Question 1
Samantha visited a tea garden, and collected data of the insects and critters she saw there. Here is the data she collected:
Solution:
Question 2
Pooja collected data on the number of tickets sold at the Bhopal railway station for a few different cities of Madhya Pradesh over a two-hour period.
| City | 📍 Vidisha | 📍 Jabalpur | 📍 Seoni | 📍 Indore | 📍 Sagar |
|---|---|---|---|---|---|
| 🎫 Tickets Sold | 24 | 20 | 16 | 28 | 16 |
She used this data and prepared a bar graph on the board to discuss the data with her students, but someone erased a portion of the graph.
a. Write the number of tickets sold for Vidisha above the bar.
b. Write the number of tickets sold for Jabalpur above the bar.
c. The bar for Vidisha is 6 unit lengths and the bar for Jabalpur is 5 unit lengths. What is the scale for this graph?
d. Draw the correct bar for Sagar.
e. Add the scale of the bar graph by placing the correct numbers on the vertical axis.
f. Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s).
Answers to Questions
a. The number to write above the Vidisha bar is 24.
b. The number to write above the Jabalpur bar is 20.
c. Scale: 1 unit length = 4 tickets(Calculation: 24 tickets ÷ 6 units = 4 tickets)
d. The bar for Sagar should be 4 units high (16 tickets ÷ 4 = 4 units).
e. The vertical axis numbers (from bottom to top) must go up by 4s: 0, 4, 8, 12, 16, 20, 24, 28.
f. No, the bar for Indore is incorrect (it is drawn too short). The bar for Seoni is correct.Indore should be 7 units high (28 tickets ÷ 4 = 7 units), making it the tallest bar.
Question 3 Text
Chinu listed the various means of transport that passed across the road in front of his house from 9 a.m. to 10 a.m.:Chinu's Transport Observations Data Grid
| Row | Column 1 | Column 2 | Column 3 | Column 4 | Column 5 | Column 6 |
|---|---|---|---|---|---|---|
| 1 | bike | car | bike | bus | bike | bike |
| 2 | bike | auto rickshaw | bicycle | bullock cart | bicycle | auto rickshaw |
| 3 | car | scooter | car | auto rickshaw | bicycle | bike |
| 4 | car | auto rickshaw | bike | scooter | bike | car |
| 5 | bicycle | scooter | bicycle | scooter | bike | bus |
| 6 | auto rickshaw | auto rickshaw | bike | bicycle | bus | bike |
| 7 | bicycle | scooter | bus | scooter | auto rickshaw | bike |
| 8 | scooter | bicycle | bike | bullock cart | auto rickshaw | scooter |
| 9 | car | scooter |
a. Prepare a frequency distribution table for the data.
b. Which means of transport was used the most?
c. If you were there to collect this data, how could you do it? Write the steps or process.
Solutions
a. Frequency Distribution Table
| Means of Transport | Tally Marks | Frequency (Count) |
|---|---|---|
| 🏍️ Bike | 卌 卌 ||| | 13 |
| 🚗 Car | 卌| | 6 |
| 🚌 Bus | |||| | 4 |
| 🛺 Auto Rickshaw | 卌||| | 8 |
| 🚲 Bicycle | 卌||| | 8 |
| 🐂 Bullock Cart | || | 2 |
| 🛵 Scooter | 卌 |||| | 9 |
| Total | 50 |
b. Most Used Transport
- Answer: Bike was used the most, with a maximum frequency of 13.
c. Data Collection Process (Steps)
- Preparation: Draw a blank table on a sheet of paper with two columns: "Means of Transport" and "Tally Marks".
- Observation: Stand safely near the side of the road facing traffic during the given hour (9 a.m. to 10 a.m.).
- Recording (Real-time): Every single time a vehicle passes, immediately put a vertical tally stroke (
|) next to that vehicle's category. - Grouping: For every 5th vehicle of the same type, draw a diagonal line across the previous 4 strokes (
卌) to make counting easier later. - Final Sum: Once the hour finishes, count up the total tally lines for each category to get the frequencies.
Question 4 Text
Roll a die 30 times and record the number you obtain each time. Prepare a frequency distribution table using tally marks. Find the number that appeared:a. The minimum number of times.
b. The maximum number of times.
c. Find numbers that appeared an equal number of times.
