In Class 8, one of the most important topics students encounter is Data Handling. This chapter introduces the concepts of data collection, organization, representation, and interpretation. You’ll learn how to represent data using various formats such as bar graphs, histograms, and pie charts, which will help in analyzing and interpreting the data effectively.
In this blog post, we will provide solutions to all the exercises from Chapter 6 and also include 40 additional practice questions to help you master the concepts and improve your problem-solving skills.
Table of Contents:
- Chapter 6 Overview: Data Handling
- Exercise 6.1: Collecting and Organizing Data
- Exercise 6.2: Pictorial Representation of Data
- Exercise 6.3: Bar Graphs and Histograms
- Exercise 6.4: Pie Charts
- 40 Additional Practice Questions with Solutions
Let’s get started!
Exercise 6.1: Collecting and Organizing Data
Q1. The following data represents the number of books read by students in a month. Organize this data in a frequency table.
Data: 2, 3, 3, 5, 4, 4, 5, 5, 3, 4, 4, 3, 2
Solution:
Frequency table:
| Number of Books (x) | Frequency (f) |
|---|---|
| 2 | 2 |
| 3 | 4 |
| 4 | 4 |
| 5 | 3 |
Q2. Find the mean of the following data: 2, 5, 7, 3, 4, 6, 8.
Solution:
Mean = Sum of all valuesNumber of values=2+5+7+3+4+6+87=357=5\frac{\text{Sum of all values}}{\text{Number of values}} = \frac{2 + 5 + 7 + 3 + 4 + 6 + 8}{7} = \frac{35}{7} = 5Number of valuesSum of all values=72+5+7+3+4+6+8=735=5
Exercise 6.2: Pictorial Representation of Data
Q3. Represent the following data using a pictograph:
| Fruits | Number of Fruits |
|---|---|
| Apples | 6 |
| Bananas | 8 |
| Oranges | 4 |
Solution: Using 1 picture = 1 fruit.
- Apples: 🍎🍎🍎🍎🍎🍎
- Bananas: 🍌🍌🍌🍌🍌🍌🍌🍌
- Oranges: 🍊🍊🍊🍊
Q4. Draw a pictograph for the following data on the number of hours spent on various activities:
| Activity | Hours |
|---|---|
| Sleeping | 8 |
| Studying | 5 |
| Playing | 3 |
| Eating | 2 |
Solution:
- Sleeping: 🛏️🛏️🛏️🛏️🛏️🛏️🛏️🛏️
- Studying: 📚📚📚📚📚
- Playing: 🎮🎮🎮
- Eating: 🍽️🍽️
Exercise 6.3: Bar Graphs and Histograms
Q5. Draw a bar graph to represent the following data:
| Days | Number of Students Present |
|---|---|
| Monday | 30 |
| Tuesday | 35 |
| Wednesday | 40 |
| Thursday | 25 |
Solution: A bar graph can be plotted by drawing a vertical axis for the number of students and a horizontal axis for the days. For each day, draw a bar that reaches the corresponding number of students.
Q6. A histogram is given below showing the distribution of scores in a class. What is the number of students scoring between 50 and 60 marks?
Solution: The number of students scoring between 50 and 60 marks is the height of the bar corresponding to that range in the histogram.
Q7. Draw a bar graph for the following data showing the number of books read by students in a month.
| Students | Number of Books |
|---|---|
| A | 5 |
| B | 7 |
| C | 6 |
| D | 8 |
Solution: To draw a bar graph, label the horizontal axis with the students’ names and the vertical axis with the number of books. For each student, draw a bar that reaches the number of books they read.
Exercise 6.4: Pie Charts
Q8. Represent the following data in a pie chart.
| Activity | Percentage |
|---|---|
| Sleeping | 25 |
| Studying | 40 |
| Playing | 20 |
| Eating | 15 |
Solution:
- The total degrees in a circle are 360°.
- Sleeping: 25%×360°=90°25\% \times 360° = 90°25%×360°=90°
- Studying: 40%×360°=144°40\% \times 360° = 144°40%×360°=144°
- Playing: 20%×360°=72°20\% \times 360° = 72°20%×360°=72°
- Eating: 15%×360°=54°15\% \times 360° = 54°15%×360°=54°
Draw a circle and divide it into the appropriate sections based on the degrees.
40 Additional Practice Questions with Solutions
Q9. The heights of students in a class are given as 150 cm, 160 cm, 155 cm, 165 cm, and 170 cm. What is the mean height of the students?
Solution:
Mean height = 150+160+155+165+1705=8005=160 cm\frac{150 + 160 + 155 + 165 + 170}{5} = \frac{800}{5} = 160 \, \text{cm}5150+160+155+165+170=5800=160cm
Q10. In a survey, 15 students like cricket, 10 like football, and 5 like basketball. Represent the data in a pictograph using a symbol for each 5 students.
Solution:
- Cricket: 🏏🏏🏏🏏🏏
- Football: ⚽⚽⚽⚽
- Basketball: 🏀🏀
Q11. A class of 40 students was surveyed on their favorite subject. The results are as follows: 12 like Mathematics, 10 like Science, 8 like English, and 10 like Social Studies. Draw a bar graph for this data.
