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13
NCERT Solutions · Maths Ch 13
Connecting The Dots
25 questions · 4 exercises
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Ex 13.1
Ex 13.2
Ex 13.3
Ex 13.4
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 13.1 · 5 QUESTIONS
Mean
Q1
Shreyas bounces a ball on a bat and counts how many times it bounces before it falls. The data for 8 attempts is 6, 2, 9, 5, 4, 6, 3, 5. Calculate the average number of bounces.
(2 marks)
Q2
Try the bat-and-ball activity on your own. Collect data for 7 or more attempts and find the average.
(3 marks)
Q3
Identify a flowering plant in your neighbourhood. Track the number of flowers that bloom every day over a week during its flowering season. What is the average number of flowers that bloomed per day?
(3 marks)
Q4
Two friends are training to run a 100 m race. Their running times over the past week are given in seconds — Nikhil: 17, 18, 17, 16, 19, 17, 18; Sunil: 20, 18, 18, 17, 16, 16, 17. Who on average ran quicker?
(3 marks)
Q5
The enrolment in a school during six consecutive years was as follows: 1555, 1670, 1750, 2013, 2040, 2126. Find the mean enrolment in the school during this period.
(3 marks)
2
EXERCISE 13.2 · 8 QUESTIONS
Mean, Median and Dot Plots
Q6
The table shows the monthly price of onions (₹/kg) at two towns. Yahapur: Jan 25, Feb 24, Mar 26, Apr 28, May 30, Jun 35, Jul 39, Aug 43, Sep 49, Oct 56, Nov 59, Dec 44. Wahapur: Jan 19, Feb 17, Mar 23, Apr 30, May 38, Jun 35, Jul 42, Aug 39, Sep 53, Oct 60, Nov 52, Dec 42. Where are onions costlier, according to you?
(3 marks)
Q7
Find the median of onion prices in Yahapur and Wahapur.
(3 marks)
Q8
Sanskruti asked her class how many domestic animals and pets each had at home. Some students were absent. The data values are 0, 1, 0, 4, 8, 0, 0, 2, 1, 1, 5, 3, 4, 0, 0, —, 10, 25, 2, —, 2, 4. Find the mean and median. How would you describe this data?
(3 marks)
Q9
Rintu takes care of a date-palm tree farm in Habra. The heights of the trees (in feet) are: 50, 45, 43, 52, 61, 63, 46, 55, 60, 55, 59, 56, 56, 49, 54, 65, 66, 51, 44, 58, 60, 54, 52, 57, 61, 62, 60, 60, 67. Fill the dot plot, and mark the mean and median. How would you describe the heights? How many trees are shorter than the average height?
(3 marks)
Q10
The daily water usage from a tap in litres for the first few days is 5.6, 8, 3.09, 12.9, 6.5, 12.1, 11.3, 20.5, 7.4. (a) Can the mean or median daily usage lie between 25 and 30? Justify. (b) Can the mean or median be lesser than the minimum value or greater than the maximum value in a data?
(3 marks)
Q11
The weights of a few newborn babies are given in kg. Boys: 3.5, 4.1, 2.6, 3.2, 3.4, 3.8. Girls: 4.0, 3.1, 3.4, 3.7, 2.5, 3.4. Fill the dot plot provided. Analyse and compare this data.
(5 marks)
Q12
The dot plots of heights of another section of Grade 5 students are shown. Whole class: Mean = 141.21, Median = 142.5. Boys: Mean = 142.05, Median = 143. Girls: Mean = 140.14, Median = 140. Compare the heights of the two sections and share your observations.
(3 marks)
Q13
The weights of some sumo wrestlers and ballet dancers are: Sumo wrestlers: 295.2 kg, 250.7 kg, 234.1 kg, 221.0 kg, 200.9 kg. Ballet dancers: 40.3 kg, 37.6 kg, 38.8 kg, 45.5 kg, 44.1 kg, 48.2 kg. Approximately how many times heavier is a sumo wrestler compared to a ballet dancer?
(3 marks)
3
EXERCISE 13.3 · 4 QUESTIONS
Bar Graphs
Q14
The infographic shows the maximum speeds of a few animals. Air: peregrine falcon 322 kph, spine-tailed swift 170, free-tailed bat 96, green darner dragonfly 64, flying fish 56. Land: cheetah 103, pronghorn antelope 88, ostrich 64, human 37, Australian tiger beetle 8. Water: sailfish 109, dolphin 40, California sea lion 40, Gentoo penguin 35, humpback whale 26. (a) What is the scale used? (b) Identify a pair where one's speed is about twice the other's. (c) Can we say a sailfish is about 4 times faster than a humpback whale? Can we say a sailfish is the fastest aquatic animal in the world? (Can we call this graph a bar graph?)
