Grouping of Data | Definition, Frequency Distribution Table, Examples

Grouping of data plays an important role while dealing with a large amount of data. This information can also be displayed using a bar graph or pictograph. You can the grouping of data definition, solved examples in the below sections of this article. Furthermore, you will be familiar with the steps to draw a frequency distribution table for grouped data in the coming modules.

What is Meant by Grouping of Data?

When the number of observations is very large, we may divide the data into several groups, by using the grouping of data concept. The data formed by arranging the individual observations of a variable into groups, so that the frequency distribution table of these groups is a convenient way of summarizing the data. The advantages of grouping data are, it improves the accuracy/ efficiency of estimation, helps to focus on the important subpopulations, and ignores irrelevant ones.

Steps to Draw Frequency Distribution Table for Grouped Data

  • From the given data, divide the data into some groups.
  • Arrange the given observations in ascending order.
  • Get the frequency of each observation.
  • Write the frequency, group name in the frequency distribution table.

Get more useful information regarding the data handling such as the types of data, definition, and terms used in the data handling.

Solved Example Questions & Answers

Example 1.

The mass of 40 students in a class is given below. The measurement of the weight will be in kgs.

55, 70, 57, 73, 55, 59, 64, 72, 60, 48, 58, 54, 69, 51, 63, 78, 75, 64, 65, 57, 71, 78, 76, 62, 49, 66, 62, 76, 61, 63, 63, 76, 52, 76, 71, 61, 53, 56, 67, 71

State the frequency distribution table for the grouped data?

Solution:

Given that,

The weight of 40 students in a class are 55, 70, 57, 73, 55, 59, 64, 72, 60, 48, 58, 54, 69, 51, 63, 78, 75, 64, 65, 57, 71, 78, 76, 62, 49, 66, 62, 76, 61, 63, 63, 76, 52, 76, 71, 61, 53, 56, 67, 71

The ascending order of the students weight is 48, 49, 51, 52, 53, 54, 55, 55, 56, 57, 57, 58, 59, 60, 61, 61, 62, 62, 63, 63, 63, 64, 64, 65, 66, 67, 69, 70, 71, 71, 71, 72, 73, 75, 76, 76, 76, 76, 78, 78

The range = 78 – 48 = 30

The intervals should separate the scale into equal parts. We could choose intervals of 5. We then begin the scale with 45 and end with 79.

Frequency Distribution Table for Grouped Data is

Mass in Kg Frequency
45 – 49 2
50 – 54 4
55 – 59 7
60 – 64 10
65 – 69 4
70 – 74 6
75 – 79 7
Total 40

Example 2.

The marks obtained by 40 students of Class VII in an examination are given below:
16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 2, 23, 5, 12, 18, 8, 12, 6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23

State the frequency distribution table for the grouped data?

Solution:

Given data,

The marks scored by 40 students is 16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 2, 23, 5, 12, 18, 8, 12, 6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23

The ascending order of the marks is 0, 1, 2, 2, 3, 3, 5, 5, 5, 6, 7, 7, 7, 8, 8, 9, 10, 10, 12, 12, 12, 13, 13, 13, 15, 16, 16, 16, 17, 18, 18, 18, 19, 20, 21, 21, 23, 23, 23, 24

Range is = 24 – 0 = 24

The intervals should separate the scale into equal parts. We could choose intervals of 5. We then begin the scale with 0 and end with 24.

Frequency Distribution Table for Grouped Data is

Marks Scored Number of Students (Frequency)
0 – 4 6
5 – 9 10
10 – 14 8
15 – 19 9
20 – 24 7
Total 40

Example 3.

The height (in cms) of 35 persons are given below:

140, 125, 128, 126, 130, 134, 134, 146, 125, 140, 140, 127, 125, 137, 132, 134, 126, 128, 128, 129, 150, 151, 131, 138, 128, 129, 126, 127, 129, 130, 135, 132, 134, 140, 152

State the frequency distribution table for the grouped data.