Simulated Dice Roll Data (30 Rolls)
Frequency Distribution Table
| Number on Die | Tally Marks | Frequency (Count) |
|---|---|---|
| ⚀ 1 | |||| | 4 |
| ⚁ 2 | 卌 | | 6 |
| ⚂ 3 | 卌 | 5 |
| ⚃ 4 | |||| | 4 |
| ⚄ 5 | 卌 || | 7 |
| ⚅ 6 | |||| | 4 |
| Total | 30 |
Solutions to Sub-Questions
- a. Minimum number of times: The numbers 1, 4, and 6 appeared the least (only 4 times each).
- b. Maximum number of times: The number 5 appeared the most (7 times).
- c. Numbers with equal frequency: The numbers 1, 4, and 6 appeared an equal number of times (4 times each).
Question 5.
Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches:
| Wickets Taken | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 🏏No of Matches | 2 | 4 | 6 | 8 | 3 | 5 | 1 | 1 |
\(\text{Total Wickets}=0+4+12+24+12+25+6+7=\mathbf{90}\text{ wickets}\)
Question 6
The following pictograph shows the number of tractors in five different villages.
Key: 🚜 = 1 Tractor
| Villages | Number of Tractors |
|---|---|
| Village A | 🚜 🚜 🚜 🚜 🚜 🚜 🚜 🚜 |
| Village B | 🚜 🚜 🚜 🚜 🚜 🚜 |
| Village C | 🚜 🚜 🚜 🚜 🚜 🚜 🚜 🚜 🚜 |
| Village D | 🚜 🚜 🚜 |
| Village E | 🚜 🚜 🚜 🚜 🚜 🚜 |
Observe the pictograph and answer the following questions:
Step 1: Count the tractors
| Village | Number of Tractors |
|---|---|
| A | 8 |
| B | 6 |
| C | 9 |
| D | 3 |
| E | 6 |
(a) Which village has the smallest number of tractors?
Village D has 3 tractors, which is the smallest number.
Answer: Village D
(b) Which village has the most tractors?
Village C has 9 tractors, which is the greatest number.
Answer: Village C
(c) How many more tractors does Village C have than Village B?
Village C = 9 tractors
Village B = 6 tractors
\[9 - 6 = 3\]
Answer: 3 tractors
(d) Komal says, “Village D has half the number of tractors as Village E.” Is she right?
Village D = 3 tractors
Village E = 6 tractors
Half of 6 is: \[6 \div 2 = 3 \]
So, Village D has exactly half the number of tractors as Village E.
Answer: Yes, Komal is right.
Question 7
The number of girl students in each class of a school is depicted by the pictograph.
Key: 👧 = 4 girls
| Class | Pictograph | Number of Girls |
|---|---|---|
| 1 | 👧👧👧👧👧 | 20 |
| 2 | 👧👧👧👧  | 18 |
| 3 | 👧👧👧👧 | 16 |
| 4 | 👧👧👧 | 14 |
| 5 | 👧👧 | 10 |
| 6 | 👧👧👧👧 | 16 |
| 7 | 👧👧👧 | 12 |
| 8 | 👧 | 6 |
(½👧 = 2 girls)
Observe the pictograph and answer the following questions:
(a) Which class has the least number of girl students?
Class 8 has 6 girls, which is the least.Answer: Class 8
(b) What is the difference between the number of girls in Class 5 and Class 6?
Class 5 = 10 girlsClass 6 = 16 girls
\[16 - 10 = 6\]
Answer: 6 girls
(c) If two more girls were admitted in Class 2, how would the graph change?
Class 2 currently has:\[18 \text{ girls}\]
After admitting 2 more girls:
\[18 + 2 = 20\]
Since one full 👧 represents 4 girls, 20 girls would be shown by:
👧👧👧👧👧
Answer: The half symbol in Class 2 would become a full 👧, making 5 full girl symbols.
(d) How many girls are there in Class 7?
Class 7 has 3 full symbols.\[3 \times 4 = 12\]
Answer: 12 girls
Question 8
Mudhol Hounds (a type of breed of Indian dogs) are largely found in North Karnataka's Bagalkote and Vijayapura districts. The Government took an initiative to support those who adopted these dogs. Due to this initiative, the number of these dogs increased.
The number of Mudhol dogs in six villages of Karnataka are as follows:
- Village A = 18
- Village B = 36
- Village C = 12
- Village D = 48
- Village E = 18
- Village F = 24
Prepare a pictograph and answer the following questions:
(a) Useful Scale (Key)
Since all numbers are multiples of 6, a convenient key is:
🐕 = 6 dogs
Pictograph
| Village | Number of Dogs | Pictograph |
|---|---|---|
| A | 18 | 🐕 🐕 🐕 |
| B | 36 | 🐕 🐕 🐕 🐕 🐕 🐕 |
| C | 12 | 🐕 🐕 |
| D | 48 | 🐕 🐕 🐕 🐕 🐕 🐕 🐕 🐕 |
| E | 18 | 🐕 🐕 🐕 |
| F | 24 | 🐕 🐕 🐕 🐕 |
Key: 🐕 = 6 dogs
(b) How many symbols will you use for Village B?
