5. Connecting the Dots...
Answers to all Figure it Out and in-text questions on statistics, mean, median, outliers and graphs. CBSE / NCERT Class 7 Ganita Prakash Part 2.
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5.1 Of Questions and Statements
A statistical question needs data. We expect the answers to vary.
Statistical: (a), (b), (c), (f) and (g).
(a) Prices differ from shop to shop. (b) The dogs have different ages. (c) We must ask every student. (f) We must compare the wickets and runs of all bowlers. (g) We need the rainfall data of many days.
Not statistical: (d) and (e).
(d) asks one person about one thing. (e) has only one answer — the count of bricks in one wall.
5.2 Representative Values
It is not fair. Shubman played 5 matches but Yashasvi played only 4 matches.
When the number of matches is different, comparing the totals is not correct.
Yes. We can use the average. Divide the total runs by the number of matches played.
Shubman: 110 ÷ 5 = 22 runs. Yashasvi: 96 ÷ 4 = 24 runs.
The book shows 110 ÷ 5 = 21 runs. The correct value is 22 runs. Yashasvi’s average (24) is still higher.
1. Find the average number of bounces: 6, 2, 9, 5, 4, 6, 3, 5.
Total = 6 + 2 + 9 + 5 + 4 + 6 + 3 + 5 = 40.
Average = 40 ÷ 8 = 5 bounces.
2 and 3. Activities
Do these yourself. Add all your values and divide by the number of values.
4. Who on average ran quicker, Nikhil or Sunil?
Nikhil: 17 + 18 + 17 + 16 + 19 + 17 + 18 = 122. Average = 122 ÷ 7 ≈ 17.43 s.
Sunil: 20 + 18 + 18 + 17 + 16 + 16 + 17 = 122. Average = 122 ÷ 7 ≈ 17.43 s.
Both have the same average. So, on average, they ran equally quickly. (Nikhil’s times are more consistent — 16 to 19 s. Sunil’s vary from 16 to 20 s.)
5. Find the mean enrolment.
Total = 1555 + 1670 + 1750 + 2013 + 2040 + 2126 = 11154.
Mean = 11154 ÷ 6 = 1859.
We can compare the averages, the medians, or count the months when the price is above ₹40.
We can also compare the prices season-wise (for example, January–June and July–December).
Yes. All 24 prices are shown as dots.
No. We cannot tell the price of a particular month. The month-wise order is lost.
Yahapur: 458 ÷ 12 ≈ ₹38.17 per kg.
Wahapur: 450 ÷ 12 = ₹37.50 per kg.
On average, onions are slightly costlier in Yahapur.
Yaangba’s family: 986 ÷ 6 ≈ 164.3 cm. Poovizhi’s family: 801 ÷ 5 = 160.2 cm.
No. 4 out of 5 members of Poovizhi’s family are 165 cm or taller. Only one young child (118 cm) pulls the average down.
Yes. Poovizhi’s median (170 cm) is close to the heights of most members. The average (160.2 cm) is not.
Heights: 165, 170, 173, 175.
Mean = 683 ÷ 4 = 170.75 cm. Median = (170 + 173) ÷ 2 = 171.5 cm.
The mean increased a lot (160.2 → 170.75). The median changed only a little (170 → 171.5).
Data: 6, 8, 5, 15, 3, 0, 2, 7, 12, 40, 10, 5, 0, 1, 8 (15 students).
Guess: the mean will be greater than the median, because of the large value 40.
Sorted: 0, 0, 1, 2, 3, 5, 5, 6, 7, 8, 8, 10, 12, 15, 40.
Mean = 122 ÷ 15 ≈ 8.13. Median = 8th value = 6.
Short stories read
Outlier: 40.
Without 40: Mean = 82 ÷ 14 ≈ 5.86. Median = (5 + 6) ÷ 2 = 5.5.
The mean dropped a lot (8.13 → 5.86). The median changed very little (6 → 5.5).
Sorted: 10, 16, 16, 18, 20, 22, 26.
Mean = 128 ÷ 7 ≈ 18.29 pages. Median = 18 pages.
Newspaper pages (Mon–Sun)
The book’s dot plot line ends at 25, but one value is 26. Extend the line a little.
(a) Close: Yaangba’s family heights and newspaper pages. The data is spread evenly, with no outlier.
(b) Mean < median: Poovizhi’s family. The outlier (118) is at the lower end.
(c) Mean > median: short stories read. The outlier (40) is at the higher end.
The two outliers pull the mean in opposite directions. So, the mean may stay close to the median.
Example: 2, 20, 21, 22, 40. Mean = 105 ÷ 5 = 21. Median = 21.
