Class 7 Mathematics

Chapter 13 Solutions — Connecting the Dots

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Solutions

Overview

Step-by-step NCERT solutions for Connecting the Dots (Chapter 13, NCERT Class 7 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Connecting the Dots textbook chapter.

Solved

What these solutions cover

All 24 questions in Connecting the Dots are solved in the PDF. Here's what's inside, exercise by exercise:

Representative Values — Mean

Shreyas counts the number of times he can bounce a ball on a bat before it falls. Data for 8 attempts: 6, 2, 9, 5, 4, 6, 3, 5. Calculate the average number of bounces.
Two friends train for a 100 m race. Running times (in seconds) over the past week: Nikhil — 17, 18, 17, 16, 19, 17, 18; Sunil — 20, 18, 18, 17, 16, 16, 17. Who on average ran quicker?
The enrolment in a school during six consecutive years was: 1555, 1670, 1750, 2013, 2040, 2126. Find the mean enrolment during this period.

Outliers and Medians

Find the median of onion prices in Yahapur and Wahapur. Yahapur (₹/kg): 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 (₹/kg): Jan 19, Feb 17, Mar 23, Apr 30, May 38, Jun 35, Jul 42, Aug 39, Sep 53, Oct 60, Nov 52, Dec 42.
Sanskruti asked her class how many domestic animals and pets each student had at home. Some students were absent (shown as —). Data: 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?
Rintu's date-palm tree farm heights (in feet): 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. Find the mean and median. How many trees are shorter than the average height?
4.
Daily water usage from a tap (in litres): 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 less than the minimum or greater than the maximum value in data?
Weights of a few newborn babies (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 Analyse and compare this data.
The dot plots of heights (cm) of another section of Grade 5 students are given with: Whole class — Mean = 141.21, Median = 142.5; Boys — Mean = 142.05, Median = 143; Girls — Mean = 140.14, Median = 140. Compare with the first section (Whole class mean = 144.4, Boys mean = 142.94, Girls mean = 146.9). Share your observations.
Weights of sumo wrestlers: 295.2 kg, 250.7 kg, 234.1 kg, 221.0 kg, 200.9 kg. Weights of 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?

Visualising Data — Clustered Bar Graphs

An infographic shows maximum speeds of animals in air, on land, and in water (scale: 1 unit = 16 kph). Speeds visible: Peregrine falcon 322 kph (air), Spine-tailed swift 170 kph (air), Free-tailed bat 96 kph (air), Green darner dragonfly 64 kph (air), Flying fish 56 kph (air); Cheetah 103 kph (land), Pronghorn antelope 88 kph (land), Ostrich 64 kph (land), Human 37 kph (land), Australian tiger…
Preyashi asked students about preferred superpowers: aquatic (w), aerial (a), spaceborne (s), or 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 both grades. Choose an appropriate scale.
Temperature variation in Jodhpur over two days (°C): Time: 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 Day 2: 37, 34, 30, 33, 37, 43, 42, 39 Draw a double-bar graph using scale 1 unit = 4°C. Can you guess which two months these days might belong to?
4.
A clustered bar graph shows electric vehicles (EV) registered per year (2022–2024) in several states. Gujarat and Delhi data (in thousands): Gujarat — 2022: 69, 2023: 89, 2024: 78; Delhi — 2022: 62, 2023: 74, 2024: 81.
- (a) Mark the bars for Gujarat and Delhi on the graph.
- (b) Describe the scale and patterns.
- (c) How would you describe changes for various states between 2022 and 2024? (d)…

Data Detective

1.
The dot plots below show the distribution of the number of pockets on clothing for a group of boys and a group of girls. Based on the dot plots, which of the following 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…
2.
Points scored by players across four games: A: 14, 16, 10, 10; B: 0, 8, 6, 4; C: 8, 11, Did not play, 13
- (a) Find the average points per game by A.
- (b) To find mean for C, divide by 3 or 4? What about B?
- (c) Who is the best performer?
Group 1 General Knowledge quiz marks (out of 100): 85, 76, 90, 85, 39, 48, 56, 95, 81, 75. Group 2: 68, 59, 73, 86, 47, 79, 90, 93, 86. Compare both groups using mean and median.
Colony survey data on favourite sport: Sport | Cricket | Basketball | 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 observations.
A group of 17 students has heights (in cm): 106, 110, 123, 125, 117, 120, 112, 115, 110, 120, 115, 102, 115, 115, 109, 115, 101. The sports teacher wants to divide them into two equal groups — one with heights below a certain value, the other with heights above it. Suggest a way.
Describe the mean and median heights of your class. Visualise heights on a dot plot.
7.
Two 7th grade sections each have 15 boys and 15 girls. In one section, the mean height is 154.2 cm. From this, what must be true about the mean height of students in the other section?
- (a) Mean of the other section is 154.2 cm.
- (b) Mean of the other section is less than 154.2 cm.
- (c) Mean of the other section is more than 154.2 cm.
- (d) The mean of the other section cannot be determined.
An infographic 'Cities with Most Skyscrapers (buildings taller than 150 m)' shows: Hong Kong 553, Shenzhen 367, New York ≈290, Dubai 251, Guangzhou 188, Shanghai 183, Tokyo ≈170, 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 ≈35. (a) Write estimated values for New York, Tokyo, and…
Estimate and then measure five objects (length of a pen, eraser, palm, geometry box, math notebook) in cm. Draw a double-bar graph (Estimate vs Measure). Find the average difference between estimated and measured values.
10.
Aditi's 'Easy' Sudoku solving times (in seconds): 410, 400, 370, 340, 360, 400, 320, 330, 310 (Week 1) and 320, 290, 380, 280, 270, 230, 220, 240 (Week 2).
- (a) Construct a dot plot for both weeks.
- (b) Describe the mean, median, and observations.

