What is 5.6 Figure It Out — End of Chapter Exercises in NCERT Class 7 Mathematics Chapter 5?

5.6 Figure It Out — End of Chapter Exercises is the topic of Part 4 of Chapter 5 (Ch 5 — Data Handling) in NCERT Class 7 Mathematics. This lesson builds intuition through examples, visuals, and graded practice.

TOPIC 16 OF 23

5.6 Figure It Out — End of Chapter Exercises

Q: What is Part 4 u2014 Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool in NCERT Class 7 Mathematics?

Part 4 u2014 Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool is a key concept covered in NCERT Class 7 Mathematics, Chapter 5: Chapter 5. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.

Q: How do I solve problems on Part 4 u2014 Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool step by step?

To solve problems on Part 4 u2014 Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 7 exercises gradually increase in difficulty u2014 start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.

Q: Is Part 4 u2014 Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool important for the Class 7 board exam?

Part 4 u2014 Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool is part of the NCERT Class 7 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.

Q: What mistakes should students avoid in Part 4 u2014 Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool?

Common mistakes in Part 4 u2014 Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.

Q: Where can I find more NCERT practice questions on Part 4 u2014 Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool?

End-of-chapter NCERT exercises for Part 4 u2014 Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 5, and solve at least one previous-year board paper to consolidate your understanding.

🎓 Class 7 Mathematics CBSE Theory Ch 5 — Data Handling ⏱ ~20 min

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5.6 Figure It Out — End of Chapter Exercises

This final part of the chapter walks through all the NCERT Figure-it-Out questions and wraps with a summary of Connecting the Dots. Work each question on paper first, then reveal the worked solution.

Q1. The dot plots below show the distribution of the number of pockets on clothing for a group of boys and a group of girls. (Boys: 1 dot at 0, 1 at 1, 4 at 2, 3 at 3, 2 at 4, 1 at 5; Girls: 2 dots at 0, 4 at 1, 3 at 2, 1 at 3, 1 at 4.) Which of the following are true? (a) Data for boys varies more than girls. (b) Median pockets for boys > girls. (c) Mean pockets for girls > boys. (d) Max pockets for boys > girls.

Dot plot — number of pockets for boys and girls.

Boys: 12 values → 0,1,2,2,2,2,3,3,3,4,4,5. Sum = 31 → Mean ≈ 2.58. Median (6th,7th) = (2+3)/2 = 2.5. Max = 5.
Girls: 11 values → 0,0,1,1,1,1,2,2,2,3,4. Sum = 17 → Mean ≈ 1.55. Median (6th) = 1. Max = 4.
(a) True — Boys range 0–5 is wider than girls 0–4. (b) True — 2.5 > 1. (c) False — girls' mean 1.55 < boys' mean 2.58. (d) True — 5 > 4.

Q2. The table shows points scored by each player in four games. Find (a) the average number of points per game by A; (b) To find the number of points scored per game by C, would you divide the total points by 4 or 3? Why? (c) Who is the best performer?

Player	Game 1	Game 2	Game 3	Game 4
A	14	16	10	10
B	0	8	6	4
C	8	11	Did not play	13

(a) A's mean = (14+16+10+10)/4 = 50/4 = 12.5. (b) C played only 3 games, so divide by 3: (8+11+13)/3 = 32/3 ≈ 10.67. (c) B's mean = 18/4 = 4.5. Best performer by mean per game = A (12.5). C (10.67) is second.

Q3. Marks of 1000 students from a General Knowledge quiz are: 85, 76, 90, 85, 39, 48, 95, 81, 75. Another group's scores in the same quiz are 68, 59, 73, 86, 47, 76, 90, 93 and 86. Compare and describe the two groups' performance using range and mean.

Group 1: sum = 674, n = 9, mean ≈ 74.9; range = 95 − 39 = 56.
Group 2: sum = 678, n = 9, mean ≈ 75.3; range = 93 − 47 = 46.
Both groups have almost the same mean. Group 1 has a wider range (more variation) — one very low score (39) pulled it down. Group 2 is more consistent.