The median is not affected much by outliers on either side.
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Boys taller than 144.4 cm: 145, 146, 146, 147, 150, 154, 155, 158 → 8.
Girls taller than 144.4 cm: 145, 148, 150, 150, 150, 154, 156 → 7.
15 students are taller than the class average.
8 boys.
Group A: mean 58.21 s, median 60 s. Group B: mean 59.28 s, median 59.5 s.
Both groups did well. Their means and medians are close to 60 seconds.
Group A has a few children who opened their eyes too early (around 42–47 s). This pulls its mean below its median.
Group B’s values are a little more balanced. Its mean and median are both close to 60 s.
Yes. If 6 or more of the 11 players score 0, the median is 0.
The other few players can score many runs. Together with extras, the total can still be 407.
1. Find the median of onion prices.
Yahapur sorted: 24, 25, 26, 28, 30, 35, 39, 43, 44, 49, 56, 59. Median = (35 + 39) ÷ 2 = ₹37.
Wahapur sorted: 17, 19, 23, 30, 35, 38, 39, 42, 42, 52, 53, 60. Median = (38 + 39) ÷ 2 = ₹38.50.
2. Pets data: find the mean and median. Describe the data.
Absent students (—) are not counted. So, there are 20 values. Total = 72.
Mean = 72 ÷ 20 = 3.6.
Sorted: 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 8, 10, 25. Median = (2 + 2) ÷ 2 = 2.
Most students have few animals. 6 students have none. The values 10 and 25 are outliers. They pull the mean above the median.
3. Palm tree heights: dot plot, mean and median.
There are 29 trees. Total = 1621 ft. Mean = 1621 ÷ 29 ≈ 55.9 ft.
Median = 15th value in sorted order = 56 ft.
Heights of date-palm trees (in feet)
The heights are from 43 ft to 67 ft. Most trees are between 50 ft and 62 ft. The mean and median are almost equal, so the data is balanced.
Quicker way: Take 55 as a base. Add the differences from 55: total extra = 1621 − 29 × 55 = 26. Mean = 55 + 26 ÷ 29 ≈ 55.9 ft.
13 trees are shorter than the average height.
4. Water usage: 5.6, 8, 3.09, 12.9, 6.5, 12.1, 11.3, 20.5, 7.4.
(a) No. All values are less than 25. The mean is a fair share of the values, so it lies between the smallest and the largest value. The median is the middle value. So, neither can be between 25 and 30.
(b) No. The mean and the median always lie between the minimum and the maximum values (they can be equal to them only if all values are the same).
5. Weights of newborn babies.
Boys: mean = 20.6 ÷ 6 ≈ 3.43 kg; median = (3.4 + 3.5) ÷ 2 = 3.45 kg.
Girls: mean = 20.1 ÷ 6 = 3.35 kg; median = (3.4 + 3.4) ÷ 2 = 3.4 kg.
Weights of newborn babies (kg)
Both groups have a similar spread (boys 2.6–4.1 kg, girls 2.5–4.0 kg). On average, the boys are slightly heavier. The difference is very small.
6. Heights of another section of Grade 5.
Here, the boys’ mean (142.05 cm) is more than the girls’ mean (140.14 cm). So, boys are a little taller in this section.
For the whole class, mean (141.21) < median (142.5). A few short students pull the mean down.
Compared to the first section (mean 144.4 cm), this section is shorter on average. In the first section, girls were taller. In this section, boys are taller.
7. About how many times heavier is a sumo wrestler than a ballet dancer?
Mean weight of sumo wrestlers = 1201.9 ÷ 5 ≈ 240.4 kg.
Mean weight of ballet dancers = 254.5 ÷ 6 ≈ 42.4 kg.
240.4 ÷ 42.4 ≈ 5.7. A sumo wrestler is about 6 times heavier.
5.3 Visualising Data
On the vertical line, 1 unit = ₹10 (marked 0, 10, 20, … 60).
Yes. The two bars of each month are side by side. So, it is easy to see where onions are costlier in each month.
Approximate values read from the graph (2021, 2022, 2023): SpaceX 31, 61, 96; CASC 48, 35, 45; Roscosmos 16, 21, 18; Arianespace 15, 6, 3; ISRO 2, 5, 7; Galactic Energy 1, 2, 7.
- Not justified. Arianespace launched fewer rockets every year.
- Justified. Only SpaceX (USA) launched more than 50 in a year. CASC’s highest is a little below 50.
- Justified. Arianespace (France): about 15 + 6 + 3 = 24 < 40.
- Justified. CASC: about (48 + 35 + 45) ÷ 3 ≈ 43, which is around 40.
