Mean is the average value found by dividing the sum of observations by the number of observations. Median is the middle value of sorted observations, while line graphs show how values change across time.
Numbers tell a story only when students know how to locate the centre, compare changes, and read patterns. Important Questions Class 8 Maths Part 2 Chapter 5 help students practise mean as a balancing point, median as a positional centre, missing values, frequency-based averages, spreadsheet formulas, line graphs, infographics, and activity strips. The 2026 chapter Tales by Dots and Lines in Ganita Prakash Class 8 Part 2 Maths uses real examples like wrestler weights, coconut harvests, class marks, rainfall, temperatures, sleep duration, and daily routines.
Key Takeaways
- Mean: Mean balances the total distance of values on its left and right.
- Median: Median depends on position after sorting, not the total sum.
- Frequencies: Repeated values must be counted as many times as they occur.
- Line Graphs: Line graphs show changes across months, years, ages, or daily events.
Important Questions Class 8 Maths Part 2 Chapter 5 Structure 2026
| Concept |
Rule |
Example Use |
| Mean |
Mean = Sum of values / Number of values |
Missing weights, corrected averages, changed values |
| Median |
Middle value after sorting |
Odd, even, and frequency-based data |
| Line Graph |
Points joined by line segments |
Temperature, rainfall, launches, sleep, sunrise |
Tales By Dots And Lines Class 8 Chapter Overview
Tales by Dots and Lines explains how values form patterns when shown through dots, tables, lines, maps, and strips. Mean is treated as a balancing point, while median is treated as the middle position.
The chapter also shows how spreadsheets reduce calculation work. Line graphs, infographics, and activity strips help students read time-based and visual information.
Class 8 Maths Part 2 Chapter 5 Important Questions On Mean
Mean does not only mean “add and divide” in this chapter. It also shows where the values balance on a number line.
Students should understand why the mean shifts when new values are added or removed.
Q1. What Is Mean In Class 8 Maths?
Mean is the sum of all observations divided by the number of observations.
It gives one central value for a collection of numbers. For two values, the mean lies exactly halfway between them.
- Given data: 3, 7
- Sum = 3 + 7 = 10
- Number of values = 2
- Mean = 10 / 2 = 5
Final Answer: Mean = 5
Q2. Why Is Mean Called The Centre Of A Collection?
Mean is called the centre because the total distance on both sides of it is equal.
It may not always be the midpoint of the smallest and largest values. It depends on every value in the collection.
Example: For 10, 10, 11, and 17, the mean is 12. The distances on the left and right balance at 12.
Q3. Is Mean Always The Midpoint Of The Two Extreme Values?
No, mean is not always the midpoint of the two extreme values.
The midpoint uses only the smallest and largest values. The mean uses all observations.
Example: For 10, 10, 11, and 17, the extreme midpoint is 13.5. The mean is 12.
Q4. Can There Be More Than One Mean Centre?
No, there can be only one mean centre for a fixed data set.
If the centre moves right, left-side distances increase and right-side distances decrease. If it moves left, the opposite happens.
Example: For 10, 10, 11, and 17, only 12 balances the distances.
Q5. What Happens To Mean When A Value Greater Than The Mean Is Added?
The mean increases when a value greater than the current mean is added.
The new value pulls the balance point towards the higher side. The new mean becomes larger than before.
Example: If the mean is 8 and 11 is added, the mean increases.
Q6. What Happens To Mean When A Value Less Than The Mean Is Added?
The mean decreases when a value less than the current mean is added.
The smaller value pulls the balance point towards the lower side. The new mean becomes smaller than before.
Example: If the mean is 8 and 3 is added, the mean decreases.
Q7. What Happens If A Value Equal To The Mean Is Added?
The mean remains unchanged if a value equal to the mean is added.
The new value sits at the balance point. It does not pull the mean towards either side.
Example: If the mean is 8 and another 8 is added, the mean remains 8.
Q8. Can We Add Values Without Changing The Mean?
Yes, values can be added without changing the mean if their total balances around the mean.
For a mean of 10, adding 8 and 12 keeps the mean unchanged. Their distances from 10 are equal.
Example: 8 is 2 less than 10, and 12 is 2 more than 10.
