## Algebra Chapter 3 Statistical Data Its Handling And Analysis

**Algebra Chapter 3 Introduction**

- We are having generally some statements like literacy in our country is below 40%; the number of child workers in our country is 60%: rupee value during January 2018 in all of India is 12 paisa with the base year of 1960.
- We find these words in newspapers, seminars, classrooms, on radios, T.V., etc. These statements may be expressed as numerical statements in figures, which are simple, precise, meaningful, and suitable for communication.
- These facts and figures of the population of a place, birth, death, income, expenditure, etc. are known as
**Statistics.** - The word
seems to be derived from the Latin word**“Statistics”**the Italian word**“Status”**or the German word**“Statista”****“Statistics”.** - The word “Statistics” is used in singular or plural.
- In the second case, it means a collection of facts i.e., figures relating to population, national income, number of public schools, and production of tea coffee in different years.
- Percentages, averages, and coefficients derived from numerical facts are also known as statistics in the plural sense.
- As a singular, statistics refers to various methods adopted for the collection, classification, analysis, and interpretation of figures or data.
- So the term
is defined in two different senses**statistics**

1.is a collection of information in numerical terms.**Statistics**

2. For example, marks obtained by the students of a class, monthly wages of the workers in a factory, numbers indicating births, deaths, and marriages in different states, etc. are statistics in this sense and they are calledas**statistics**3. Statistics is the science that deals with the collection, analysis, and interpretation of numerical data.**Statistical Data.**

4. In this sense, statistics is defined as statistical methods which are used for the collection, analysis, and interpretation of numerical observations.

## Algebra Chapter 3 Statistical Data

**Definition: **

- Data is a collection of observations expressed in numerical figures.
- This collection may be done either by measurement or by counting.
- The word
which is the plural form of the word Datum refers to a collection of observations of characteristics of individuals or items and is expressed in numerical figures obtained through measurement or counting.**“data”** - The collection of facts or data is the very first step in an investigation.
- The data to be collected can broadly be classified into two types:

1. Primary Data

2. Secondary Data. - Primary data refer to those data which are collected by the investigator either on his / her own or through some agency, set up for a specific purpose, directly from the field of enquiry for the first time.
: Reserve Bank of India Bulletin (monthly)**Examples**

Coal Bulletin (monthly)

Railway Board Annual Bulletin etc.- Secondary data refer to those data which have been previously collected by some other agencies, private or public for one purpose and which are usually available in journals, magazines or research publications which are used for another purpose.
: Annual statement of the Foreign Trade**Examples**

International Labour Bulletin (monthly)

Annual Statistical Abstract of India etc.- Let us suppose someone asks you “What is the total number of members of your very neighboring family?
- Your answer is 6 How many boys and girls are there in the family?
- Your answer is that the family has 2 girls and one boy.
- How many boys and girls are there in the family, who have passed Madhyamik Examination?
- Your answer is that only one girl has passed Madhyamik Examination and she is the eldest girl.
- What class does the boy read in?
- You say that the boy reads in class six.
- Actually, the person was not known about your very neighboring family and now he knows something about the family through you.
- These figures (numbers) are known to him though you are called
**“Datas”.** - The collection of facts (which are previously unknown and now known) through an investigation is called Data.

## Algebra Chapter 3 Collection Of Data

**Actually, the data are collected by two methods: **

** 1. Census or Complete Enumeration**:

- Census or Complete Enumeration refers to the study of all the items (or observations) in the population.
- In this connection, the two terms namely
and**Population**are to be well acquainted.**Sample** - A
is defined as an aggregate or whole of objects possessing certain common characteristics.**Population** - So all the observations under consideration of a statistical inquiry constitute a population.
is a selected number of objects or observations, each of which is a part of the population.**A sample**- So a sample is defined as a part of the population selected for estimating one or more characteristics of the population.
- So in the census method, the entire population is investigated. It requires a large number of investigators and it involves much money and time.
- But the data are much more reliable and accurate.

