Statistics - Part II

2. Frequency and frequency table
We have seen what are scores and what is the meaning of mean or average of a particular measurement. The number of times the same score occurs is called the frequency of that score. For example in the example 2 in the previous section, the number of students getting 50 marks is 10. Thus the frequency for the class of 30 students getting 50 marks in science exams is 10.

Example 5 : The marks obtained by 20 students in their maths tests (out of 10 marks) are :

5, 7, 4, 3, 8, 9, 10, 4, 5, 3, 6, 6, 7, 8, 5, 5, 3, 4, 6, 6

It can be seen that
the number of times 3 marks are obtained is 3
the number of times 4 marks is obtained is 3
the number of times 5 marks is obtained is 5
the number of times 6 marks is obtained is 4
the number of times 7 marks is obtained is 2
the number of times 8 marks is obtained is 2
the number of times 9 marks is obtained is 0
the number of times 10 marks is obtained is 1.

The frequency of the above score can be arranged in a table as shown below.

Frequency Table

Scores	Frequency
0	0
1	0
2	0
3	3
4	3
5	5
6	4
7	2
8	2
9	0
10	1
Total	20

The table shows how the marks are distributed. Note that total of the frequency is the total number of students.

Thus a frequency table also gives the frequency distribution of the sample under study.

When the sample is large, the frequency distribution table can be made by tally marks.

Example 6 : There are 50 families in a building. The number of members in each family is given below.

2, 3, 6, 7, 10, 4, 3, 2, 1, 6,
5, 4, 7, 10, 1, 3, 4, 7, 3, 5,
2, 1, 4, 6, 3, 2, 3, 3, 5, 5,
4, 5, 6, 7, 8, 8, 3, 2, 2, 1,
10, 9, 6, 5, 6, 5, 6, 5, 6, 3.

Arrange this data in a frequency table.

Since the number is large, it is best to use tally marks. First make a table as shown below.

Score (number of family members)	Tally marks	Frequency
1
2
3
4
5
6
7
8
9
10

Now from the data mark one vertical line for each score that you read. Mark such four lines. For every fifth line, mark a slanted line . Thus a bunch of 5 will be formed which is easier to count.

Here the first number is 2, in the row where score 2 is written mark a vertical line . The next score is 3, so in the row of score for three draw .

Score (number of family members)	Tally marks	Frequency
1		4
2		6
3		9
4		5
5		8
6		8
7		4
8		2
9		1
10		3
	Total	50

Count the number of tally marks and write the corresponding number in the frequency column against that score. The addition of frequencies should be equal to the number of the score

Example 7 : Given below is the monthly expenditure in rupees, of a family for 12 months. Prepare a frequency table to show this information.

4000, 4500, 5000, 4000, 5500, 4500, 5000, 6000, 4000, 4500, 5500, 5000.

We have seen that it is easy to handle data by the use of tally marks.

First make a table as shown below.

Score (Monthly expenditure in rupees)	Tally marks	Frequency
4000
4500
5000
5500
6000
6500

As done in the previous example, make a vertical line for each score.

Score (Monthly expenditure in rupees)	Tally marks	Frequency
4000		3
4500		3
5000		3
5500		2
6000		1
6500		0
	Total	12

Thus the data can be neatly presented in a frequency table with tally marks. The sum of all the frequencies is equal to the number of scores. Note that in a row where 6500 is written, there is no entry, hence it is written as 0.

If you make a row for the score that does not exist, it does not really matter. Write zero against the score and go on filling the frequency table as you read the data.

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