CBSE Class 7 Maths Important Questions Chapter 3 - Data Handling

1 Mark 

1. Insert a number between \[\dfrac{1}{4}{\text{ and }}\dfrac{1}{7}{\text{ }}{\text{. }}\]

Ans. To insert a number between two numbers, first we add both numbers and divide the sum by two.

$\dfrac{{\dfrac{1}{4} + \dfrac{1}{7}}}{2} = \dfrac{{\dfrac{{7 + 4}}{{28}}}}{2}$

$= \dfrac{{11}}{{2 \times 28}} = \dfrac{{11}}{{56}}$

2. Give the formula to find mean.

Ans. Formula to find mean is given by, 

${\text{ Mean }} = \dfrac{{{\text{ Sum of all observations }}}}{{{\text{ Number of observations }}}}$

Example: Mean of \[2,4,6,8,10\;\]= $\dfrac{{2 + 4 + 6 + 8 + 10}}{5}\, = \;\dfrac{{30}}{5}\; = \,6$

3. Define Mode. 

Ans. The most frequently occurring value in a data set Is called Mode.

For example, in set \[2,3,4,5,5,5,7,7\]

$5$ occurs $3$ times. Hence $5$ will be the mode of the given data. 

4. Define Average.

Ans. In mathematics, an average is referred to as a mean. It may be obtained by adding the numbers together and then dividing the result by the total number of numbers.

Example average of \[8,10\;\]= $\dfrac{{8 + 10}}{2}\, = \;\dfrac{{18}}{2}\; = \,9$

5. Insert a number between \[-3{\text{ and}}-4{\text{ }}.\]

Ans. To insert a number between two numbers, first we add both numbers and divide the sum by two.

 $\dfrac{{ - 3 - 4}}{2} = \dfrac{{ - 7}}{2} =  - 3.5$

2 Mark Questions

6. Find the mode for the given set of data :
\[1,{\text{ }}2,{\text{ }}3,{\text{ }}5,{\text{ }}6,{\text{ }}7,{\text{ }}2,{\text{ }}1,{\text{ }}4,{\text{ }}1,{\text{ }}6,{\text{ }}1\]

Ans. Given data is \[1,{\text{ }}2,{\text{ }}3,{\text{ }}5,{\text{ }}6,{\text{ }}7,{\text{ }}2,{\text{ }}1,{\text{ }}4,{\text{ }}1,{\text{ }}6,{\text{ }}1\]

Arranging this data in ascending order 

\[{\text{1,1,1,1,2,2,3,4,5,6,6,7,7,8}}\]

$1$ is repeating most frequently that is $4$ times

Therefore, mode of the given data is $1$

7. Find the median of the data \[1,{\text{ }}2,{\text{ }}23,{\text{ }}48,{\text{ }}26,{\text{ }}33,{\text{ }}4\]

Ans. Given data is \[1,{\text{ }}2,{\text{ }}23,{\text{ }}48,{\text{ }}26,{\text{ }}33,{\text{ }}4\]

Arranging this data in ascending order 

\[{\text{1,}}\;{\text{2,}}\;{\text{23,}}\;{\text{26,}}\;{\text{35,}}\;{\text{45,}}\;{\text{48}}\]

We know that, median of a data is middle term.

Here, we have a total of $7$ terms. 

And here the middle term is the 4th  term i.e.  26.

Therefore, the median of the data is 26.

8. Theja studies 8 hours, 6 hours and 2 hours on three consecutive days. How many hours did he study daily? 

Ans.  Given, Theja studied  \[8{\text{ hours}},{\text{ }}6{\text{ hours and 2 hours}}\].

Theja studied daily = Average of  $8,\;6,\;2$= $\dfrac{{{\text{sum}}\;{\text{of}}\;{\text{given}}\;{\text{data}}}}{{{\text{Number}}\;{\text{of}}\;{\text{days}}}}$

$\dfrac{{8 + 6 + 2}}{3}\; = \;\dfrac{{16}}{3}\; = \;5.33\;\;{\text{hours}}$

Theja studied $5.33\;\;{\text{hours}}$.