Q4. Consider this data from a survey of a colony. Choose a scale and draw a double-bar graph comparing how both groups chose each option.

Favourite Sport	Cricket	Basket Ball	Swimming	Hockey	Athletics
Watching	1240	470	510	430	250
Participating	620	320	320	250	105

Choose scale 1 unit = 100 people. Draw paired bars for each sport — one for watching, one for participating. Cricket dominates both categories. Watching > Participating for every sport — most people prefer watching sports to playing them.

Q5. Consider a group of 17 students with the following 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 2 groups with equal number of students; one group has students with height less than a particular height, the other group has students with heights greater than that particular height. Suggest a way to do this. Can you guess the approximate height?

Sort: 101,102,106,109,110,110,112,115,115,115,115,115,117,120,120,123,125. 17 values → median is 9th value = 115 cm. Use 115 cm as the dividing height: 8 students are < 115, 1 student is exactly 115, and 8 students are > 115 — the median naturally splits the class in half.

Q6. Describe the mean and median of your class height. You can visualise the heights on a dot plot.

Open-ended. Measure all classmates' heights, make a dot plot, compute mean = (sum)/(n) and identify middle value(s) for median. Comment on whether any outliers pull mean away from median.

Q7. 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 heights of students in the other section? (a) 154.2 cm (b) less than 154.2 (c) greater than 154.2 (d) cannot be determined.

Answer: (d) cannot be determined. The mean of one section tells us nothing about the other section. The two sections could have very different average heights.

Q8. Standing tall in the storm — the graph "Cities with Most Skyscrapers (taller than 150 m)" shows: Hong Kong 553, Shenzhen 367, New York 317, Dubai 251, Shanghai 189, Tokyo 185, Kuala Lumpur 154, Chongqing 144, Jakarta 112, Bangkok 116, Singapore 96, Mumbai 92, Seoul 81, Toronto 81, Melbourne 74, Paris 71, Istanbul 47, Moscow 48, Miami 46, London 37. (a) Write estimated values for New York, Tokyo and London. (b) Are these 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.

(a) NY ≈ 317, Tokyo ≈ 185, London ≈ 37. (b)(i) True — 12 cities listed above Mumbai. (ii) True — 7 cities below Mumbai (Seoul, Toronto, Melbourne, Paris, Moscow, Istanbul, Miami, London — if exactly 7 are below the threshold, count accordingly). (iii) False — the graph shows skyscraper count, not building height. The tallest building (Burj Khalifa) is in Dubai.

Q9. Estimate and then measure 5 objects (length of pen, eraser, palm, geometry box, maths notebook). Find the positive difference between estimate and measure, then draw a double-bar graph. How accurate were your estimates? Find the average difference between estimated and measured values.

Open-ended. Sample table: Pen (est 14, meas 15, diff 1), Eraser (est 4, meas 5, diff 1), Palm (est 10, meas 12, diff 2), Geometry box (est 25, meas 23, diff 2), Notebook (est 28, meas 28, diff 0). Mean diff = 6/5 = 1.2 cm. Draw side-by-side bars for each object (estimate vs measure).

Q10. Aditi is solving puzzles. In Week 1 her times (seconds) were 410, 400, 370, 340, 360, 400, 320, 310, 290, 280, 280, 270, 230, 220, 240. In Week 2 they were 380, 280, 300, 270, 240, 260. (a) Construct a dot plot for each week. (b) Describe the mean, median, and observations you have about the data.

Week 1 (15 values): sum = 4920, mean = 328 s, median (8th) after sort = 310 s. Week 2 (6 values): sum = 1730, mean ≈ 288.3 s, median = (270+280)/2 = 275 s. Aditi has improved: both mean and median times have dropped — she is solving the puzzles faster with practice.

Q11. Individual Project — Pick at least one: (a) How Long is a Sentence? Pick any two textbook pages from different subjects and collect data from the first page. Use a dot plot to compare. (b) What is in a Name? Find mean and median number of letters in your classmates' names. (c) Which letters are most popular in English, in Hindi, in your mother tongue? Pick a page in each language and tally. (d) Plot a double-bar graph — how many vowels and consonants in each line?

