CBSE Class 8 Mathematics Tales by Dots and Lines Very Short Answer Questions with Answers

Very Short Answer Questions

Question 1. Define the mean of a data set.
Answer:
The mean is the sum of all the values divided by the number of values. It is the balance point of the data.

Teacher's Note:
1. Mean = sum ