NCERT Solutions for Class 7 Maths Chapter 3: Data Handling - Exercise 3.4

Exercise 3.4

Refer to pages 12-13 for Exercise 3.4 in the PDF

1. Tell whether the following is certain to happen, impossible can happen but not certain.

(i) You are older today than yesterday.

Ans: It is certain to happen.

(ii) A tossed coin will land heads up.

Ans: It can happen but not certain.

(iii) A die when tossed shall land up with 8 on top.

Ans: It is impossible as there are only six faces on a dice marked as 1, 2, 3, 4, 5, 6 on it.

(iv) The next traffic light seen will be green.

Ans: It can happen but not certain.

(v) Tomorrow will be a cloudy day.

Ans: It can happen but not certain.

2. There are 6 marbles in a box with numbers from 1 to 6 marked on each of them.

(i) What is the probability of drawing a marble with number 2?

Ans: Total marbles from 1 to 6 marked in a box\[ = 6\].

\[{\text{Probability = }}\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of possible outcomes}}}}\]

Then the probability of drawing a marble with number 2.

\[\; \Rightarrow {\text{P}}\left( {{\text{Appearance of  2 }}} \right) = \dfrac{1}{6}\]

(ii) What is the probability of drawing a marble with number 5?

Ans: The probability of drawing a marble with number 5.

\[ \Rightarrow \;{\text{P}}\left( {{\text{Appearance of  5 }}} \right) = \dfrac{1}{6}\]

3. A coin is flipped to decide which team starts the game. What is the probability that your team will start?

Ans: A coin has two possible outcomes: Head and Tail.

\[{\text{Probability = }}\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of possible outcomes}}}}\]

Probability of getting Head or Tail is equal.

\[\therefore P{\text{ }}\left( {{\text{Starting game}}} \right) = \dfrac{1}{2}\]

Class 7 Maths Chapter 3 Exercise 3.4 NCERT Solutions- How are they Helpful?

The NCERT solution for Class 7 Maths Chapter 3 Exercise 3.4 will naturally help you improve your learning and understanding of the subject. When you are in Class 7, you will naturally want to use these NCERT solutions for Class 7 Maths Chapter 3 to improve your foundation for future Classes. You can easily practice Class 7 Exercise 3.4 NCERT solutions to improve your marks in your examination. The NCERT Class 7 Maths Chapter 3 Exercise 3.4 solutions are created by Vedantu’s expert teachers who know the types of questions that are usually asked in examinations. 

These expert teachers have ample experience in Class 7 Maths ex 3.4 NCERT solutions and will help you prepare accordingly. The Maths Class 7 Chapter 3 Exercise 3.4 will help you understand the major concepts and problems. The data handling Class 7 Exercise 3.4 solutions will help you gain more confidence ahead of your examination.

Class 7 Maths Exercise 3.4- Why it can be a Really Handy Option 

The NCERT Maths Class 7 Chapter 3 solutions are always really helpful if you are studying for your exam. The more you practice Maths, the more perfect you will become at the subject. The NCERT solution Class 7 Maths ex 3.4 is bound to improve your grasp of the subject accordingly. The NCERT solutions cover the concept of Data Handling. You can simply download the free PDFs which contain material for your perusal. Probability is another concept covered in this Chapter. This is the concept where the likelihood of any occurrence is predicted and worked out through division of the number of outcomes which are favorable by the overall number of outcomes which are possible. Suppose a coin is flipped. Then there are just two outcomes possible from this, i.e. heads or just tails. The solutions and ways of understanding these concepts have been clearly outlined by Vedantu’s expert teachers in the NCERT PDFs. 

This Chapter covers data and how it is handled. Various types of data are covered in this Chapter and will help you create a solid foundation for Maths. The NCERT Solutions will help you learn at your own pace. Handling of data is one of the major activities in the Maths curriculum. This enables improved analysis, sorting and organization of elements. Presentation of data is another vital part of handling data. Data handling is a procedure where data is gathered, analyzed, arranged and presented in a format which is perfectly understandable.

Chapter 3 Itself Contains the Following Components: 

• Introduction - Students are given an introduction to the multiple methods by which one can identify data via several useful examples. 

• Collection - Data collection is covered thoroughly in this section and the ways of ensuring the same. This section also informs the reader that data which is gathered has to be suitably processed to ensure a suitable result. 

• Organization - Collected data may have to be organized suitably for making it more presentable. Organization lends a framework to data which enables more efficiency in the long run. 

• Representative Values - The values symbolizing a group of data/persons is called representative values. This is also the average of the entire group. 

• Arithmetic Mean- Arithmetic Mean or the Mean is the average value for a group of units. Arithmetic Mean is equal to sum of the total value of unit and the total number of units. 

• Range - The range is the difference between the lowest and highest values. 

• Mode - This is the value obtained post division of the total of the unit with the total number. 

• Mode of Large Data - This is tabulated and the frequency enables easier finding of the mean for this data. 

• Median - This is the mid-value dividing the entire unit into two halves which are equal. 

• Usage of Bar Graphs with Varying Purposes - This topic covers various uses of bar graphs for presenting data with frequency of mode. 