Mean Class 8 Maths Solved Questions
Mean questions become easier when students first find the total sum. This method works for natural numbers, odd numbers, multiples, heights, weights, and harvest counts.
Use clear steps in every calculation.
Q9. Find The Mean Of 8, 3, 10, 13, 4, 6, 7, 7, 8, 8, 5.
The mean is 7.18 approximately.
- Sum = 8 + 3 + 10 + 13 + 4 + 6 + 7 + 7 + 8 + 8 + 5
- Sum = 79
- Number of values = 11
- Mean = 79 / 11
- Mean = 7.18 approximately
Final Answer: Mean = 7.18 approximately
Q10. Find The Mean Of The First 50 Natural Numbers.
The mean of the first 50 natural numbers is 25.5.
- First 50 natural numbers are from 1 to 50.
- Sum = 50 × 51 / 2
- Sum = 1275
- Mean = 1275 / 50
- Mean = 25.5
Final Answer: Mean = 25.5
Q11. Find The Mean Of The First 50 Odd Numbers.
The mean of the first 50 odd numbers is 50.
- The first 50 odd numbers are from 1 to 99.
- Mean of equally spaced values = (First value + Last value) / 2
- Mean = (1 + 99) / 2
- Mean = 100 / 2
- Mean = 50
Final Answer: Mean = 50
Q12. Find The Mean Of The First 50 Multiples Of 4.
The mean of the first 50 multiples of 4 is 102.
- First multiple = 4
- 50th multiple = 4 × 50 = 200
- Mean = (4 + 200) / 2
- Mean = 204 / 2
- Mean = 102
Final Answer: Mean = 102
Q13. If Every Value In A Collection Increases By 10, What Happens To The Mean?
The mean also increases by 10.
Adding the same number to every observation shifts the full collection equally. The relative position of the mean stays unchanged.
Example: If the original mean is 7.18, the new mean becomes 17.18.
Q14. If Every Value In A Collection Is Doubled, What Happens To The Mean?
The mean also gets doubled.
Multiplying each observation by the same number multiplies the mean by that number. This follows the distributive property.
Example: If the original mean is 7.18, the doubled collection has mean 14.36.
Finding Unknown Value Using Mean
Finding unknown value using mean starts with the total sum. Once the total is known, the missing or corrected value can be found directly.
The chapter uses this idea in wrestler weights, coconut harvests, and height correction questions.
Q15. How Do You Find An Unknown Value Using Mean?
An unknown value is found by using total sum = mean × number of values.
After finding the required total, subtract the known values. The remaining value gives the unknown observation.
Example: If 5 values have mean 9, their total is 45.
Q16. The Mean Of 10 Weights Is 39.2 Kg. Nine Weights Sum To 349 Kg. Find The Missing Weight.
The missing weight is 43 kg.
- Mean = 39.2 kg
- Number of players = 10
- Total weight = 39.2 × 10 = 392 kg
- Known weight total = 349 kg
- Missing weight = 392 - 349 = 43 kg
Final Answer: 43 kg
Q17. A Coconut Harvest Average Is 25.6 For 15 Trees. One Count Is 3 More Than Actual. Find The Correct Average.
The correct average harvest is 25.4 coconuts per tree.
- Wrong mean = 25.6
- Number of trees = 15
- Wrong total = 25.6 × 15 = 384
- Correct total = 384 - 3 = 381
- Correct mean = 381 / 15 = 25.4
Final Answer: 25.4 coconuts per tree
Q18. The Average Height Of 24 Students Is 150.2 Cm With Shoes. Shoes Add 1 Cm. Find The Correct Average.
The correct average height is 149.2 cm.
- Given average with shoes = 150.2 cm
- Shoe height added to every student = 1 cm
- Correct average = 150.2 - 1
- Correct average = 149.2 cm
Final Answer: 149.2 cm
Q19. The Mean Of 8, 13, 10, 4, 5, 20, y, 10 Is 10.375. Find y.
The value of y is 13.
- Number of values = 8
- Mean = 10.375
- Total sum = 10.375 × 8 = 83
- Known sum = 8 + 13 + 10 + 4 + 5 + 20 + 10 = 70
- y = 83 - 70 = 13
Final Answer: y = 13
Q20. The Mean Of 15 Values Is 134. Find The Sum Of The Data.
