 26 22 25 28 30 22 18 16 26

22 26 18 14 18 30 28 16 26 26

The data in this form, obtained as a result of observations in original form, is called raw data or ungrouped data.

If this raw data is re-arranged in ascending or descending order, the new arrangement is called an array.

Thus the data, given above, can be arranged to form an array as follows:

12 14 14 14 16 16 16 18 18 18

20 22 22 22 22 22 25 25 26 26

26 26 26 26 28 28 28 30 30 30

As discussed above, an array can also be obtained by writing data in descending order, i.e., the array can be of the form:

30 30 30 28 28 28 26 26 26 26

26 26 25 25 22 22 22 22 22 20

18 18 18 16 16 16 14 14 14 12

Teacher's Note

Raw data is like unsorted groceries from a market, while an array is like organizing them neatly on a shelf in order.

33.4 Frequency And Frequency Distribution

The number of times a particular number occurs, in the given set of data, is called its frequency.

For Example

The above set of data, shows the marks of 30 students in which marks 14 occur 3 times, so we say that frequency of 14 is 3. Similarly, 22 occur 5 times, so the frequency of 22 is 5. In the same way, frequency of 12 is 1, frequency of 26 is 6 and so on.

When the given set of data is written in the form of a table showing each data with its frequency, the table so obtained is called a frequency distribution table.

In order to construct a frequency distribution table, make a table as shown below:

Frequency Distribution Table

In the first column, write the marks in ascending order.

The marks of different children are recorded in the second column (headed with Tally Marks) by marking a short slant line called a stroke.

The marking of strokes is done as follows:

(i) The first mark in the given data is 12, so make a stroke in the Tally Marks Column opposite marks 12.

(ii) The next mark is 14, so make a stroke opposite marks 14 and so on.

(iii) When four strokes are made opposite any particular mark, don't make the fifth stroke in the same way but make a stroke across the first four. This gives a bundle of five strokes. The next stroke starts a new bundle.

(iv) When marking of the strokes is completed, count the strokes against each mark and write the corresponding number (frequency) in the column headed as: frequency.

The table obtained above shows ungrouped frequency distribution. The distribution can be further condensed by grouping the numbers in classes and then writing the frequency of each class.

For this, first of all the given set of data is divided into suitable class-intervals and then the frequency of each class is found with the help of tally marks shown below:

In this table, marks of 30 students are divided in class-intervals 1-10, 11-20 and 21-30. Then, if a number belongs to the class 11-20 a stroke is marked for it in the column with heading 'Tally Marks' and against the class interval 11-20. In the same way, for each given number (mark) a stroke is marked. Finally, the frequency of marks in each class-interval is obtained and is written in column with heading 'Frequency'.

The table showing class-intervals with their frequencies is called a grouped frequency distribution.

In this table the frequency of class-interval 11-20 is 11. This means there are 11 students who scored marks from 11 to 20. Similarly, the frequency of class-interval 21-30 is 19 means there are 19 students who scored marks from 21 to 30.

Teacher's Note

Frequency helps us understand patterns in data, like knowing which shoe size is most popular in a store.

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