- Justified. ISRO: about 14 rockets. Galactic Energy: about 10 rockets.
- Not justified. Roscosmos (Russia): about 16 + 21 + 18 = 55, which is less than 60.
SpaceX, ISRO and Galactic Energy.
About 96 + 45 + 18 + 3 + 9 + 3 + 7 + 7 + 6 + 26 ≈ 220.
Answer: (b) 200 to 400.
June: about 18 hours out of 24 → about 3/4 of the day.
December–January: about 6 hours out of 24 → about 1/4 of the day.
- Yes. The blue team batted all 20 overs, so it batted first. The red team has bars only up to over 18 and lost no wickets. It reached the target early. So, the red team won.
- The blue team scored 15 runs in over 12.
- The red team scored the least runs in over 4 (2 runs).
- No. We must add the runs of all 20 overs of the blue team (and the extras). Then the target is that total + 1.
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1. Animal speeds infographic. Can we call it a bar graph?
Yes. The length of each bar shows the speed of the animal. The bars are just drawn upright.
(a) 1 unit = 16 km/h (marked 16, 32, 48, 64, …).
(b) Do it yourself. Example: a falcon dives faster than any car on a highway.
(c) Peregrine falcon (322 km/h) and spine-tailed swift (170 km/h). Also sailfish (109 km/h) and flying fish (56 km/h).
(d) 109 ÷ 26 ≈ 4.2. Yes, a sailfish is about 4 times faster than a humpback whale.
But we cannot say it is the fastest aquatic animal in the world. The graph shows only a few animals.
2. Superpower choices: draw a double-bar graph.
Count the letters (w = aquatic, a = aerial, s = spaceborne, n = none).
Grade 5: aquatic 6, aerial 13, spaceborne 2, none 4 (total 25).
Grade 9: aquatic 6, aerial 8, spaceborne 9, none 2 (total 25).
Superpower choices
Most Grade 5 students chose aerial. Most Grade 9 students chose spaceborne.
3. Jodhpur temperatures: draw a double-bar graph (1 unit = 4°C).
Temperature over two days in Jodhpur
Day 1 is cool (16°C to 34°C). It may be a winter month like December or January.
Day 2 is very hot (30°C to 43°C). It may be a summer month like May or June.
4. Electric vehicle registrations.
(a) Gujarat: 2022 between 65,000 and 70,000 lines, 2023 between 85,000 and 90,000, 2024 between 75,000 and 80,000.
Delhi: 2022 between 60,000 and 65,000, 2023 between 70,000 and 75,000, 2024 between 80,000 and 85,000.
Completed graph with Gujarat and Delhi
(b) The states are on the horizontal line. Each state has 3 bars for 2022, 2023 and 2024. On the vertical line, 1 unit = 25,000 vehicles. The thin lines are 5,000 apart. In the given states, the bars grow from 2022 to 2024.
(c) All five given states had more registrations in 2024 than in 2022. West Bengal grew the most (about 4 times). Andhra Pradesh and Odisha about doubled. Uttarakhand grew only a little.
(d) Assam: about 60,000 in 2023 and 40,000 in 2022. So, about 20,000 more.
(e) West Bengal: about 10,000 in 2022 and 43,000 in 2024. So, about 4 times.
(f) No. Each bar shows the registrations in that year, not the total. Uttarakhand had about 16,000 in 2023 and 19,000 in 2024. That is not “very few”. The small change only means the yearly numbers were almost the same.
5.4 Data Detective
In every grade, students of School B are much taller than those of School A.
In both schools, heights increase from Grade 6 to Grade 8.
Boys and girls of the same grade have almost the same mean height.
- Justified. At every age, the 2019 heights are more than the 1989 heights, for both boys and girls.
- Not justified. 13-year-old girls in 1989: 143.2 cm. 14-year-old girls in 2009: 148 cm.
- Justified. 15-year-old boys in 2019: 159 cm. 16-year-old boys in 1989: 158.9 cm.
- Not justified. The table gives only averages. Some 11-year-old girls can be taller than some 13-year-old girls.
- Not justified. At ages 11 and 12, girls are taller on average (also at 10 and 5 in 2019).
- Not justified. The table stops at age 19. (Growth between 18 and 19 is very small.)
Boys: between 12 and 13 years (142.2 → 148.4 = 6.2 cm).
Girls: between 10 and 11 years (132.8 → 138.6 = 5.8 cm).
A child is about 107 cm at age 5. So, the height grows from 50 cm to 107 cm in 5 years. Growth is fastest in the first year.
