Data, Range, Frequency, Frequency Distribution Table

# Data, Range, Frequency, Frequency Distribution Table

## Data

The pieces of information collected for some purpose are called data.
The data is also defined as the collection of facts and figures.

## Raw Data

The data originally collected, observed or received are usually unorganized in nature and is called raw data. After the collection of raw data, it is organized and put in the form of a table.
We cannot find any useful information easily from the raw data. To reach on any conclusion, we organize raw data in form of tables and graphs.

## Range

The difference between the highest and the lowest value of the variable in a set of data is called the range.
For example: The runs scored by a cricket player in 10 matches is as follows:
34       56          12            75               23             38                10              18            95           25
Lowest value: 10
Highest value: 95
Range = Highest value - Lowest value
= 95 - 10 = 85

## Arranged Data

The data may be arranged in ascending or descending order. This arrangement of data is called arranged or arrayed data.

## Frequency

Frequency of a value is the number of times it occurs in a given data set. Data can be presented with the help of a table called frequency distribution table. There are two types of frequency distribution table:
1. Ungrouped frequency distribution table
2. Grouped frequency distribution table

## Ungrouped Frequency Distribution Table

It is the tabular representation of the frequency of each individual piece of data. Consider the following example:

Example: The marks obtained by 20 students in a test (out of 40) are given below:
38  32  39  35  36  31  37  35  32  33  36  35  33  34  33  32  32  31  34  31

We arrange them in ascending order as follows:
31  31  31  32  32  32  32  33  33  33  34  34  35  35  35  36  36  37  38  39

From above, we can see that 31 marks are obtained by 3 students whereas 34 marks are obtained by 2 students. Thus, 3 and 2 are respectively the frequencies of 31 and 34. Similarly, we can find the frequencies of the other values of the variable and arrange them in a tabular form having two columns.

The frequency distribution table is prepared by moving systematically down the column of numbers given and marking tally marks ( l ) in the tally column against the appropriate group. The tally marks are in groups of 5 which makes it easy for us to count. We then count the tally marks and write the total in the frequency column. To check, we add the numbers in the frequency column. The total should be equal to the total number of observations (in this case 20).

 Marks Tally marks Frequency 31 lll 3 32 llll 4 33 lll 3 34 ll 2 35 lll 3 36 ll 2 37 l 1 38 l 1 39 l 1 Total 20

Such a table is called ungrouped frequency distribution table.

## Grouped Frequency Distribution Table

Another way of organizing raw data is in form of a grouped frequency distribution table. Here, the heights (cm) of 72 students are given. We can group the data into classes or categories by writing down the number of students who fall into each class.

Consider the data,
147   143   148   134   146   156   139   144   148   135   136   152   148   149   142  136 136   150   132   148   142   159   149   135   139   137   152   143   162   159   146   152  142 149   145   149   129   149   139   148   149   141   142   154   149   145   142   151   146  142 152   134   141   137   136   142   148   149   149   133   157   152   148   137   153   146  148   153   139   131   153   148

First arrange this data in ascending or descending order.

## Class Intervals

We will make groups such as 125–130, 130–135, etc. which are called classes or class intervals.

### Lower class limit and upper class limit

In the interval 125–130, 125 is called the lower class limit and 130 is called the upper class limit.

### Width of the class

The difference between the upper class limit and lower class limit is called the size or width of the class. Here, the class width is 5.

In the table, it would seem that a number such as 135 would fall in two classes viz. 130–135 and 135–140. However, by convention, 135 is included in the class 135–140. Similarly, a number like 150 would be included in the class 150–155.