Open-ended project. For (b), if your class has 20 names with lengths: 4,5,5,6,6,6,6,7,7,7,7,8,8,8,9,9,10,11,11,12 → sum = 151, mean = 7.55, sort middle (10th, 11th) = (7+7)/2 = 7 → median 7. Observe which letters repeat most often (mode).

Q12. Individual Project (long term) — Collect data about your house in a day for five days. For each day: (i) describe the variability and central tendency of this data; (ii) do you find anything interesting about this data; (iii) share your observations; (iv) can you ask any of your family members or friends to do this as well?

Open-ended. Possible data: temperature at 3 times/day, number of visitors, time spent studying, TV hours, etc. Describe spread using range, and central tendency using mean/median. Interesting findings could be weekday vs weekend differences.

Q13. Small-Group project — Pick at least one. (a) Our heights vs our family's. Collect data of your heights and those of family members and share your observations. (i) Make a dot plot using heights of just your family members. Describe its variability and central tendency. (ii) Make a double-bar graph showing every student's mean 1 minute estimate and mean 3 minute estimate. (iii) Look at everyone's data and share your observations.

Open-ended group project. Aim: appreciate natural variability within and across families. A dot plot per family + a combined class plot brings out outliers (e.g. very young siblings) that deflate the mean vs median.

Activity — "Connect the Dots" Number-Lock Puzzle

L5 Evaluate

Materials: Paper and pencil. Hints (as in the NCERT puzzle):

2 8 1 — one digit is correct and well placed.
5 3 8 — one digit is correct but wrongly placed.
6 4 7 — two digits are correct but wrongly placed.
2 1 6 — nothing is correct.
7 8 9 — one digit is correct but wrongly placed.

Predict first: Guess one digit that you think must be in the code before reading on.

From hint 4 eliminate 2, 1, 6 entirely.
Hint 1 — "2 8 1, one correct and well placed". Since 2 and 1 are eliminated, 8 is correct AND in position 2.
Hint 2 — "5 3 8 one correct wrongly placed". 8 is already in position 2, so the "correct" digit here must be 5 or 3. If 8 then it'd be well placed (contradicts "wrongly placed") — so 8 isn't the one from hint 2. Try 3: it can't be in pos 2 (that's 8), so 3 is in pos 1 or 3.
Hint 3 — "6 4 7 two correct wrongly placed". 6 eliminated, so 4 and 7 are correct but not in their current positions → 4 not pos 2 (anyway it's 8), and 7 not pos 3.
Hint 5 — "7 8 9 one correct wrongly placed". 8 is already in pos 2 (well placed), so the correct-but-wrongly-placed digit is 7 or 9. From hint 3 we know 7 is correct, so 7 comes from here too — not pos 1.
So 7 is in position 2? No, pos 2 is 8. So 7 must be in pos 3… but hint 3 says 7 is NOT in pos 3. Therefore 9 is the one from hint 5, and 7 being in the code came from hint 3 — pos of 7 must be pos 1 (since not pos 2, not pos 3).
That leaves 4 in pos 3 (from hint 3: 4 wrongly placed, so not pos 2 — since pos 2 taken by 8 — and not in its own pos 2, so pos 1 or 3; since pos 1 is 7 → 4 in pos 3).
Final code: 7 8 4.

Code = 7 8 4. Good logical deduction uses elimination just like a detective handling data outliers — remove impossible options, then use the remaining clues.

Summary — Connecting the Dots

★ Key Ideas from Chapter 5 ★

Dot plots help us get a quick glimpse of the variability^? of the data — minimum, maximum, range, and how the data is clustered or spread out.
Arithmetic mean = Sum of all values ÷ Number of values. It is affected by extreme values (outliers^?).
The median is the number in the middle of any sorted data. If there are an even number of values, the median is the average of the two middle numbers.
The mode is the value that occurs most often. A dataset may have one mode, several modes, or no mode at all.
We can describe and compare data in several ways including by referring to the minimum, maximum, total, range, mean, median and mode.
We learn how to read and make clustered bar graphs. These graphs help us compare data across categories and across time.
Examining data can lead to new questions and directions to probe further — this is the mindset of a data detective.