The sum of the data is 2010.
- Mean = Sum / Number of values
- 134 = Sum / 15
- Sum = 134 × 15
- Sum = 2010
Final Answer: Sum = 2010
Median Class 8 Maths Important Questions
Median is about order, not total. Students must arrange the values before finding the middle.
When the number of observations is even, the median is the mean of the two middle values.
Q21. What Is Median In Class 8 Maths?
Median is the middle value when observations are arranged in order.
It divides the collection into two equal parts. Equal numbers of values lie before and after the median.
Example: In 4, 7, and 9, the median is 7.
Q22. Find The Median Of 8, 10, 19, 23, 26, 34, 40, 41, 41, 48, 51, 55, 70, 84, 91, 92.
The median is 41.
- Number of values = 16
- Middle positions = 8th and 9th
- 8th value = 41
- 9th value = 41
- Median = (41 + 41) / 2 = 41
Final Answer: Median = 41
Q23. What Happens To Median When A Value Greater Than The Median Is Added?
The median may increase when a value greater than the median is added.
The added value can shift the middle position to the right. The chapter shows median changing from 8 to 9.5 after adding 11.
Example: If the middle values become 8 and 11, the new median is 9.5.
Q24. What Happens To Median When A Value Less Than The Median Is Added?
The median may decrease when a value less than the median is added.
The added value can shift the middle position to the left. The final change depends on the number and placement of values.
Example: Adding a small value before the middle can lower the median.
Q25. Can Median Remain Unchanged After Adding A Value?
Yes, median can remain unchanged after adding a value.
It stays unchanged when the middle position still gives the same value. This depends on the ordered list.
Example: Adding 41 to a list where 41 remains central can keep the median at 41.
Q26. Which Values Can p Take If The Median Of 12, 47, 8, 73, 18, 35, 39, 8, 29, 25, p Is 29?
The value p can be 25 or 29.
- There are 11 values, so the median is the 6th value.
- Fixed values in order: 8, 8, 12, 18, 25, 29, 35, 39, 47, 73.
- For 29 to remain 6th, p must not push 29 to the 7th position.
- p can be 25 or 29 from the given options.
Final Answer: p = 25 or p = 29
Mean And Median With Frequencies Class 8
Frequency means how many times a value occurs. Students should not average only the distinct values.
The chapter’s family-size example shows why repeated observations must be counted properly.
Q27. How Do You Find Mean From A Frequency Table?
Mean from a frequency table is found by multiplying each value by its frequency.
Then add all products and divide by the total frequency. This counts every repeated observation.
Formula: Mean = Sum of value × frequency / Total frequency
Q28. Find The Mean Family Size From This Frequency Table.
| Family Size |
Frequency |
| 3 |
3 |
| 4 |
11 |
| 5 |
9 |
| 6 |
7 |
| 7 |
3 |
| 8 |
1 |
| 9 |
1 |
| 10 |
1 |
The mean family size is 5.22.
- Sum of products = 3×3 + 4×11 + 5×9 + 6×7 + 7×3 + 8×1 + 9×1 + 10×1
- Sum of products = 9 + 44 + 45 + 42 + 21 + 8 + 9 + 10
- Sum of products = 188
- Total frequency = 36
- Mean = 188 / 36 = 5.22
Final Answer: Mean family size = 5.22
Q29. Find The Median Family Size From The Same Frequency Table.
The median family size is 5.
- Total frequency = 36
- Middle positions = 18th and 19th
- Cumulative frequency up to 3 = 3
- Cumulative frequency up to 4 = 14
- Cumulative frequency up to 5 = 23
- The 18th and 19th values are both 5
Final Answer: Median family size = 5
Q30. Why Is 6.5 Not The Correct Mean For The Family-Size Table?
6.5 is wrong because it averages only the distinct family sizes.
The value 4 occurs 11 times, while 10 occurs once. Their frequencies are not equal.
Correct calculation uses repeated values, giving mean = 188 / 36 = 5.22.
Dot Plot Class 8 Maths Questions
A dot plot places observations as dots over a number line. It makes balance, clusters, spread, and repeated values visible.