9. Answer the following by observing the given data
The age’s of cricket players of ICC is as follows:
\[21,{\text{ }}23,{\text{ }}25,{\text{ }}26,{\text{ }}32,{\text{ }}34\]

a) What is the age of the eldest players?

b) What is the age of the youngest players in the team?

Ans.  Given data is \[21,{\text{ }}23,{\text{ }}25,{\text{ }}26,{\text{ }}32,{\text{ }}34\]

a) Here the highest term is $34$ .

Therefore, the age of the eldest player is $34\;{\text{years}}$

b) Here the lowest term is $21$.

Therefore, the age of the youngest player is $21\;{\text{years}}$.

10. The goals scored by Lakshya in five matches are 3, 1, 2, 3, 1. Find the mean goal scored by her. 

Ans.  Goals scored by Lakshya in five matches = 3, 1, 2, 3, 1

${\text{Mean goal }} = \dfrac{{{\text{Sum of}}\;{\text{goal's}}\;{\text{scored}}\;{\text{in}}\;{\text{all}}\;{\text{matches}}}}{{{\text{ Number of Matches}}}}$

$= \dfrac{{3 + 1 + 2 + 3 + 1}}{5}$

$ = \dfrac{{10}}{5}\; = 2$

Mean goal is $2$.

11. Find the range of heights of cricket players (in cm) the heights are follows
\[158,{\text{ }}150,{\text{ }}156,{\text{ }}162,{\text{ }}155,{\text{ }}152,{\text{ }}154,{\text{ }}164,{\text{ }}153,{\text{ }}165,{\text{ }}160\]

Ans.  Range = Highest value – Lowest Value 

Here, Highest Value = $165$

Lowest Value = $150$

 Range = $165 - 150$ = $15\;{\text{cm}}$

12. Runs scored by a cricket player is in few matches is as follows:
\[28,{\text{ }}25,{\text{ }}38,{\text{ }}46,{\text{ }}58,{\text{ }}32\]. Find the average runs. 

Ans.  ${\text{Average}}\;{\text{Runs}}\;{\text{ = }}\dfrac{{{\text{Sum}}\;{\text{of}}\;{\text{all}}\;{\text{runs}}}}{{{\text{Number}}\;{\text{of}}\;{\text{Matches}}}}$

Here Number of Matches = $6$

${\text{Average}}\;{\text{Runs}}\;{\text{ = }}\dfrac{{28 + 25 + 38 + 46 + 58 + 32}}{6}$

$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = \;\dfrac{{277}}{6}\;\; = \;37.38$

${\text{Average}}\;{\text{Runs}} = \;37.38\;{\text{Runs}}$

13. Kids borrow books from a library from Monday to Friday. A week value is recorded and is as follows. Find the average \[65,{\text{ }}148,{\text{ }}351,{\text{ }}481,{\text{ }}390.\]

Ans. ${\text{Average}}\;\;{\text{ = }}\dfrac{{{\text{Sum}}\;{\text{of}}\;{\text{all}}\;{\text{books}}\;{\text{issued}}}}{{{\text{Number}}\;{\text{of}}\;{\text{days}}}}\;$

${\text{ = }}\dfrac{{5 + 148\; + 351{\text{  + }}\;481\; + {\text{ }}390.}}{5}$

$= \;\dfrac{{1435}}{5}\;\; = \;287$

14. The score of 10 kids in mathematics shows below. Find mean
\[33,{\text{ }}48,{\text{ }}27,{\text{ }}49,{\text{ }}30,{\text{ }}32,{\text{ }}19,{\text{ }}25,{\text{ }}37,{\text{ }}35\]

Ans. ${\text{Mean}}\;\;{\text{ = }}\dfrac{{{\text{Sum}}\;{\text{of}}\;{\text{all}}\;{\text{scores}}}}{{{\text{Number}}\;{\text{of students}}}}\;$

${\text{ = }}\dfrac{{33\; + \;\;48\; + 27\; + \;49\; + \;30\; + {\text{ }}32\; + 19\; + {\text{ }}25\; + {\text{ }}37\; + {\text{ }}35}}{5}$

$= \;\dfrac{{335}}{{10}}\;\; = \;33.5$

Thus, the average score of kids In Mathematics is $33.5$.