• Scale Choosing - This enables choosing of a scale or measuring object for graphs. 

• Chance & Probability - This covers probability and chances. 

• Chance - This is the prediction for the outcome. Probability is the chance of taking place through an outcome.

Sample Questions at a Glance

Question 1:

Define the terms:

(i) Data

(ii) Raw data

(iii) Array

(iv) Tabulation of data

(v) Observations

(vi) Frequency of an observation

(vii) Statistics

Question 2:

A die was thrown 20 times and the following outcomes were recorded:

5, 2, 1, 3, 4, 4, 5, 6, 2, 2, 4, 5, 5, 6, 2, 2,4, 5, 5, 1.

Arrange the above data in ascending order and prepare the frequency table.

Question 3:

The daily wages (in Rs) of 15 workers in a factory are given below.

200, 180, 150, 150, 130, 180, 180, 200, 150, 130, 180, 180, 200, 150, 180.

Arrange the above data in ascending order and prepare the frequency table.

Question 4:

Write the data given below in ascending order and prepare the frequency table.

7, 8, 7, 10, 6, 8, 9, 7, 10, 5, 7, 6, 8, 5, 6, 7, 8, 9, 7, 6, 7, 8.

Question 5:

Fill in the blanks:

(i) Data means information in the form of ...... figures.

(ii) Data obtained in the ..... form is called raw data.

(iii) Arranging the numerical figures in ascending of descending order is called an ...... .

(iv) The number of times a particular observation occurs is called its ...... of data.

(v) Arranging the data in the form of a table is called ...... of data.

Question 6:

Find the mean of first five natural numbers.

Question 7:

Find the mean of first six odd natural numbers.

Question 8:

Find the mean of first seven even natural numbers.

Question 9:

Find the mean of first five prime numbers.

Question 10:

Find the mean of first six multiples of 5.

Question 11:

The following table shows the weights (in kg) of 15 workers in a factory:

Calculate the mean weight.

Question 12:

The daily wages (in rupees) of 60 workers in a factory are given below:

Find the mean daily wages.

Question 13:

The heights (in cm) of 90 plants in a garden are given below:

Find the mean height.

Question 14:

The ages (in years) of 50 players of a school are given below:

Find the mean age

Question 15:

The heights (in cm ) of 40 boys were measured and recorded and under:

Find the mean height.

Question 1:

Find the median of:

(i) 3, 11, 7, 2, 5, 9, 9, 2, 10

(ii) 9,25, 18, 15, 6, 16, 8, 22, 21

(iii) 21, 15, 6, 25, 18, 13, 20, 9, 16, 8, 22

Question 2:

Find the median of:

(i) 10, 32, 17, 19, 21, 22, 9, 35

(ii) 55, 60, 35, 51, 29, 63, 72, 91, 85, 82

Question 3:

Find the median of first 15 odd numbers.

Question 4:

Find the median of first 10 even numbers.

Question 5:

Find the median of first 50 whole numbers.

Question 6:

The marks of 15 students (out of 50) in an examination are

20, 22, 26, 31, 40, 19, 17, 19, 25, 29, 23, 17, 24, 21, 35

Find the median marks.

Question 7:

The ages (in years) of 10 teachers in a school are

34, 37, 53, 46, 52, 43, 31, 36, 40, 50.

Find the median age.

Question 8:

Find the median weight for the following data:

Question 9:

Calculate the median for the following data:

Question 10:

The heights (in cm) of 50 students of a Class are given below:

Find the median height.

Question 1:

Find the mode of the data:

(i) 10, 8, 4, 7, 8, 11, 15, 8, 6, 8

(ii) 27, 23, 39, 18, 27, 21, 27, 27, 40, 36, 27

Question 2:

The ages (in years) of 11 cricket players are given below:

28, 34, 32, 41, 36, 32, 32, 38, 32, 40, 31.

Find the mode of the ages.

Question 3:

Daily wages of 45 workers in a factory are given below:

Find the median and the mean.

Using empirical formula, calculate its mode.

Question 4:

The following table shows the marks obtained by 41 students of a Class.

Find the median and mean marks.

Using empirical formula, calculate its mode.

Question 5:

The following table shows the weight of 12 players:

Find the median and mean weights.

Using empirical formula, calculate its mode.

Question 1:

A coin is tossed 300 times and we get head : 136 times and tail : 164 times.

When a coin is tossed at random, What is the probability of getting (i) a head, (ii) a tail?

Question 2:

Two coins are tossed simultaneously 200 times and we get two heads: 58 times, one head: 83 times: 0 head: 59 times.

When two coins are tossed at random, what is the probability of getting (i) 2 heads, (ii) 1 head, (iii) 0 head?

Question 3:

A dice is thrown 100 times and the outcomes are noted as given below:

When a dice is thrown at random, what is the probability of getting a (i) 3, (ii) 6, (iii) 6, (iv) 1?

Question 4: 

In a survey of 100 ladies it was found that 36 like coffee while 64 dislike it.

Out of these ladies, one is chosen at random. What is the probability that the chosen lady (i) likes coffee, (ii) dislikes coffee?

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