Solution:

Given that,

The height of 35 persons are 140, 125, 128, 126, 130, 134, 134, 146, 125, 140, 140, 127, 125, 137, 132, 134, 126, 128, 128, 129, 150, 151, 131, 138, 128, 129, 126, 127, 129, 130, 135, 132, 134, 140, 152

Ascending order of the 35 persons height is 125, 125, 125, 126, 126, 126, 127, 127, 128, 128, 128, 128, 129, 129, 129, 130, 130, 131, 132, 132, 134, 134, 134, 134, 135, 137, 138, 140, 140, 140, 140, 146, 150, 151, 152

The range is 152 – 125 = 27

The intervals should separate the scale into equal parts. We could choose intervals of 4. We then begin the scale with 125 and end with 152.

Frequency Distribution Table for Grouped Data is

Height (in Cms) Number of Persons (Frequency)
125 – 128 12
129 – 132 8
133 – 136 5
137 – 140 6
141 – 144 0
145 – 148 1
149 – 152 3
Total 35

Frequently Asked Questions on Grouping of Data

1. What is grouped and ungrouped data?

Grouped data is the data given in intervals whereas ungrouped data is the data without a frequency distribution.

2. What is a group of data called?

The frequency table is also called the grouped data. Grouped data is used in data analysis.

3. How can we convert ungrouped data to grouped data?

The first step of the conversion is to determine how many classes you have and find the range of data. And then divide the number of classes into groups.

Frequency Distribution Definition | How to find Frequency Distribution?

The frequency distribution is a topic in statistics related to data handling. The term frequency is how often something occurs and distribution means dividing and sharing something. Get the examples, the definition of frequency distribution, and learn about the frequency distribution table. Find the solved examples that help you to understand the concept clearly.

Frequency Distribution Definition

The frequency distribution describes how frequencies are distributed over the data. It is a representation either in tabular or graphical format, that displays the number of observations within the given interval.

The terms of the frequency distribution are listed here:

  • Presentation of Data: After collecting the data, shortly in the tabular form in order to study its features, such arrangement is known as the data presentation.
  • Observation: Each entry collected as a numerical number in the given data is called the observation.
  • Frequency: The number of times a particular observation repeat is known as the frequency.
  • Frequency Distribution Table: It is one form of representation of the data. It contains the observations and how many times those observations occur.

Steps to Draw a Frequency Distribution Table

  • Arrange the given data in ascending order.
  • And find the frequency of each data value.
  • Take the data value and frequency as the two columns in the table.
  • Write each data value frequency in the table.

Get more useful information regarding the data handling such as the types of data, definition, and terms used in the data handling.

Example of Frequency Distribution

Example 1.

Suppose the runs scored by the 11 players of the Indian cricket team in a match are given as follows:

25, 65, 03,12, 35, 46, 67, 56, 00, 31, 17

State the frequency of each player?

Solution:

Given that,

Runs scored by the 11 players of the cricket team in a match are 25, 65, 03,12, 35, 46, 67, 56, 00, 31, 17

Arranging the data in ascending order, we get the observations as

00, 03, 12, 17, 25, 31, 35, 46, 56, 65, 67

We find that Each value has occurred only once.

We may represent the above data in a tabular form, showing the frequency of each observation. This representation is called a frequency distribution.

Frequency Distribution Table

Player Runs Scored By Each Player (Frequency)
Player 1 00
Player 2 03
Player 3 12
Player 4 17
Player 5 25
Player 6 31
Player 7 35
Player 8 46
Player 9 56
Player 10 65
Player 11 67
Overall score in the match 357

Example 2.

In a quiz, the marks obtained by 20 students out of 30 are given as:

12, 15, 15, 29, 30, 21, 30, 30, 15, 17, 19, 15, 20, 20, 16, 21, 23, 24, 23, 21

State the frequency of each student.

Solution:

Given that,

Marks obtained by 20 students in quiz out of 30 are 12, 15, 15, 29, 30, 21, 30, 30, 15, 17, 19, 15, 20, 20, 16, 21, 23, 24, 23, 21

Arranging the data in ascending order, we get the marks list as

12, 15, 15, 15, 15, 16, 17, 19, 20, 20, 21, 21, 21, 23, 23, 24, 29, 30, 30, 30

The highest marks obtained student is 30, the lowest marks are 12, the range is 30 – 12 = 18

From the data, we find that

12 marks scored by one student,

15 marks scored by 4 students,

16, 17, 19 marks scored by one student,

20 marks scored by 2 students,

21 marks scored by 3 students,

23 marks scored by 2 students,

24, 29 marks scored by one student,

30 marks scored by 3 students,

We may represent the above data in a tabular form, showing the frequency of each observation. The number of times data occurs in a data set is known as the frequency of data

This tabular form of representation is called a frequency distribution.