This chapter uses dot plots to explain mean, median, missing values, and changing data.
Q31. What Is A Dot Plot In Class 8 Maths?
A dot plot is a number-line display where each dot represents one observation.
Repeated observations appear as stacked dots. This makes frequency visible.
Example: Four students riding cycles twice appear as four dots above 2.
Q32. How Does A Dot Plot Help In Finding Mean?
A dot plot helps show mean as the balance point.
The total distance of dots on the left equals the total distance on the right. This explains why mean is a centre.
Example: Dots at 3 and 7 balance at 5.
Q33. How Can A Missing Dot Be Found If The Mean Is Given?
A missing dot can be found by using the total sum required by the mean.
- Multiply mean by total number of observations.
- Add the visible observations.
- Subtract visible sum from required sum.
- Place the missing dot at the remaining value.
Example: If mean is 9 for 5 dots, total sum must be 45.
Q34. How Do You Check Whether 17 Is The Average From A Dot Plot?
17 is the average only if the total sum equals 17 times the number of dots.
- Count all dots.
- Multiply 17 by the number of dots.
- Add all plotted values.
- Compare both totals.
Final Answer: 17 is the mean only when both totals match.
Spreadsheet Class 8 Maths Questions
Spreadsheets are digital tables made of rows, columns, and cells. They help calculate totals and averages using formulas.
The chapter uses Sudhakar’s class marks to explain cell references, ranges, SUM, and AVERAGE.
Q35. What Is A Spreadsheet In Class 8 Maths?
A spreadsheet is a digital table made of cells arranged in rows and columns.
Cells can contain text, numbers, or formulas. Each cell has a name based on its column and row.
Example: Farooq’s Mathematics marks are in cell E5 in the chapter table.
Q36. What Is A Cell Reference In A Spreadsheet?
A cell reference identifies a cell using its column letter and row number.
B3 means column B and row 3. A range uses the first and last cells.
Example: B3:G3 means all cells from B3 to G3.
Q37. Which Formula Calculates Nagesh’s Total Marks From B3 To G3?
The formula is =SUM(B3:G3).
It adds all marks in cells B3 to G3. This saves time when many subjects are listed.
Example: The chapter uses this format to calculate total marks across subjects.
Q38. Which Formula Calculates Gowri’s Average Marks From B7 To D7?
The formula is =AVERAGE(B7:D7).
It calculates the average of values from B7 to D7. This range includes Gowri’s marks in three subjects.
Example: =AVERAGE(B7:D7) finds the mean of Odia, Telugu, and English marks.
Line Graph Class 8 Maths Important Questions
Line graphs show how values change across time. The chapter uses them for temperature, space launches, rainfall, births, salt prices, sleep time, sunrise, and moonrise.
Students must read axes, scale, markers, rise, fall, and steepness.
Q39. What Is A Line Graph In Class 8 Maths?
A line graph represents data points joined by line segments.
It is generally used to visualise change over time. Months, years, or ages often appear on the horizontal axis.
Example: Monthly maximum temperature can be shown through a line graph.
Q40. How Should Students Read A Line Graph?
Students should identify the title, axes, scale, markers, and pattern.
- Read what the horizontal axis shows.
- Read what the vertical axis shows.
- Check the scale.
- Find the highest and lowest points.
- Compare rise, fall, and flat sections.
Final Answer: Only graph-supported observations are valid.
Q41. What Does A Steeper Line Segment Mean?
A steeper line segment shows a greater change between two points.
A steep rise shows quick increase. A steep fall shows quick decrease.
Example: In the space-launch graph, steeper years show larger increases.
Q42. Why Is A Line Graph Better Than A Column Graph For Many Years?
A line graph is better when many time points must be compared.
A column graph can become crowded with many bars. A line graph keeps the trend clearer.
Example: A 13-year graph with 4 categories would need 52 bars.
Q43. What Can Students Infer From The Kerala And Punjab Temperature Graph?
Students can infer that Punjab’s temperature varies more than Kerala’s.
Punjab rises from January to June and falls after September. Kerala stays mostly flat through the year.
Example: Punjab reaches about 38°C, while Kerala peaks around 33°C.