Competency-Based Questions

A school nurse records the pulse rates (beats per minute) of 11 students after a short run: 118, 124, 120, 122, 118, 126, 150, 118, 122, 124, 120. The nurse wants to summarise the data.

Q1. Find the mean, median, mode and range of the pulse rates.

L3 Apply

Sum = 1362, n = 11, mean = 123.8. Sort: 118,118,118,120,120,122,122,124,124,126,150 → median (6th) = 122. Mode = 118 (3 times). Range = 150 − 118 = 32.

Q2. One student has a pulse rate of 150 — much higher than others. Which measure(s) of central tendency change the most if we remove this outlier? Show your work.

L4 Analyse

Remove 150 → sum = 1212, n = 10 → new mean = 121.2 (drop of 2.6). Sorted 10 values → median (5th,6th) = (120+122)/2 = 121 (drop of 1). Mode still 118. Mean changes most because it depends on every value's magnitude.

Q3. The nurse must decide one number to report to the school principal. Which measure is most appropriate and why?

L5 Evaluate

The median (122) is most appropriate because one very high value (150) pulls the mean upward and misrepresents typical students. Median resists outliers.

Q4. Invent a dataset of 7 students' pulse rates whose mean is 120, median is 118, and mode is 115. List your 7 values.

L6 Create

Try: 110, 115, 115, 118, 125, 130, 127. Sum = 840, mean = 120 ✓. Sorted: 110,115,115,118,125,127,130 → median (4th) = 118 ✓. Mode = 115 (twice) ✓.

Assertion–Reason Questions

Assertion (A): A double-bar graph is the best way to compare how two groups performed across the same set of categories.
Reason (R): Two bars placed side by side for each category make the comparison visual and immediate.

(a) Both true, R explains A.

(b) Both true, R doesn't explain A.

(c) A true, R false.

(d) A false, R true.

Answer: (a) — Side-by-side bars make relative differences easy to see at a glance.

Assertion (A): In a 9-value dataset, the median is always one of the original data values.
Reason (R): For an odd number of values, the median is the middle value after sorting.

(a) Both true, R explains A.

(b) Both true, R doesn't explain A.

(c) A true, R false.

(d) A false, R true.

Answer: (a) — 9 is odd, so median = 5th sorted value, which is exactly a data point.

Assertion (A): Range gives a complete picture of how spread out a dataset is.
Reason (R): Range is the difference between the maximum and minimum values.

(a) Both true, R explains A.

(b) Both true, R doesn't explain A.

(c) A true, R false.

(d) A false, R true.

Answer: (d) — A is false: range ignores how values are distributed between the extremes (two datasets with the same range can cluster very differently). R is the correct definition.

Frequently Asked Questions — Chapter 5

What is Part 4 — Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool in NCERT Class 7 Mathematics?

Part 4 — Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool is a key concept covered in NCERT Class 7 Mathematics, Chapter 5: Chapter 5. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.

How do I solve problems on Part 4 — Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool step by step?

To solve problems on Part 4 — Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 7 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.

What are the most important formulas for Chapter 5: Chapter 5?

The essential formulas of Chapter 5 (Chapter 5) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.

Is Part 4 — Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool important for the Class 7 board exam?

Part 4 — Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool is part of the NCERT Class 7 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.

What mistakes should students avoid in Part 4 — Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool?

Common mistakes in Part 4 — Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.

Where can I find more NCERT practice questions on Part 4 — Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool?

End-of-chapter NCERT exercises for Part 4 — Figure-it-Out Exercises & Summary | Class 7 Maths Ch 5 | MyAiSchool cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 5, and solve at least one previous-year board paper to consolidate your understanding.

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