** 2. Sample Survey**:

- A sample Survey stands for the study of some specific items drawn from the populations.
- So in the sample survey method, the entire population is not investigated, only a part of the population is investigated.
- It involves less time and less labor.
- If we measure the heights of all the students of the school which form the population and then calculate the average height of the population.
- This method is called the
**Census or Complete Enumeration.** - If we select 100 students from the school and measure the height of these 100 students, which form the sample.
- The average height of these 100 students is calculated.
- This method is known as
**Sample Survey.**

**The following methods are used to collect the data:**

: In this method, the investigator goes to the field of inquiry to have on-the-spot information.**Direct Personal observation**: In this method information is collected indirectly from persons who are acquainted with the fact under study by interviewing them.**Indirect oral investigation**: In this method, information is received through the mail where a set of questions with blank spaces for answers along with the instruction are sent to the investigators with a request that they should return them duly filled in.**Questionnaires sent through mail**

## Algebra Chapter 3 Raw Data

Suppose you have collected the facts of the numbers of members of 10 families of a locality of Bishnupur village in the district of Bankura:

** The collected facts or data are:**

- These data are called
**Raw Data.** - These data are not organized.
When statistical data is arranged in an arbitrary manner, we call it to be raw data.**Definition:**- So statistical data may originally appear in a form, where the collected data are not organized numerically.
- We call them raw data.

## Algebra Chapter 3 Tally Mark

- A tally mark is a slanted stroke (/) for counting.
- We know that when data are arranged in an arbitrary manner, then the collected data are called raw data.
- If the data be arranged in ascending order of magnitudes, then the presentation of the data is called
**Array.** - An array does not reduce the bulk of records. To reduce the large bulk of data present them with the help of
**Tally marks.** - A tally mark is an upward-slanted stroke (/) that is put against each occurrence of a value.
- For every occurrence of the value, we put each time a tally mark.
- When a value occurs more than four times, for every fifth occurrence a cross (\) tally mark is put which is running diagonally, across the four tally marks.
- This facilitates the counting of tally marks at the end.
- From the table of the previous article, we see that 4 families have a number of members 4.
- For this, we have to put 4 tally marks as shown in the following table.

**In the same way, we can construct tally marks for all other families:**

**The rule for putting tally marks :**

- For counting any raw data if the number of one kind of quantity is very large
- Suppose that the number of families having 4 members is 22
- Then put 4 tally marks, the fifth tally mark should be a cross tally mark (\) running diagonally across the 5 tally marks.
**Putting the tally marks is shown below:**- This facilitates the counting of tally marks and the possibility of wrong counting of tally marks will be less.

## Algebra Chapter 3 Frequency

- Suppose the marks obtained in Mathematics by 30 students of class VI in a certain school are collected by an investigator from the official records.
- The collected data are as follows (out of a total of 40 marks):
- 28, 20, 30, 10, .25, 28, 17, 28, 28, 30, 9, 18, 19, 28, 30, 20, 18, 26, 17, 10, 9, 25, 17, 10, 26, 20, 17, 25, 20, 28.
- These are the raw data collected by the investigator and the variable is the “marks obtained in Mathematics”.
- The recorded raw data appear in a complex and arbitrary manner. One cannot fully grasp the true significance of the figures.
- So some modification in the arrangements of the data is necessary. Therefore the data should be arranged in a definite order either ascending or descending.
- The above data are arranged in ascending order as follows:
- 9, 9, 10, 10, 10, 17, 17, 17, 17, 18, 18, 19, 20, 20, 20, 20, 25, 25, 25, 26, 26, 28, 28, 28, 28, 28, 28, 30, 30, 30.
- The 30 observations are not all different, some of them are repeated. The distinct observations are known as the values of the variable.
- The above arrangement can also be represented in the form of a table as shown below.
- From the above table, we see that 2 students have got 9 marks

3 students got 10 marks

4 students got 17 marks

2 students got 18 marks

1 student got 19 marks

4 students got 20 marks

3 students got 25 marks

2 students got 26 marks

6 students got 28 marks and

3 students got 30 marks. - Here the number of students 2, 3, 4, 2, 1, 4, 3, 2, 6, 3 are called the Frequency of the marks 9, 10, 17, 18, 19, 20, 25, 26, 28, 30 respectively (the marks obtained are the values of the variable).
- A characteristic that can be expressed numerically is called the variable.
- The number of times that each value of variable occurs is known as its frequency.
- Here an important characteristic of the frequency is that the sum of the frequencies of the variable values is the total number of sample values over which the data are collected.
- In the above table, the sum of the frequencies i.e. the total frequency = 30 which is the sample value i.e. the total number of students.

## Algebra Chapter 3 Frequency Distribution

- We know that when the collected data from the field of inquiry are arranged in an arbitrary manner is called Raw Data.
- Then these raw data are arranged properly in ascending order.
- A classification showing the different values of a variable and their respective frequencies i.e., the number of times each value occurs, side by side is called a Frequency Distribution of the values.