(3 marks)
Q15
Preyashi asked her students: 'If you were to get a super power to become aquatic (w), aerial (a), or spaceborne (s) which one would you choose?' Some chose none (n). Grade 5: w, a, a, a, w, n, s, a, n, w, a, a, a, a, a, w, w, s, a, a, n, w, a, a, n. Grade 9: n, w, s, a, s, w, s, s, a, a, w, s, s, a, s, a, n, w, s, s, a, w, a, w, a. Draw a double-bar graph comparing how both grades chose each option. Choose an appropriate scale.
(3 marks)
Q16
The temperature variation over two days in Jodhpur is given. 12 am, 3 am, 6 am, 9 am, 12 pm, 3 pm, 6 pm, 9 pm: Day 1: 20, 18, 16, 20, 26, 34, 30, 24 (°C); Day 2: 37, 34, 30, 33, 37, 43, 42, 39 (°C). Draw a double-bar graph. Use the scale 1 unit = 4°C. Can you guess which two months these days might belong to?
(3 marks)
Q17
The clustered-bar graph shows the number of electric vehicles registered in some states every year from 2022 to 2024. (a) Gujarat 2022: 69000, 2023: 89000, 2024: 78000; Delhi 2022: 62000, 2023: 74000, 2024: 81000 — mark the bars. (b) What scale is used? (c) Describe the change between 2022 and 2024. (d) Approximately how many more registrations did Assam get in 2023 than in 2022? (e) How many times more did West Bengal increase from 2022 to 2024? (f) Is this correct — 'There were very few new registrations in Uttarakhand in 2023 and 2024, as the increase in the bar lengths is minimal'?
(3 marks)
4
EXERCISE 13.4 · 8 QUESTIONS
End of Chapter
Q18
The dot plots show the number of pockets on clothing for a group of boys and a group of girls. Boys: 3 pockets – 1 dot; 4 – 4 dots; 5 – 5 dots; 6 – 2 dots. Girls: 0 – 1 dot; 2 – 1; 3 – 4; 4 – 5; 5 – 1; 6 – 1. Which statements are true? (a) The data varies more for the boys than for the girls. (b) The median number of pockets for the boys is more than that for the girls. (c) The mean number of pockets for the girls is more than that for the boys. (d) The maximum number of pockets for boys is greater than that for the girls.
(5 marks)
Q19
The table shows the points scored by each player in four games. A: 14, 16, 10, 10; B: 0, 8, 6, 4; C: 8, 11, Did not play, 13. (a) Find the average number of points scored per game by A. (b) To find the mean number of points scored per game by C, would you divide the total points by 3 or by 4? Why? What about B? (c) Who is the best performer?
(3 marks)
Q20
The marks (out of 100) in a General Knowledge quiz are 85, 76, 90, 85, 39, 48, 56, 95, 81 and 75 for one group and 68, 59, 73, 86, 47, 79, 90, 93, 86 for another. Compare and describe both groups' performance using mean and median.
(5 marks)
Q21
Survey of a colony: Cricket, Basket Ball, Swimming, Hockey, Athletics — Watching: 1240, 470, 510, 430, 250; Participating: 620, 320, 320, 250, 105. Choose an appropriate scale and draw a double-bar graph. Write down your observations.
(3 marks)
Q22
A group of 17 students has the following heights (cm): 106, 110, 123, 125, 117, 120, 112, 115, 110, 120, 115, 102, 115, 115, 109, 115, 101. The sports teacher wants to divide the class into two groups with an equal number of students: one group with heights less than a particular height, the other with heights greater than it. Suggest a way. Can you guess the age of these students based on the table in 'Telling Tall Tales'?
(3 marks)
Q23
There are two 7th grade sections at a school. Each section has 15 boys and 15 girls. In one section, the mean height of students is 154.2 cm. From this information, what must be true about the mean height in the other section? (a) It is 154.2 cm. (b) It is less than 154.2 cm. (c) It is more than 154.2 cm. (d) It cannot be determined.
(2 marks)
Q24
Standing tall in the storm (cities with most skyscrapers — buildings taller than 150 m). The bar graph lists: Hong Kong 553, Shenzhen 367, New York, Dubai 251, Guangzhou 188, Shanghai 183, Tokyo, Kuala Lumpur 154, Chongqing 144, Jakarta 112, Bangkok 110, Singapore 95, Mumbai 86, Seoul 82, Toronto 81, Melbourne 69, Miami 58, Istanbul 48, Moscow 46, London. (a) Write estimated values for New York, Tokyo and London. (b) Are the statements valid? (i) Only 12 cities have more skyscrapers than Mumbai. (ii) Only 7 cities have fewer skyscrapers than Mumbai. (iii) The tallest building in the world is in Hong Kong.
(3 marks)
Q25
Aditi's times (in seconds) to solve Sudoku puzzles are 410, 400, 370, 340, 360, 400, 320, 330, 310, 320, 290, 380, 280, 270, 230, 220, 240. The first nine values are Week 1 and the rest Week 2. (a) Construct a dot plot showing the data for both weeks. (b) Describe the mean, median, and any observations.
(5 marks)