Marks obtained in the quiz Number of students(Frequency)
12 1
15 4
16 1
17 1
19 1
20 2
21 3
23 2
24 1
29 1
30 3
Total 20

Example 3.

The numbers of newspapers sold at a local shop over the 10 days are:

22, 20, 18, 23, 20, 25, 22, 20, 18, 20

State the frequency.

Solution:

Given that,

The total number of newspapers sold at the local shop past 10 days are 22, 20, 18, 23, 20, 25, 22, 20, 18, 20

By arranging the newspapers numbers in ascending order is 18, 18, 20, 20, 20, 20, 22, 22, 23, 25

The frequency table for the papers sold is given here:

Paper Sold Frequency
18 2
20 4
22 2
23 1
25 1
Total 10

Data Handling | Definition, Solved Example Questions on Data Handling

Data Handling is an important topic in statistics. It deals with the collecting set of data and maintaining security, confidentiality, and the preservation of the research data. Here data is nothing but a set of numeric values. Get more useful information regarding the data handling such as the types of data, definition, and terms used in the data handling. You can check out the solved example questions in the following sections of this page.

Data Handling Definition

Data handling is the process of collecting, recording, and representing information in a way that is helpful to others. Data is a collection of all numerical figures, observations that represents a particular kind of information.

Data handling is performed depending on the types of data. Data is classified into two types, such as Quantitative Data, Qualitative Data. Quantitive data gives numerical information, while qualitative data gives descriptive information about anything.

Important Terms of Data Handling

  • Data: The collection of numerical figures regarding a kind of information is called the data.
  • Raw Data: The collection of observations that are gathered initially is called the raw data.
  • Range: The difference between the highest and lowest values in the data collection is called the range.
  • Statistics: It deals with the collection, representation, analysis, and interpretation of numerical data.

Ways to Represent Data

The following are the simple ways to represent the data. Choose anyone for a better presentation.

  • Bar Graph
  • Line Graph
  • Pictographs
  • Histograms
  • Stem and Leaf Plot
  • Dot Plots
  • Frequency Distribution
  • Cumulative Tables and Graphs

Solved Examples on Data Handling

Example 1.

Given below are the marks (out of 150) in mathematics obtained by 20 students of a class in an annual examination.

86   75   69   23   72   120   56   82   96   45

100  66   73  46   19   55     46   99  110  105

Arrange the above data in ascending order and find

(i) the lowest marks obtained,

(ii) the highest marks obtained,

(iii) the range of the given data.

Solution:

Given data is

86   75   69   23   72   120   56   82   96   45

100  66   73  46   19   55     46   99  110  105

Arranging the above data in ascending order, we get

19  23  45  46  46  55  56  66  69  72

73  75  82  86  96  99  100  105  110  120

From the above data analysis, we can say that

The lowest marks obtained is 19.

The highest marks obtained is 120.

The range of the data is 120 – 19 = 101.

Example 2.

Given below are the heights (in cm) of 15 boys of a class:

135, 128, 146, 149, 127, 130, 145, 140, 131, 125, 136, 142, 144, 133, 129

Arrange the above data in ascending order and find

(i) the height of the tallest boy,

(ii) the height of the shortest boy,

(iii) the range of the given data.

Solution:

Given data sample is

135, 128, 146, 149, 127, 130, 145, 140, 131, 125, 136, 142, 144, 133, 129

The ascending order of the data is

125, 127, 128, 129, 130, 131, 133, 135, 136, 140, 142, 144, 145, 146, 149

From the above ascending order, we can find

(i) The height of the tallest boy is 149 cm

(ii) The height of the shortest boy is 125 cm.

(iii) The range is 149 – 125 = 24.

Example 3.

The daily wages of 24 laborer who works in the construction field are given below:

280, 150, 160, 500, 520, 460, 780, 590, 860, 450, 410, 425, 360, 1000, 950, 560, 590, 620, 250, 350, 380, 515, 790, 240

Arrange the above data in ascending order and find

(i) the highest amount is taken per day,

(ii) the lowest amount is taken per day,

(iii) the range of the given data.

