NCERT Solutions for Class 7 Maths Chapter 13 Connecting the Dots… (PDF) – 2027

Statistical questions: (a), (b), (c), (f) and (g). Not statistical: (d) and (e). A statistical question is answered by collecting data that varies.

Yashasvi performed better in this series. Both played 4 matches, so the totals can be compared: Yashasvi scored 175 runs, Shubman 128. Yashasvi was also more consistent (18 to 67), while Shubman swung from 0 to 90.

Yashasvi performed better — he averaged more runs per match, even though Shubman’s total is larger.

Her arithmetic is right, but her conclusion is not safe. The two totals are not comparable, because they come from different numbers of matches.

Yes — one number can represent a group, but it can never replace it.

• The total is one such number, and it works when the groups are the same size.
• The mean (average) works even when the groups differ in size, because it balances the highs and the lows: Shubman 22, Yashasvi 24.
• The highest score and the range are also single numbers, but each tells only one thing.

Each member of Shreyas’s group gets more — 6 guavas each, against 5 each in Parag’s group.

5 flowers per day.

5 bounces per attempt.

Record at least 7 attempts, add the counts and divide the total by the number of attempts.

Sample answer: suppose your 8 attempts give 3, 5, 1, 7, 4, 6, 4, 2.

Count the flowers on one plant at the same time each day for 7 days (write 0 on a day with none), add the counts and divide by 7.

Sample answer: a hibiscus plant gives 4, 6, 0, 3, 5, 7, 3 flowers over one week.

Neither. Their averages are exactly the same — about 17.43 seconds each.

Mean enrolment = 1859 students.

On the whole, onions are slightly costlier in Yahapur — its total (₹458 against ₹450), its average (≈ ₹38.17 against ₹37.50) and its number of dearer months (6 against 5) are higher. But the two towns are very close: Wahapur has the higher median and the single highest price.

Yes. Some other ways:

• Compare the medians (₹37 and ₹38.50).
• Compare the prices month by month.
• Count the months above ₹50 (Yahapur 2, Wahapur 3).
• Group the prices into bands (₹11–20, ₹21–30, …) and count — as a dot plot does.
• Compare the two halves of the year (Jan–Jun and Jul–Dec).

No. The dot plot keeps every price, but it throws away every month.

No, we cannot. The dot plot shows that Yahapur had a price of ₹25 at some point in the year, but nothing on it says when.

Yahapur ≈ ₹38.17 per kg; Wahapur = ₹37.50 per kg.

Why are onions cheapest in February and dearest in October–November in both towns? Do the seasons and the new crop decide the price? Why are Wahapur’s prices more spread out than Yahapur’s?

Averages: Yaangba’s family ≈ 164.3 cm, Poovizhi’s family = 160.2 cm. But we cannot safely say Yaangba’s family is taller: four of Poovizhi’s five members are taller than 164 cm, and their average is pulled down by one very short child (118 cm).

Yes — sort the data and take the middle value. That number is called the Median.

Yes, for Poovizhi’s family. Its median (170 cm) is close to most members’ heights, while its mean (160.2 cm) is lower than 4 of the 5 heights because of the outlier 118 cm. For Yaangba’s family (no outlier) the mean and median are almost equal, so either works.

Without the outlier the mean jumps by more than 10 cm, while the median barely moves.

Guess: the mean will be greater than the median, because one student read 40 stories — far more than everyone else.

The number line runs from 0 to 40. Place one dot for each value, stacking repeats. Then draw a solid line at the mean 8.13 and a dashed line at the median 6.

40 is the outlier.

Removing 40 pulls the mean down by more than 2 stories; the median drops by only half a story.

Different. The number of pages changes from day to day. For the newspaper in the book it is 16, 18, 20, 22, 26, 16, 10 from Monday to Sunday — most on Friday (26) and fewest on Sunday (10).

The number line runs from 0 to 25 and a little beyond. Place the seven dots, stacking the two 16s, then draw the mean at 18.29 and the median at 18.

Each of the three examples illustrates exactly one of the three cases.

With outliers on both sides the two pulls work against each other. The median hardly changes; the mean moves towards the outlier that is farther from the middle, and stays near the median if the two outliers balance.

the class is about 145 cm tall on average (mean 144.5 cm, median 145 cm), and every student is between 128 cm and 158 cm. Boys: mean ≈ 142.94 cm, median 144 cm; girls: mean ≈ 146.9 cm, median 148 cm.

Four things can be said, and the book states them all.