Chapter 3 - Data Handling

Data handling refers to the process of collecting, recording and displaying information, for example in graphs or charts, in a way that is beneficial to others. Data handling is also known as statistics.

Steps in Data Handling

• Data collection using a scheduled technique.

• Recording data with accuracy and precision.

• Data analysing to draw conclusions.

• Sharing data in a way that is helpful to everyone.

Data Collection

Data collection is a term used to describe a process of planning and gathering data. The aim of the collection of data is to obtain the information to be registered, to make decisions on significant issues, to pass on information to others.

Ex: A teacher has assigned students to collect the average temperature data for the month of February. The only thing the teacher wants is Average data.

So, students have to decide at what time daily they have to measure the temperature data. So for these, they have to do proper planning and also they have to gather suitable temperature measuring devices. 

This process of collecting temperature data for 28/29 days in the month of February is called Data collection.

Organisation of Data

Data organisation refers to the organised arrangement of raw data so that the data can be readily interpreted and further statistical treatment is more convenient.

In the data organisation, we will use tables and charts to show the collected data rather than just giving the raw numbers. This is because the person who is collecting data knows more about the raw data representation if we are showing it to someone they have to easily understand the data representation. So we use tables, graphs and charts to represent the data.

The representative value of a set of measurements is the one that we assume is nearest to the measurement's real value. If we carry out our series of calculations, their average will be the indicative value, except those values that we have shown to be far from the true value.

Arithmetic Mean

The arithmetic mean is the simplest and most commonly used measurement system used to calculate the mean or average of a data. It simply involves taking the sum of a number group, then dividing that sum by the number of numbers that are used in the sequence.

Ex: The data of height(cm) of students in the class is given as follows. Calculate the arithmetic mean.

150, 155, 152, 150, 158, 154, 152, 156, 154, 152.

Ans: So to find Arithmetic mean, first we have to calculate the sum of the data.

Sum = 150 + 155 + 152 + 150 + 158 + 154 + 152 + 156 + 154 + 152 = 1533

Total number of students = 10

The arithmetic mean = Sum of heights / Total number of students

Arithmetic mean = 1533 / 10 = 153.3

Range

In Statistics, the difference between the largest and the smallest values in the range of a set of data.

Ex: The data of height(cm) of students in the class is given as follows. Calculate the range.

150, 155, 152, 150, 158, 154, 148, 156, 154, 152

Ans: L To calculate range first we have to find the height of taller students and shorter students in the class. So the taller student height is 158 cm and shorter student height is 148 cm. 

So the range will be the difference between these two heights.

Range = 158 - 148 = 10 cm

Mode

The mode is the value that appears in a data set most frequently. A data set can have one mode, more than one mode, or no mode at all.

Ex: The data of height(cm) of students in the class is given as follows. Calculate the mode.

150, 155, 152, 150, 158, 154, 152, 156, 154, 152.

Ans: Here 152 cm is the most frequent height of 3 students. Therefore the Mode of the following height data set will be 152 cm.

Median

In a sorted, ascending or descending, list of numbers, the median is the middle number and may be more representative of that data set than the average.

In comparison to the mean, the median is often used when there are outliers in the series that could distort the average of the values.

If there are odd numbers, the median value is the number in the centre, with numbers below and above the same sum.

The middle pair must be estimated, added together, and divided by two to find the median value if there is an even number in the set.