Solution:

Given that,

The daily wages of 24 laborer in the construction field are 280, 150, 160, 500, 520, 460, 780, 590, 860, 450, 410, 425, 360, 1000, 950, 560, 590, 620, 250, 350, 380, 515, 790, 240

The ascending order of the given data is

150, 160, 240, 250, 280, 350, 360, 380, 410, 425, 450, 460, 500, 515, 520, 560, 590, 590, 620, 780, 790, 860, 950, 1000

From the ascending order, we can find

The highest amount on daily basis is 1000

The lowest amount taken is 150

The range of the given data is 1000 – 150 = 850

FAQs on Data Handling

1. What are the uses of data handling?

Various real-time uses of data handling are for recording water levels in rivers, for doctors to keep records of patients, to record the economical income of each household, etc.

2. What is the difference between data and information?

Data means raw and unorganized facts. While information is the proper structured and organized data.

3. What are the various methods of collecting data?

The various methods of collecting data are questionnaire, interview, schedule, case study, observation, and projective case study.

Percentage (How to Calculate, Formula and Tricks)

In Maths, a Percentage is a Number or Ratio Expressed as a Fraction Over 100. In other words, percent means parts per hundred and is given by the symbol %. If we need to calculate the percent of a number you just need to divide the number by whole and multiply with 100. Percentages can be represented in any of the forms like decimal, fraction, etc.

You can get entire information regarding Percentage like Definition, Formula to Calculate Percentage, Conversions from Percentage to another form, and vice versa in the coming modules. Learn the Percentage Difference, Increase or Decrease Concepts too that you might need during your academics or in your day to day calculations.

List of Percentage Concepts

Access the concepts that you want to learn regarding the Percentage through the quick links available. Simply tap on the concept you wish to prepare and get the concerned information explained step by step. Clarify all your queries and be perfect in the corresponding topics.

Percentage Formula

To make your calculations quite simple we have provided the Percentage Formula here. Make use of it during your calculations and arrive at the solution easily.

Formula to Calculate Percentage is given by = (Value/Total Value) *100

How to Calculate Percentage of a Number?

To find the Percent of a Number check the following procedure

Consider the number to be X

P% of number = X

Removing the % sign we have the formula as under

P/100*Number = X

Percentage Change

% Change = ((New Value – Original Value)*100)/Original Value

There are two different types when it comes to Percent Change and they are given as under

  • Percentage Increase
  • Percentage Decrease

Percentage Increase

If the new value is greater than the original value that shows the percentage change in the value is increased from the original number. Percentage Increase is nothing but the subtraction of the original number from the new number divided by the original number.

% increase = (Increase in Value/Original Value) x 100

% increase = [(New Number – Original Number)/Original Number] x 100

Percentage Decrease

When the new value is less than the original value, that indicates the percentage change in the value shows the percent decrease in the original number. Percentage Decrease is nothing but the subtraction of new number from the original number.

% Decrease = (Decrease in Value/Original Value) x 100

% Decrease = [( Original Number – New Number)/Original Number] x 100

Percentage Difference

If you need to find the Percentage Difference if two values are known then the formula to calculate Percentage Difference is given by

Percentage Difference = {|N1 – N2|/(N1+N2/2)}*100

Conversion of Fraction to Percentage

To convert fraction to percentage follow the below-listed guidelines.

  • Divide the numerator with the denominator.
  • Multiply the result with 100.
  • Simply place the % symbol after the result and that is the required percentage value.

Conversion of Decimal to Percentage

Follow the easy steps provided to change between Decimal to Percentage. They are as such

  • Obtain the decimal number.
  • Simply multiply the decimal value with 100 to get the percentage value.

Solved Examples on Percentage

1. What is 50% of 30?

Solution:

Given 50% of 30

= (50/100)*30

= 1500/100

= 15

Therefore, 50% of 30 is 15.

2. Find 20% of 40?

Solution:

Given 20% of 40

= (20/100)*40

= (20*40)/100

= 800/100

= 8

3. What is 15% of 60 equal to?

Solution:

= (15/100)*60

= (15*60)/100

= 900/100

= 9

4. There are 120 people present in an examination hall. The number of men is 50 and the number of women is 70 in the examination hall. Calculate the percentage of women present in the examination hall?

