Data Collection and Organization

Introduction to data and information

Around us, we come across different types of information that help to take some decision or to reach some type of conclusion or to help in giving a better suggestion to someone.
If we take a glimpse of what information we see around and what the source of such information is? We can say there are many sources from our daily life those provide us information like television, newspaper, websites, interaction with people.
What has been collected from these sources is known as the information. It could be of any type, like train information collected from the train chart on the railway station, the most expecting winner of the match from scoreboard, the most expecting winner party of the polls from the polls results board, information about absent students in a school.
So is there anything still behind the information, from where it gets generated?
The answer is data. Data is the basic building block on which information is built up. So such information sources collect data and work on it to provide useful information that reaches us and is understandable by humans. Let’s take a deeper look next to know about data and information with examples.

So, in the above example, we got to know about data, information and how information helps taking decisions and making conclusions.
Next, we see how statistics handles data mathematically and how information is collected from data.

What is data in statistics?

Data is a plural form of datum which is a latin word. Data is a value which can further be used to prepare information about something. The value of data can be anything from facts or numerical figures.

Each value of data collected is called an observation. The data collected at initial stage is called raw data.
In statistics, we study data which can be measured numerically.

Therefore, from above example, we can say that a collection of observations is called as data.

Next, we see how the data is collected and organised in tables in statistics.

Collection of data

Collection of data starts from collecting the raw data from sources. Sources can be any source like television, newspaper, websites, interaction with people etc. This raw data collected can be a bulk data and usually comes in unorganised forms.

The raw data is a mixture of unorganised data, which can not be used anywhere to extract information. When raw data is processed or cleaned using for example sorting or some refinements then it becomes worth using and is form of data.

We can classify this data in two types, depending upon how we collect it:

1. Primary data

When data is collected directly from some experiments or questionnaires or interviews is called as primary data.
Primary data is firsthand data in other words. It is not used by anyone else that firsthand person.

2. Secondary data

Secondary data is not firsthand data. It has been collected by someone and processed to use. This type of data is not collected by the individual himself but obtained from published or unpublished sources.

Organization of data

To get the meaningful information from raw data, it gets processed which involves cleaning of data, which includes sorting it, transferring it into tables or charts or representing it graphically. Data is filled up in tables in columns. The table can have a sequence number against each row of data entered into the table.

Mostly, raw data that is collected to analyse can be seen in unorganised form initially. This unorganised data is always difficult to use to get some meaningful information.
So, to draw and reach a meaningful conclusion, the raw data is organised in some systematic manner. Some of the important and common ways that are used to organise raw data are:

1. Alphabetical order or in a sequence
2. Ascending order
3. Descending order

The above three ways to organize the data just rearrange the data alphabetically, in ascending or descending orders if it is numerical data.
The raw data when we put in ascending order or descending order is called an array or arrayed data.
Below is an example of organizing numerical data in ascending and descending order.

What is frequency in statistics?

In general, frequency means how many times an observation or an event occurs in a specific period or for a specific value. In statistics, it is more related to the number of observations that occur for a range of values.
By definition, the number of times a particular entry or an observation occurs, is called frequency.

To understand frequency distribution, let’s start with the following example.

The Table-5 provides information about the total number of students who like a specific fruit.
That means, cherry is liked by total of 5 students in a class and similarly, apple is liked by 6 students, grapes are liked by 4 students, banana is liked by 2 students, pineapple is liked by 1 student and orange is liked by 2 students.

Here fruit is called as variate and number of students who liked a particular fruit is called frequency of variate.

This example, which is about fruit liked by how many students, is an example of frequency. Here, an observation is to find how many students are there for a specific value which is a fruit.

The table 5 can be revised to show frequency in terms of tally marks and the table is known as frequency distribution.
Let’s see next how?

Tally marks in frequency distribution

Tally marks are used to show the frequency distribution of an observation. Tally mark is written using the symbol “|” a straight vertical line. Tally mark is a counter which counts the frequency of an observation. Single tally mark “|” shows the count one and two tally marks show “||” the count two of an observation.
We keep on adding one tally mark as the count increases. When the count reaches five, we do not use fifth tally mark after four tally marks. Instead a crossed line is drawn on the first four tally marks.

Count = 1, tally marks = |
Count = 2, tally marks = ||
Count = 3, tally marks = |||
Count = 4, tally marks = ||||
Count = 5, tally marks = \(\bcancel{||||}\)
Count = 6, tally marks = \(\bcancel{||||}\)|
Count = 7, tally marks = \(\bcancel{||||}\)||
Count = 8, tally marks = \(\bcancel{||||}\)|||
Count = 9, tally marks = \(\bcancel{||||}\)||||
Count = 10, tally marks = \(\bcancel{||||}\)\(\bcancel{||||}\)

How are tally marks used?

In frequency distribution table, the first column contains name of observation like marks, height, age etc. The second column contains tally marks and the third column keeps the value of number of tally marks.

Let’s revise Table-5 with tally marks.

Table 6: Frequency distribution of number of students who like a specific fruit

Interpretation of Table 6

In table 6, the first column of the table has the name of the observation, which is the fruit’s name.
Second column of the table has vertical lines by observing values from the first column.
For each student who eats a fruit a tally mark is written in the second column next to each other. This process is repeated until all observations are completed from the raw data.
If an observation repeats twice, two vertical lines are used i.e. || and so on up to four lines.
When an observation repeats five times, first four vertical lines are used and one line across the first four is drawn drawn diagonally on the first four lines which will be counted as fifth tally marks i.e. |||| \(\bcancel{|}\).
In the third column of the table we count the number of tally marks corresponding to each row.

Types of frequency distribution

In frequency distribution, raw data is represented into table form using tally marks so that information contained in raw data can be easily understandable.
Frequency distribution is of two types.

1. Discrete frequency distribution
2. Continuous frequency distribution or grouped frequency distribution

1. Discrete frequency distribution

Discrete frequency distribution is used when the value of observation is discrete or a single value. For example, the table 6 of frequency distribution of number of students who like a specific fruit is an example of discrete frequency distribution, because the value of observation is a name of fruit in first column, which is a single value.

Here, the number of observations in table 7 were only 6. But when the number of observations is very large then it is best to make a group of observations and find the frequency.
Continuous or grouped frequency distribution is a such method to group the observations.
Let’s see next, how it helps to find frequencies of large data.

2. Continuous or grouped frequency distribution

As said earlier also, grouped frequency distribution is suitable when the number of observations are large. In grouped frequency distribution, raw data is arranged into groups.

The groups are made in such a way that the difference between the greatest and the smallest observation in a group is large. These grouped observations are also called a class.