**For this observe the following table:**

**A table containing the title:**The members of a family, tally mark, frequency, is prepared.- This table is called the
**Frequency Distribution Table.** - So
**the table which is prepared when the raw data are arranged with the help of tally marks and the frequency is called the Frequency Distribution Table.** **How is the Frequency Distribution Table prepared?**- The frequency distribution table is prepared according to the following rule:
: The collected raw data are arranged in ascending order of magnitude**Step-1**: Determine the number of occurrences of the same kind of quantity or number.**Step-2**

In the above table, the families containing 4 members are one kind and the families containing 5 members are another kind, etc.Construct different horizontal rooms or spaces of each kind of quantity or number in the table.**Step-3:****Step-4:**Now construct different vertical columns for each sample, tally mark, frequency, etc. in the table.**Step-5:**Insert tally marks of each of the horizontal rows in the tally column.**Step-6:**Then insert the frequency of each of the horizontal rows in the frequency column.**Step-7:**Give a title of the table (according to the data available) above the table.

Then prepare a space below the frequency column and add the frequencies of the rows.

This will give the total frequency of this whole data.

Completing all the steps described above, you are able to prepare or construct a complete frequency distribution table.

## Algebra Chapter 3 Bar Graph Or Bar Chart

- Bar Graph or Bar Chart Simply a Bar diagram is a popular method of graphical presentation of data. In graph paper, the bar diagram is constructed.
- A bar implies a thick line having a small breadth.
- A bar diagram consists of parallel bars, each of which has the same breadth.
- All these bars are drawn on a common baseline and the distance between two consecutive bars is always the same.
- The height of each bar represents the frequency of each item of the data.
- Bar Graphs are classified into two types: Horizontal Bar graphs or charts; Vertical Bar graphs or charts.
- In the horizontal bar diagram (or graph of chart), a set of parallel bars are drawn horizontally on a vertical baseline called the Y-axis.
- In the vertical bar diagram (or graph or chart), a set of parallel bars are drawn vertically on a horizontal baseline called the X-axis.
- Suppose a frequency distribution table of the dolls prepared by Binaybabu of Kumor Para in the last week is obtained as follows
- We have to prepare a vertical bar diagram using the above data.
- In a graph paper, we draw two perpendicular straight lines in the space available in the graph paper; one is taken as X-axis and the other is taken as the Y-axis.
- This Vertical Bar graph is showing weekly production of dolls on different dates
- In the above vertical bar graph, the days are represented along the horizontal axis and the number of dolls prepared to be represented along the vertical axis., 6 vertical rectangular bars are drawn which are placed at equal distances and they are standing on the horizontal axis for 6 days respectively. Observing these vertical bar graphs we can easily determine how many dolls are prepared on which days.
- So a bar graph or bar diagram consists of rectangular parallel bars which are drawn according to the collected data, each bar has the same breadth and they are drawn on graph paper horizontally of vertically on a common baseline so that the distance between two consecutive bars is always the same.

**Characteristics of Bar Diagram:**

- One variable (in the above diagram the variable is the days) is plotted along the horizontal axis i.e., along the X-axis.
- The other variable (in the above diagram the variable is the number of dolls produced) is plotted along the vertical axis i.e., along the Y-axis.
- The bars will be rectangular in shape.
- The bars can be drawn either horizontally or vertically.
- The bars are of equal widths or breadths.
- The distance between any two consecutive bars is always the same.
- The scale of units along the X-axis and along the Y-axis must be shown separately.
- Generally, the scale of units both along the X-axis and along the Y-axis is expressed in terms of 1 small square division in the graph paper.
- The height of each bar represents the value (or frequency) of each item of the data.
- How the bar diagram be drawn?
- The following working steps are to be noted while drawing a bar
**Step-1:**We first draw two perpendicular straight lines on the same graph paper, one is drawn horizontally to indicate the X-axis, and the other is drawn vertically to indicate the Y-axis.

Let the X-axis be denoted by OX and the Y-axis be denoted by OY.

The point of intersection of these two perpendicular straight lines i.e., the two axes is O which is taken as the origin.

Straight lines can be drawn with the help of scale and pencil.**Step-2:**Omitting one or 2 small square divisions in the graph paper from O, mark the breadth or widths of the consecutive bars with a pencil along, OX.

Special care is to be taken here that the widths of each bar should be the same and the distance between any two consecutive bars is always the same.**Step-3:**Similarly insert the numbers which are to be plotted along the Y-axis i.e., along OY taking the unit of scale in terms of one square division in the graph paper or any convenient unit of scale.

Actually, the frequencies are plotted along Y-axis.**Step-4:**Now mark the numbers involving frequencies on graph paper with a pencil.

According to these, mark the extremities or endpoints of the bars.**Step-5:**Draw the rectangular bars clearly.

This completes the drawing of bar graphs.