Solution:

Number of Women = 70

Percentage of Women = (70/100)*120

= (70*120)/100

= 8400/100

= 84%

The Percentage of Women in the Examination Hall is 84%.

5. What is the percentage change in the rent of the house if in the month of January it was Rs. 20,000 and in the month of March, it is Rs. 15,000?

Solution:

We can clearly say that there is a decrease in the rent

Decreased Value  = 20,000 – 15, 000

= 5, 000

Percent Change = (Decreased Value/Original Value)*100

= (5000/20,000)*100

= (1/4)*100

= 25%

Hence, there is a 25% decrease in the rent.

FAQs on Percentage

1. What is meant by Percentage?

A percentage is a Number or Ratio Expressed as a Fraction Over 100.

2. What is the Formula for Percentage?

The formula for Percentage is (Value/Total Value) *100

3. What is the Symbol of Percentage?

The percentage is denoted by the symbol %.

4. What is 10% of 45?

10% of 45 is given by 10/100*45 i.e. 4.5

Graph of Area vs. Side of a Square | Draw the Graph of Area of Square Vs Side of the Square

This page defines the relationship between the square side length and square area via a coordinate graph. Take the square area, square side as the coordinates of a point. And plot those points on the graph and read the unknown values from the graph easily. You can get the solved example questions on how to draw a graph of area vs side of a square in the following sections.

Relation Between Square Side Length & Area

The square area is defined as the product of the length of each side with itself. Its formula is given as side_length².

So, the relationship between the square side and the area is a square graph.

Square Area A = side² = s².

Solved Example Questions

Example 1.

Draw a graph of area vs side of a square. From the graph, find the value of the area, when the side length of the square = 3.

Solution:

Square Area A = side² = s².

For different values of s, we get the corresponding value of A.

When s = 0, A = 0² = 0

When s = 1, A = 1² = 1

When s = 2, A = 2² = 4

s 0 1 2
A 0 1 4

Thus, we have the points O (0, 0), A (1, 1), B (2, 4).

Plot these points on a graph paper and join them successively to obtain the required graph given below.

Reading off from the graph of area vs. side of a square:

On the x-axis, take the point L at s = 3.

Draw LP ⊥ x-axis, meeting the given graph at P.

Clearly, PL = 9 units.

Therefore, s = 3 ⇒ A = 9.

Thus, when s = 3 units, then A = 9 sq. units

Example 2.

Draw a graph for the following.

Side of the square (in cm) 1, 2, 3, 4 and Area (in cm) 1, 4, 9, 16 Is it a linear graph?

Solution:

Area of the square A = side² = s².

Draw these square side, area on a table.

s 1 2 3 4
A 1 4 9 16

Take the side of the square on the x-axis, area on the y-axis.

Plot the points P (1, 1), Q (2, 4), R (3, 9), s (4, 16) on the graph paper.

From the graph, we can say that square area vs side does not form a linear graph. It forms a square graph.

Example 3.

(a). Consider the relation between the area and the side of a square, given by A = s². Draw a graph of the above function.

(b). From the graph, find the value of A, when s = 2.5, 3.5.

Solution:

Given that,

Square Area A = s².

For different values of s, we get the corresponding value of A.

s = 0 ⇒ A = 0² = 0

s = 0.5 ⇒ A = 0.5² = 0.25

s = 1 ⇒ A = 1² = 1

s = 1.5 ⇒ A = 1.5² = 2.25

s 0 0.5 1 1.5
A 0 0.25 1 2.25

Thus, we get the points O (0, 0), A (0.5, 0.25), B (1, 1), C 1.5, 2.25)

Plot these points on a graph paper and join them successively to obtain the required graph given below.

(b). Reading off from the graph of area vs. side of a square:

On the x-axis, take the point L at s = 2.5.

Draw LP ⊥ x-axis, meeting the given graph at P.

Clearly, PL = 6.25 cm².

Therefore, s = 2.5 ⇒ A = 6.25.

Thus, when s = 2.5 cm, then A = 6.25 cm²

On the x-axis, take the point M at s = 3.5.

Draw MQ ⊥ x-axis, meeting the given graph at Q.

Clearly, MQ = 12.25 cm².

Therefore, s = 3.5 ⇒ A = 12.25 cm²

Thus, when s = 3.5 cm, then A = 12.25 cm²