Rough estimates: age 1 ≈ 75 cm, age 2 ≈ 86 cm, age 3 ≈ 95 cm, age 4 ≈ 102 cm.
From 2009 to 2019, heights increased by about 2 to 3 cm at each age. Add the same increase again.
Boys: age 5 ≈ 109 cm, age 10 ≈ 136 cm, age 15 ≈ 162 cm, age 19 ≈ 168 cm.
Girls: age 5 ≈ 110 cm, age 10 ≈ 136 cm, age 15 ≈ 155 cm, age 19 ≈ 157 cm.
These are estimates. Your values may be a little different.
1. Pockets on clothing. Which statements are true?
Boys (12): 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6. Range 3 to 6. Median = 5. Mean = 56 ÷ 12 ≈ 4.7.
Girls (13): 0, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 6. Range 0 to 6. Median = 4. Mean = 45 ÷ 13 ≈ 3.5.
(a) False — the girls’ data varies more. (b) True. (c) False. (d) False — both have a maximum of 6.
2. Points scored in four games.
(a) A: (14 + 16 + 10 + 10) ÷ 4 = 50 ÷ 4 = 12.5 points.
(b) C did not play Game 3. So, divide by 3: 32 ÷ 3 ≈ 10.67. B played all 4 games (0 is a score), so divide by 4: 18 ÷ 4 = 4.5.
(c) A is the best performer. A has the highest average and never scored below 10.
3. GK quiz: compare the two groups.
Group 1 (10 students): mean = 730 ÷ 10 = 73; median = (76 + 81) ÷ 2 = 78.5.
Group 2 (9 students): mean = 681 ÷ 9 ≈ 75.7; median = 79.
Group 2 did slightly better. In Group 1, the low scores 39 and 48 pull the mean below the median. Group 1’s scores are more spread out (39 to 95).
4. Favourite sport survey: draw a double-bar graph.
Favourite sport in a colony
Cricket is the most popular for watching and for playing. Athletics is the least popular.
In every sport, more people watch than take part. For cricket, the number watching (1240) is exactly double the number playing (620).
5. 17 students’ heights: divide into two equal groups.
Sorted: 101, 102, 106, 109, 110, 110, 112, 115, 115, 115, 115, 115, 117, 120, 120, 123, 125.
Find the median. It is the 9th value, 115 cm. Line up the students by height. The 8 students before the middle student form one group. The 8 after form the other group.
Note: five students are 115 cm tall. So, a few 115 cm students will be in the taller group.
Age: the median height is about 115 cm. In the table (2019), 6-year-olds are about 113 cm and 7-year-olds about 118 cm. So, the students are about 6 to 7 years old.
6. Your class heights.
Do it yourself. Measure everyone, make a dot plot, and find the mean and median.
7. The mean height of one section is 154.2 cm. What about the other section?
(d) It cannot be determined. The heights of one section tell us nothing about the other section.
8. Cities with most skyscrapers.
(a) New York ≈ 315, Tokyo ≈ 165, London ≈ 30 (estimated from the bar lengths).
(b)(i) Valid (in this graph). 12 cities are above Mumbai.
(ii) Valid (in this graph). Seoul, Toronto, Melbourne, Miami, Istanbul, Moscow and London — 7 cities.
(iii) Not valid. The graph shows the number of skyscrapers, not their heights. (The tallest building, Burj Khalifa, is in Dubai.)
9. Estimate and measure objects.
Do it yourself. Positive difference = bigger value − smaller value. Average difference = total of the differences ÷ 5.
10. Aditi’s Sudoku times.
Time taken to solve (seconds)
Week 1: total 3240. Mean = 3240 ÷ 9 = 360 s. Median = 360 s.
Week 2: total 2230. Mean = 2230 ÷ 8 ≈ 278.75 s. Median = (270 + 280) ÷ 2 = 275 s.
Aditi became faster in Week 2. 380 s in Week 2 is an unusually slow attempt.
11, 12 and 13. Projects
These are projects. Collect your own data. Use dot plots, the mean and the median.
Puzzle: Connect the Dots…
036 — nothing is correct. So, 0, 3 and 6 are not in the code.
064 — one digit correct, wrongly placed. 0 and 6 are out, so 4 is in the code, but not in the third place.
542 — two digits correct, wrongly placed. 4 is not in the middle. So, 4 is in the first place.
265 — one digit correct and well placed. 2 cannot be first (4 is there). So, 5 is in the third place.
From 542, the two correct digits are 4 and 5. So, 2 is not in the code.
271 — one digit correct, wrongly placed. It must be 1 (7 could only go in its own middle place). So, 1 is in the middle.
The code is 415.