• The boys’ heights are more spread out, from 128 to 158 cm. The girls lie in a narrower band, 136 to 156 cm.
• Both the tallest and the shortest student in the class are boys.
• Yet the boys’ mean is below the class mean and below the girls’ mean. In this class the girls are taller on average.
• For both groups mean < median (142.94 < 144 and 146.9 < 148), which shows a small pull from values on the lower side.

15 students out of 28 are taller than the class average of 144.5 cm.

8 boys are taller than 144.5 cm.

Both groups did well — most children opened their eyes between about 55 and 65 seconds. Group B was slightly better as a whole: its mean (59.28 s) is closer to 60 s and almost equal to its median (59.5 s). Group A’s median is exactly 60 s, but a few very early openers (as early as 42 s) pull its mean down to 58.21 s. Group A’s dots spread from 42 s to 68 s, Group B’s from 47 s to 71 s.

Yes, it can. The median only depends on the middle value of the sorted scores, so it says nothing about the total.

Yahapur: ₹37. Wahapur: ₹38.50.

Mean = 3.6 animals; Median = 2 animals. The two dashes are absent students, so they are left out: 20 values.

Description: most students have 0 to 2 animals; 25 is an outlier, so the mean is pulled above the median. The median (2) describes a typical home better.

Mean ≈ 55.9 feet, Median = 56 feet; 13 trees are shorter than the average.

Description: heights from 43 to 67 ft, mostly in the 50s and low 60s; no outlier, and mean ≈ median. Quicker way: add the differences from 55 ft (total +26), so mean = 55 + 26 ÷ 29 ≈ 55.9 ft.

(a) No. The largest reading is only 20.5 litres. The mean is a fair share of the total, so it cannot be more than the largest value; the median is a middle value of the sorted data, so it also lies between 3.09 and 20.5. (Here the mean ≈ 9.71 L and the median = 8 L.)

(b) No. The mean and the median always lie between the minimum and the maximum of the data (they can equal them, but never go outside).

Dot plot of the twelve weights (drawn here from 2 to 4.5 kg):

Comparison: the two groups are very alike — the same range (1.5 kg), and means and medians that differ by less than 0.1 kg. These boys and girls weighed about the same at birth, roughly 3.4 kg.

• Girls’ heights are more spread out (about 126 to 158 cm) than boys’ (about 130 to 148 cm), so the tallest and the shortest students are both girls.
• Most boys are bunched at 142–146 cm, so the boys are taller on average in this section (mean 142.05 cm against 140.14 cm).
• Whole class and boys: mean < median, a small pull from a few short students; girls: mean ≈ median.
• Compared with Section 1 (page 109), this section is shorter on average (mean 141.21 cm against 144.5 cm), and the result reverses — there the girls were taller, here the boys are.

About 5.7 times — roughly 6 times heavier.

Yes, it matches. Check the two bars of each cluster against the two rows of the table, month by month.

1 unit length = ₹10 per kg. The vertical line is marked 0, 10, 20, 30, 40, 50, 60.

Yes — much easier. The two bars for each month stand side by side, so we see at once which town was dearer that month and roughly by how much (for example, May: Wahapur dearer by ₹8; June: equal).

Observations: SpaceX (USA) launched by far the most rockets, and its launches grew fast (about 31 → 61 → 96). CASC (China) comes second. Roscosmos (Russia), Arianespace (France), Rocket Lab and United Launch Alliance (USA), ISRO (India), Galactic Energy and Expace (China) launched far fewer. ISRO’s launches rose every year; Arianespace’s fell every year.

Organisation: each organisation has three adjacent bars, for 2021, 2022 and 2023. Scale: 1 unit length = 20 rockets (marks 0, 20, 40, 60, 80, 100). Patterns: SpaceX increases year on year (its 2022 bar is almost double its 2021 bar); Arianespace decreases year on year (2023 about half of 2022); United Launch Alliance increases, then decreases. ‘Others’ groups many small organisations.

• The USA, China and Russia are the leading rocket-launching countries.
• SpaceX launched about twice as many rockets in 2022 as in 2021, and about 35 more in 2023 than in 2022.
• Arianespace’s launches fell every year.
• United Launch Alliance launched more in 2022 than in 2021, but fewer in 2023 than in either year.
• Other organisations launched about 25 rockets in 2023.

Justified: (b), (c), (d) and (e). Not justified: (a) and (f).

Reading the three bars of each cluster from dark to light, the ones that get longer every single time are:

• SpaceX — about 31 → 61 → 96
• ISRO — about 2 → 5 → 7
• Galactic Energy — about 1 → 2 → 7

(b) 200 to 400. Adding the ten 2023 bars (the lightest ones) gives roughly 220.

Why does the USA launch so many more rockets than other countries? What were the numbers before 2021 and after 2023? Which organisations are inside ‘Others’? How many of these launches were successful?