Q44. What Can Students Infer From A Rainfall Line Graph?
Students can identify peak rainfall months, dry months, and city-wise patterns.
West coast cities like Udupi, Mumbai, and Kovalam show strong rainfall around June to August. Rameswaram gets more rain around October to December.
Example: January to March are low-rainfall months for the listed cities.
Q45. How Can A Sleep-Time Line Graph Be Read?
A sleep-time line graph shows how average sleep changes with age.
The chapter shows about 9.5 hours for 6-year-olds. It falls near 8 hours between ages 30 and 50.
Example: After 50, average sleep time rises to about 8.5 hours.
Tales By Dots And Lines Questions And Answers On Infographics And Activity Strips
Visual information can appear through maps, colour scales, and strips. These formats need careful observation before answering.
The chapter uses a rice-wheat preference map and Manoj’s 48-box daily activity strips.
Q46. What Is An Infographic In Tales By Dots And Lines Class 8?
An infographic presents information through visuals, colours, labels, and scales.
It helps compare values quickly. A colour scale tells what each shade represents.
Example: The chapter uses an infographic to compare rice and wheat preference across states.
Q47. What Does A Value Of +100 Mean In The Rice-Wheat Infographic?
A value of +100 means the strongest preference towards rice in that comparison.
It does not mean wheat is never consumed. It shows the highest difference between rice and wheat consumption.
Example: The scale compares preference, not absolute eating habits.
Q48. What Is An Activity Strip In Class 8 Maths?
An activity strip records a day through equal time boxes.
The chapter uses 48 boxes for 24 hours. Each box represents 30 minutes.
Example: Colours can show sleep, food, study, travel, exercise, hobbies, and family time.
Q49. What Can A 48-Box Activity Strip Show?
A 48-box activity strip shows how a person spends one full day.
It can show school hours, sleep time, travel time, lunch break, and leisure time. Different colours mark different activities.
Example: A long single-colour stretch can show sleep duration.
Q50. Why Does The Chapter Use Activity Strips?
The chapter uses activity strips to show time distribution visually.
Students can compare weekdays, holidays, and adult routines. The strip turns time use into a visible pattern.
Example: A school day strip usually has more study blocks than a vacation strip.
Mean Median Questions With Answers Class 8
These questions combine calculation and reasoning. Students should identify whether the problem needs sum, order, frequency, or visual interpretation.
The same chapter asks students to justify whether statements are always true, sometimes true, or never true.
Q51. Give Three Numbers Whose Mean Is 8.
One possible set is 6, 8, and 10.
- Sum = 6 + 8 + 10 = 24
- Number of values = 3
- Mean = 24 / 3
- Mean = 8
Final Answer: 6, 8, 10
Q52. Give Four Numbers Whose Median Is 15.5.
One possible set is 10, 15, 16, and 20.
- Ordered data = 10, 15, 16, 20
- Middle values = 15 and 16
- Median = (15 + 16) / 2
- Median = 15.5
Final Answer: 10, 15, 16, 20
Q53. Give Five Numbers Whose Mean Is 13.6.
One possible set is 10, 12, 14, 15, and 17.
- Required total = 13.6 × 5
- Required total = 68
- Sum = 10 + 12 + 14 + 15 + 17
- Sum = 68
Final Answer: 10, 12, 14, 15, 17
Q54. Is The Average Of Two Even Numbers Always Even?
No, the average of two even numbers is sometimes even.
Example: Average of 2 and 6 is 4, which is even. Average of 2 and 4 is 3, which is odd.
Final Answer: Sometimes true
Q55. Is The Average Of Any Two Multiples Of 5 Always A Multiple Of 5?
No, it is sometimes a multiple of 5.
Example: Average of 5 and 15 is 10, a multiple of 5. Average of 5 and 10 is 7.5.
Final Answer: Sometimes true
Q56. Is The Average Of Any Five Multiples Of 5 Always A Multiple Of 5?
Yes, the average of any five multiples of 5 is a multiple of 5 when the quotient sum is divisible by 5.
For example, 5, 10, 15, 20, and 25 have mean 15. Another set may give a non-whole average.
Final Answer: Not always true unless the total divides evenly by 5
Class 8 Maths Important Questions Chapter-Wise