Solution:
Label the horizontal axis with subjects and the vertical axis with the number of students. Draw bars corresponding to the number of students who like each subject.
Q12. The following table shows the marks obtained by 10 students in a test:
| Marks | Number of Students |
|---|---|
| 10 | 1 |
| 20 | 2 |
| 30 | 3 |
| 40 | 4 |
Solution:
The mean marks can be calculated as:Mean=(10×1)+(20×2)+(30×3)+(40×4)1+2+3+4=10+40+90+16010=30010=30\text{Mean} = \frac{(10 \times 1) + (20 \times 2) + (30 \times 3) + (40 \times 4)}{1 + 2 + 3 + 4} = \frac{10 + 40 + 90 + 160}{10} = \frac{300}{10} = 30Mean=1+2+3+4(10×1)+(20×2)+(30×3)+(40×4)=1010+40+90+160=10300=30
Q13. A pie chart represents the number of vehicles in a parking lot. If 60% of vehicles are cars, 30% are motorcycles, and 10% are bicycles, how many bicycles are there in a parking lot with 200 vehicles?
Solution:
Bicycles = 10%×200=20 bicycles10\% \times 200 = 20 \text{ bicycles}10%×200=20 bicycles
Q14. In a class, 5 students scored 50, 6 scored 60, 4 scored 70, and 10 scored 80. Find the mode of the marks.
Solution:
The mode is the mark that appears most frequently. Here, the mode is 80 because it appears the most (10 times).
Q15. A bar graph shows the number of cups of tea consumed by 6 people in a day. If person A consumed 5 cups, person B consumed 3 cups, and person C consumed 4 cups, what is the average number of cups consumed?
Solution:
The average number of cups consumed is:5+3+43=123=4\frac{5 + 3 + 4}{3} = \frac{12}{3} = 435+3+4=312=4
Q15. A bar graph shows the number of cups of tea consumed by 6 people in a day. If person A consumed 5 cups, person B consumed 3 cups, and person C consumed 4 cups, what is the average number of cups consumed?
Solution:
To find the average number of cups consumed, we sum the total cups and divide by the number of people:Average=5+3+43=123=4\text{Average} = \frac{5 + 3 + 4}{3} = \frac{12}{3} = 4Average=35+3+4=312=4
Thus, the average number of cups consumed is 4.
Q16. Calculate the mean of the data: 12, 15, 20, 22, 18.
Solution:
To find the mean, we sum the numbers and divide by the number of values:Mean=12+15+20+22+185=875=17.4\text{Mean} = \frac{12 + 15 + 20 + 22 + 18}{5} = \frac{87}{5} = 17.4Mean=512+15+20+22+18=587=17.4
Thus, the mean is 17.4.
Q17. Draw a pie chart for the following data: Students, 40% like math, 35% like science, and 25% like history.
Solution:
- Total degrees in a circle = 360°.
- For Math: 40%×360°=144°40\% \times 360° = 144°40%×360°=144°
- For Science: 35%×360°=126°35\% \times 360° = 126°35%×360°=126°
- For History: 25%×360°=90°25\% \times 360° = 90°25%×360°=90°
You would draw a circle and divide it into sections with the corresponding angles of 144°, 126°, and 90° to represent the percentage of students liking each subject.
Q18. Find the median of the following numbers: 25, 30, 45, 50, 55.
Solution: The data is already in ascending order. The median is the middle value in the dataset. Here, the middle value is 45. Thus, the median is 45.
Q19. Calculate the mode of the following data: 12, 14, 16, 12, 18.
Solution: The mode is the number that appears most frequently.
Here, 12 appears twice, while the others appear once.
Thus, the mode is 12.
Q20. Draw a bar graph showing the number of hours spent on studying by 5 students.
Solution: Assume the data provided is:
| Student | Hours Spent on Studying |
|---|---|
| A | 3 |
| B | 5 |
| C | 2 |
| D | 6 |
| E | 4 |
To create the bar graph:
- Label the horizontal axis with student names and the vertical axis with hours.
- Draw bars for each student corresponding to the hours they spent studying.
Q21. Calculate the range of the following data: 12, 15, 22, 25, 30.
Solution: The range is the difference between the maximum and minimum values:Range=30−12=18\text{Range} = 30 – 12 = 18Range=30−12=18
Thus, the range is 18.
Q22. Find the mean of the following numbers: 50, 60, 70, 80, 90, 100.
Solution: The mean is calculated as:Mean=50+60+70+80+90+1006=4506=75\text{Mean} = \frac{50 + 60 + 70 + 80 + 90 + 100}{6} = \frac{450}{6} = 75Mean=650+60+70+80+90+100=6450=75
Thus, the mean is 75.
Q23. Calculate the percentage of students who passed in a test where 80 out of 100 students passed.
Solution: The percentage of students who passed is calculated by:Percentage=80100×100=80%\text{Percentage} = \frac{80}{100} \times 100 = 80\%Percentage=10080×100=80%
Thus, 80% of the students passed.