Sample

Worked examples

3 questions from Connecting the Dots, solved step by step.

Representative Values — Mean

Two friends train for a 100 m race. Running times (in seconds) over the past week: Nikhil — 17, 18, 17, 16, 19, 17, 18; Sunil — 20, 18, 18, 17, 16, 16, 17. Who on average ran quicker?

Lower running time means faster speed.

Nikhil's total = 17 + 18 + 17 + 16 + 19 + 17 + 18 = 122

Nikhil's mean time = 122 ÷ 7 ≈ 17.43 seconds

Sunil's total = 20 + 18 + 18 + 17 + 16 + 16 + 17 = 122

Sunil's mean time = 122 ÷ 7 ≈ 17.43 seconds

Both have the same total (122) and the same number of attempts (7), so their average times are equal.

Answer: Both Nikhil and Sunil ran equally quickly on average — their mean time is 122/7 ≈ 17.43 seconds each.

Outliers and Medians

Find the median of onion prices in Yahapur and Wahapur. Yahapur (₹/kg): 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 (₹/kg): Jan 19, Feb 17, Mar 23, Apr 30, May 38, Jun 35, Jul 42, Aug 39, Sep 53, Oct 60, Nov 52, Dec 42.

For median with 12 values, take the average of the 6th and 7th values in sorted order.

Yahapur sorted: 24, 25, 26, 28, 30, 35, 39, 43, 44, 49, 56, 59

6th value = 35, 7th value = 39

Median (Yahapur) = (35 + 39) ÷ 2 = 74 ÷ 2 = 37

Wahapur sorted: 17, 19, 23, 30, 35, 38, 39, 42, 42, 52, 53, 60

6th value = 38, 7th value = 39

Median (Wahapur) = (38 + 39) ÷ 2 = 77 ÷ 2 = 38.5

Answer: Median price in Yahapur = ₹37/kg; Median price in Wahapur = ₹38.5/kg.

Data Detective

Group 1 General Knowledge quiz marks (out of 100): 85, 76, 90, 85, 39, 48, 56, 95, 81, 75. Group 2: 68, 59, 73, 86, 47, 79, 90, 93, 86. Compare both groups using mean and median.

Group 1 (n = 10):

Sum = 85+76+90+85+39+48+56+95+81+75 = 730

Mean = 730 ÷ 10 = 73

Sorted: 39, 48, 56, 75, 76, 81, 85, 85, 90, 95

Median = (76 + 81) ÷ 2 = 78.5

Group 2 (n = 9):

Sum = 68+59+73+86+47+79+90+93+86 = 681

Mean = 681 ÷ 9 ≈ 75.67

Sorted: 47, 59, 68, 73, 79, 86, 86, 90, 93

Median (5th value) = 79

Comparison:

Group 2 has a higher mean (75.67 > 73) and higher median (79 > 78.5).

Group 1 has a very low score (39) pulling its mean down — 39 is an outlier.

Group 1's mean (73) < median (78.5) confirms the low outlier's effect.

Group 2's scores are more consistent — no extreme outliers.

Overall, Group 2 performed slightly better.

Answer: Group 1: mean = 73, median = 78.5. Group 2: mean ≈ 75.67, median = 79. Group 2 performed slightly better on both measures. Group 1 has an outlier (39) that lowers its mean below its median.

All 24 questions in Connecting the Dots are solved step by step in the Solutions PDF above.

Keep solving

Chapter 13 Solutions — Connecting the Dots

Overview

What these solutions cover

Representative Values — Mean

Outliers and Medians

Visualising Data — Clustered Bar Graphs

Data Detective

Worked examples

Two friends train for a 100 m race. Running times (in seconds) over the past week: Nikhil — 17, 18, 17, 16, 19, 17, 18; Sunil — 20, 18, 18, 17, 16, 16, 17. Who on average ran quicker?

Find the median of onion prices in Yahapur and Wahapur. Yahapur (₹/kg): 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 (₹/kg): Jan 19, Feb 17, Mar 23, Apr 30, May 38, Jun 35, Jul 42, Aug 39, Sep 53, Oct 60, Nov 52, Dec 42.

Group 1 General Knowledge quiz marks (out of 100): 85, 76, 90, 85, 39, 48, 56, 95, 81, 75. Group 2: 68, 59, 73, 86, 47, 79, 90, 93, 86. Compare both groups using mean and median.

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