The data is the number of hours of daylight in each month (hours when the Sun is at least partly above the horizon).

Reason: dividing by the number of days gives a sensible number of hours per day (City 1: 564 ÷ 30 ≈ 18.8 h in June, 186 ÷ 31 = 6 h in December), and the two cities change in opposite directions through the year.

Yes. City 1 has its longest days in June, so it is in the Northern Hemisphere; City 2 has its shortest days in June, so it is in the Southern Hemisphere. The large change in day length through the year shows that both are far from the Equator. (City 1 is Helsinki, Finland; City 2 is Wellington, New Zealand.)

How long are the days in my own town in each month? What happens at the Equator, and near the poles, where the Sun can be seen at midnight in summer? Does longer daylight always mean hotter weather?

Yes, it can be worked out: the blue team batted first, and the blue team won by 11 runs.

First read the bars, over by over. The scale is 1 unit = 5 runs.

The blue team had 156 runs after 19 overs — already more than the red team’s 152 — yet it still batted the 20th over, so it was not chasing: blue batted first. The red team batted second, and its innings stopped after 18 overs.

15 runs.

Over 4, with 2 runs — the shortest red bar in the whole graph.

No, not easily. The graph shows the runs in each over, not the running total. To find the target we must read all 20 blue bars and add them: 163 runs, so the target was 164.

Yes. Each animal has one bar whose length shows its top speed, all on the same scale.

(a) 1 unit length = 16 kilometres per hour (marks 0, 16, 32, 48, … up to 322 kph).

(b) Sample answer: the fastest animal is a bird, the peregrine falcon (322 kph). I would like to explore which animals are fastest for their body size.

(c) Sailfish (109 kph) and flying fish (56 kph): 109 ÷ 56 ≈ 2. (Also: peregrine falcon 322 kph and spine-tailed swift 170 kph.)

(d) No, to both. The humpback whale is not in this infographic, so the first claim cannot be checked. The graph shows only four water animals, so it tells us only that the sailfish is the fastest of these four.

First count each letter. Both grades have 25 students, so the two sets of bars can be compared directly.

Scale: 1 unit length = 2 students (the largest count is 13, so the vertical line goes up to 14).

Observation: most Grade 5 students chose aerial (13 of 25); Grade 9 students chose spaceborne most (9, against only 2 in Grade 5). Both grades had 6 students choosing aquatic.

With the scale 1 unit = 4°C, the vertical line is marked 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44. The highest reading is 43°C, so 44 is the top gridline.

Months: Day 2 (30°C to 43°C) is a peak-summer day — May or June. Day 1 (16°C to 34°C) is a milder day — about February–March or October–November.

(a) Draw the Gujarat and Delhi bars to the heights in the table (for example, Gujarat 2023 just below the 90,000 line — the tallest bar of all).

(b) Three bars per state (2022, 2023, 2024); labels every 25,000, guidelines every 5,000.

(c) Every state registered more in 2024 than in 2022; West Bengal grew fastest (more than 4 times); Gujarat fell in 2024.

(d) About 60,000 − 40,000 = 20,000 more. (e) About 43,000 ÷ 10,000 ≈ 4 times.

(f) No. Each bar shows that year’s new registrations — about 16,000 in 2023 and 19,000 in 2024 in Uttarakhand — which is not “very few”. The small change in bar length only shows that the yearly number grew slowly.

• School B’s students are much taller than School A’s in every grade (Grade 6 boys: 149.84 cm against 134.8 cm — about 15 cm more).
• Heights increase from Grade 6 to Grade 8 in both schools.
• Boys and girls of the same grade have almost the same mean height; sometimes the girls are a little taller, sometimes the boys.
• The dots in each plot are spread over about 20 cm, so many girls are taller than many boys.

Sample findings:

• At every age, both boys and girls were taller in 2019 than in 1989 (5-year-olds by about 6 to 7 cm).
• Boys are a little taller at ages 5 to 9; girls are taller at ages 11 and 12; from 13 onwards boys are taller (by 11.3 cm at age 19 in 2019).
• In 2019 girls grew fastest between ages 10 and 11, boys between 12 and 13; by 18–19 growth has almost stopped.

Can be justified: 1 and 3. Cannot be justified: 2, 4, 5 and 6.

Boys grew most between ages 12 and 13 (+6.2 cm). Girls grew most between ages 10 and 11 (+5.8 cm).

Sample estimate: growth is fastest in the first year and then slows down, so heights of about 75 cm at age 1, 87 cm at age 2, 95 cm at age 3 and 101 cm at age 4 (from 50 cm at birth to about 107 cm at age 5 in 2019).