Ex: 

1. The Data of Height(cm) of Students in the Class is Given as Follows. Calculate the Median Height.

150, 155, 152, 150, 158, 154, 152, 156, 154, 152.

Ans: The total number of students in the class is 10 which is even, so we have added the middle terms i.e 5th and 6th term and divide them by 2 to find the median.

Median = (158 + 154) / 2 = 156 cm.

Therefore the median height of the class is 156 cm.

2. The Weight(Kg) of the Students of the Class is Given as Follows. Calculate the Median Weight.

45, 48, 52, 47, 46, 50, 44

Ans: The total number of students in the class is 7. So the middle term of this weight data set will be our Median weight.

Median = 47 Kg.

Representation of Data Using Bar Graphs

A bar chart or bar graph is a chart or graph that provides rectangular bars with categorical data with heights or lengths proportional to the values they represent. It is possible to plot the bars vertically or horizontally. Sometimes, a vertical bar map is called a column chart.

5 Important Formulas of Class 7 Chapter 3 Data Handling You Shouldn’t Miss!

Data handling is an important aspect of mathematics in Class 7. Understanding key formulas helps students analyse and interpret data effectively. Here are five important formulas to remember in Chapter 3:

1. Mean (Average):  

The mean is calculated by adding all the values together and then dividing by the number of values.

$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$

2. Median:  

The median is the middle value when the data is arranged in ascending order. If there is an even number of observations, the median is the average of the two middle values.

- For odd numbers:

$\text{Median} = \text{Middle value of sorted data}$

- For even numbers:

$\text{Median} = \frac{\text{Value at position } \frac{n}{2} + \text{Value at position } \left(\frac{n}{2} + 1\right)}{2}$

3. Mode:  

The mode is the value that appears most frequently in a data set. A data set can have:

- One mode (unimodal)

- More than one mode (bimodal or multimodal)

4. Range:  

The range gives an idea of how spread out the values are in a data set. It is calculated by subtracting the smallest value from the largest value.

$\text{Range} = \text{Maximum value} - \text{Minimum value}$

5. Frequency Distribution:  

A frequency distribution table shows how often each value occurs in a data set. The formula to calculate the frequency of a specific value is:

$\text{Frequency} = \text{Number of times a value appears}$

These formulas are essential for analysing data and are fundamental for understanding statistics. Be sure to practise them to gain confidence in handling data effectively!

Benefits of Referring to the Important Questions of Class 7 Chapter 3 Data Handling

Students must go through the important questions of each chapter of Mathematics for the following benefits:

• These questions help you to evaluate your knowledge and understanding of any particular chapter.

• If you refer to other questions that are not given in your NCERT book, then you will prepare yourself for the examination, where you might be asked some tricky questions.

• It also helps you to understand the topic in depth.

• These important questions and answers are given in easy-to-understand language and a step-by-step process. 

• It helps students’ thinking ability and problem-solving abilities, which enable students to secure good marks not only in the current class but in all academic sessions. 

Conclusion

Vedantu's Important Questions for CBSE Class 7 Maths Chapter 3 - Data Handling offers a comprehensive and valuable resource for students to master this fundamental topic. With a vast array of meticulously curated questions, the platform ensures a thorough understanding of data handling concepts. The well-structured and engaging material enables students to strengthen their analytical and problem-solving skills. By focusing on real-life scenarios and practical applications, Vedantu empowers learners to grasp the relevance of data handling in daily life. With this resource, students can build a strong foundation, instilling confidence to tackle more complex challenges in mathematics. Vedantu's dedication to enhancing learning experiences proves instrumental in nurturing confident and capable mathematicians.

Important Study Materials for Class 7 Maths Chapter 3

Related Study Materials for Class 7 Maths Chapter 4 Simple Equations

Chapter-wise Important Questions Links for Class 7 Maths

Important Study Materials for Class 7 Maths