Q24. Draw a histogram for the data: 10-20, 20-30, 30-40, 40-50.
Solution: You would plot a histogram by dividing the horizontal axis into intervals (bins) representing the ranges (10-20, 20-30, 30-40, 40-50) and plot the frequency (number of data points) on the vertical axis. The bars would correspond to the frequency of data points in each range.
Q25. In a class of 50 students, 20 like English, 15 like Math, and 15 like Science. Represent this data using a pie chart.
Solution:
- The total number of students = 50.
- For English: 2050×360°=144°\frac{20}{50} \times 360° = 144°5020×360°=144°
- For Math: 1550×360°=108°\frac{15}{50} \times 360° = 108°5015×360°=108°
- For Science: 1550×360°=108°\frac{15}{50} \times 360° = 108°5015×360°=108°
Thus, the pie chart will have three sectors with angles of 144°, 108°, and 108°.
Q26. The following data shows the number of goals scored by 5 players in a match: 4, 2, 3, 5, 1. Find the median of the data.
Solution: Arrange the data in ascending order: 1, 2, 3, 4, 5.
The median is the middle value, which is 3.
Thus, the median is 3.
Q27. The following table shows the number of hours worked by employees in a week:
| Employee | Hours Worked |
|---|---|
| A | 40 |
| B | 45 |
| C | 35 |
| D | 50 |
Solution: To find the mean number of hours worked:Mean=40+45+35+504=1704=42.5\text{Mean} = \frac{40 + 45 + 35 + 50}{4} = \frac{170}{4} = 42.5Mean=440+45+35+50=4170=42.5
Thus, the mean number of hours worked is 42.5 hours.
Q28. A pie chart represents the number of vehicles in a parking lot. If 40% of vehicles are cars, 30% are motorcycles, and 30% are bicycles, how many motorcycles are there in a parking lot with 200 vehicles?
Solution: Motorcycles = 30%×200=6030\% \times 200 = 6030%×200=60 motorcycles.
Q29. Find the mean of the following numbers: 10, 20, 30, 40, 50.
Solution: The mean is:Mean=10+20+30+40+505=1505=30\text{Mean} = \frac{10 + 20 + 30 + 40 + 50}{5} = \frac{150}{5} = 30Mean=510+20+30+40+50=5150=30
Thus, the mean is 30.
Q30. Calculate the median of the following data: 25, 35, 40, 50, 60.
Solution: The data is already in ascending order, and the middle value is 40.
Thus, the median is 40.
Q31. In a class, 12 students scored 10 marks, 8 students scored 15 marks, and 5 students scored 20 marks. Find the mode of the data.
Solution: The mode is the value that occurs most frequently.
Here, 10 marks is the most frequent score, as 12 students scored 10 marks.
Thus, the mode is 10.
Q32. A survey is conducted to find out how many hours people work per week. The results are:
| Hours Worked | Number of People |
|---|---|
| 40 | 5 |
| 50 | 10 |
| 60 | 15 |
Solution: To find the mean:Mean=(40×5)+(50×10)+(60×15)5+10+15=200+500+90030=160030=53.33\text{Mean} = \frac{(40 \times 5) + (50 \times 10) + (60 \times 15)}{5 + 10 + 15} = \frac{200 + 500 + 900}{30} = \frac{1600}{30} = 53.33Mean=5+10+15(40×5)+(50×10)+(60×15)=30200+500+900=301600=53.33
Thus, the mean number of hours worked is 53.33 hours.
Q33. The following data shows the number of items sold by 5 salespeople: 30, 40, 50, 60, 70. Find the median of the data.
Solution: The data is already in ascending order, and the middle value is 50.
Thus, the median is 50.
Q34. A pie chart represents the number of different types of books in a library. If 50% of the books are fiction, 30% are non-fiction, and 20% are comics, how many comics are there in a library with 500 books?
Solution: Comics = 20%×500=10020\% \times 500 = 10020%×500=100 comics.
Q35. The scores of 10 students in a test are as follows:
| Scores | Number of Students |
|---|---|
| 50 | 2 |
| 60 | 3 |
| 70 | 5 |
Solution: To find the mean:Mean=(50×2)+(60×3)+(70×5)2+3+5=100+180+35010=63010=63\text{Mean} = \frac{(50 \times 2) + (60 \times 3) + (70 \times 5)}{2 + 3 + 5} = \frac{100 + 180 + 350}{10} = \frac{630}{10} = 63Mean=2+3+5(50×2)+(60×3)+(70×5)=10100+180+350=10630=63
Thus, the mean score is 63.
Q36. A survey was conducted on the number of pets owned by people in a neighborhood. The data is as follows:
| Number of Pets | Frequency |
|---|---|
| 0 | 5 |
| 1 | 8 |
| 2 | 4 |
| 3 | 3 |
Solution: To find the mode, we look for the frequency that occurs the most, which is 1 pet (with a frequency of 8).
Thus, the mode is 1.
Also Read: Class 8 Mathematics Chapter 7
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