Village B has 36 dogs.
\[36 \div 6 = 6\]
Answer: 6 symbols
(c) Is Kamini right?
Dogs in Village B and D:
\[36 + 48 = 84\]
Dogs in the other four villages:
\[18 + 12 + 18 + 24 = 72\]
Since
\[84 > 72\]
Kamini is correct.
Answer: Yes, Kamini is right because Village B and D together have 84 dogs, which is more than the 72 dogs in the other four villages.
Question 9
A survey of 120 school students was conducted to find out which activity they preferred to do in their free time.
| Preferred Activity | Number of Students |
|---|---|
| Playing | 45 |
| Reading story books | 30 |
| Watching TV | 20 |
| Listening to music | 10 |
| Painting | 15 |
Draw a bar graph to illustrate the above data taking the scale of 1 unit length = 5 students. Which activity is preferred by most students other than playing?
Solution
Scale
1 unit length = 5 students
Bar Graph Data
| Activity | Students | Height of Bar (Units) |
|---|---|---|
| Playing | 45 | 9 |
| Reading story books | 30 | 6 |
| Watching TV | 20 | 4 |
| Listening to music | 10 | 2 |
| Painting | 15 | 3 |
Rough Bar Graph
Number of Students
45 | █
40 | █
35 | █
30 | █ █
25 | █ █
20 | █ █ █
15 | █ █ █ █
10 | █ █ █ █ █
5 | █ █ █ █ █
--------------------------------
P R W L Pa
P = Playing
R = Reading Story Books
W = Watching TV
L = Listening to Music
Pa = Painting
Which activity is preferred by most students other than playing?
Playing = 45 studentsReading story books = 30 students
Watching TV = 20 students
Painting = 15 students
Listening to music = 10 students
Answer: Reading story books is preferred by the most students other than playing (30 students). ✅
Question 10
Students and teachers of a primary school decided to plant tree saplings in the school campus and in the surrounding village during the first week of July. The number of saplings planted on different days is shown in the bar graph.
(a) The total number of saplings planted on Wednesday and Thursday is ________.
Solution:
Wednesday = 30 saplings
Thursday = 40 saplings
Total = 30 + 40 = 70 saplings
Answer: 70 saplings
(b) The total number of saplings planted during the whole week is ________.
Solution:
Total saplings planted
= 50 + 40 + 30 + 40 + 50 + 60 + 40
= 310 saplings
Answer: 310 saplings
(c) The greatest number of saplings were planted on ________ and the least number were planted on ________.
Solution:
Greatest number = 60 saplings on Saturday
Least number = 30 saplings on Wednesday
Answer:
Greatest number: Saturday
Least number: Wednesday
Possible reason: More people may have been available on Saturday because it is usually a holiday, so more saplings were planted. Fewer people may have been available on Wednesday, resulting in fewer saplings being planted.
Question 11
The number of tigers in India went down drastically between 1900 and 1970. Project Tiger was launched in 1973 to track and protect the tigers in India. Starting in 2006, the exact number of tigers in India was tracked. Shagufta and Divya collected information about the number of tigers in India between 2006 and 2022 at four-year intervals. They prepared a frequency table and a bar graph to present the data, but there are a few mistakes in the graph.
| Year | Number of Tigers (Approx.) |
|---|---|
| 2006 | 1400 |
| 2010 | 1700 |
| 2014 | 2200 |
| 2018 | 3000 |
| 2022 | 3700 |
Find the mistakes in the graph and correct them.
Answer
Mistakes in the Given Graph
The years on the vertical axis are not arranged in chronological order.
The bars do not represent the correct tiger population values.
The bar lengths are not proportional to the numbers given in the table.
Correct Data for the Bar Graph
| Year | Number of Tigers |
|---|---|
| 2006 | 1400 |
| 2010 | 1700 |
| 2014 | 2200 |
| 2018 | 3000 |
| 2022 | 3700 |
Correct Horizontal Bar Graph
Conclusion: The tiger population increased steadily from 1400 in 2006 to 3700 in 2022.
Number of Tigers in India (2006–2022)
Correct bar graph based on the given data.
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