Look first at how much each age gained in the most recent ten years, 2009 → 2019, and then add a similar amount again.

The rule of thumb: add about 2 to 3 cm to each 2019 value — a little more at the younger ages, a little less at 18 and 19.

The countries are placed along the horizontal line, roughly from the shortest to the tallest. The vertical line shows height in cm and starts at 145 cm (zoomed in). Each country has four marks — × for boys, ▲ for girls; orange for 1989, blue for 2019. Every mark is the average height of 19-year-olds.

• Heights differ a lot between countries — 19-year-old boys average about 184 cm in the Netherlands but only about 160 cm in Timor-Leste.
• In every country the boys are taller than the girls on average.
• Most countries became taller from 1989 to 2019; China and South Korea gained the most, while a few, such as Pakistan, hardly changed.
• India is in the lower part of the chart (boys about 166.5 cm, girls about 155 cm in 2019).

Only (b) is true.

(a) (14 + 16 + 10 + 10) ÷ 4 = 50 ÷ 4 = 12.5 points per game.

(b) For C, divide by 3: C did not play Game 3, so that game has no value. For B, divide by 4: B played all 4 games, and 0 is a real score. (C: 32 ÷ 3 ≈ 10.67; B: 18 ÷ 4 = 4.5.)

(c) A is the best performer — highest mean (12.5), highest total (50), and never below 10 points.

Group 2 did slightly better on both measures, and Group 1’s marks are far more spread out.

The largest value is 1240, so take 1 unit length = 200 people and run the vertical line to 1400.

Observations: in every sport more people watch than take part; cricket is the most popular for both watching (1240) and participating (620); athletics is the least popular for both.

Use the median height, 115 cm, as the dividing height. Since 17 is odd and five students are exactly 115 cm tall, the groups can only be as equal as 9 and 8: put the students below 115 cm with two of the 115 cm students, and the rest in the other group.

Age: the mean (≈ 113.5 cm) and median (115 cm) are close to the 2019 average height at age 6 (about 113 cm), so these students are probably about 6 to 7 years old.

Method: measure every student’s height, find the mean (sum ÷ number of students) and the median (middle of the sorted heights), and draw a dot plot.

Sample answer for a Grade 7 class of 20 students:

The heights run from 138 cm to 164 cm; the mean (149 cm) and median (148.5 cm) are close, so the data is fairly balanced.

(d) The mean height of students in the other section cannot be determined.

(a) New York ≈ 315, Tokyo ≈ 165, London ≈ 30 (estimated from the bar lengths).

(b) (i) Valid — 12 cities are above Mumbai on the chart. (ii) Not valid — 7 cities on this chart have fewer, but the chart shows only the top 20 cities; every other city in the world also has fewer. (iii) Not valid — the chart counts how many tall buildings a city has, not how tall any one building is.

Estimate all five lengths first, then measure them, and find each positive difference (larger − smaller).

Double bar graph: for each object draw two bars side by side — the estimate and the measurement — with a scale such as 1 unit = 5 cm.

Observations: Aditi became much faster in Week 2 (her mean dropped by about 81 s). In Week 2 the 380 s puzzle is an outlier, so the mean is a little above the median.

Sample answer (part b, 12 classmates): name lengths 5, 4, 6, 5, 5, 5, 6, 5, 6, 5, 5, 6 letters → mean = 63 ÷ 12 = 5.25 letters, median = 5 letters; the lengths vary only from 4 to 6. The sorted initials A, A, D, I, K, M, N, P, R, S, T, V have their median between M and N, so about half the names start with A–M and half with N–Z.

(v) The double-bar graph. Sort every name into one of four boxes and count boys and girls separately.

(30 days): 2, 3, 2, 4, 5, 6, 1, 2, 3, 3, 2, 5, 7, 1, 2, 3, 2, 4, 5, 6, 0, 2, 3, 3, 2, 4, 6, 1, 2, 3.
Mean = 94 ÷ 30 ≈ 3.13 times a day; median = 3; range = 7 − 0 = 7. The dot plot runs from 0 to 7 with the tallest stack at 2; mean ≈ median, so the data is balanced.

Sample answer (a): family heights 168, 155, 172, 149, 161 cm → mean = 805 ÷ 5 = 161 cm, median = 161 cm, range = 172 − 149 = 23 cm; no outlier.

Sample answer (b): 1-minute estimates 52, 58, 61, 47, 65 s → mean = 56.6 s, median = 58 s; 3-minute estimates 150, 172, 195, 138, 205 s → mean = median = 172 s. Both are a little short of the true time, and the 3-minute estimates spread much more (range 67 s against 18 s).

The code is 415.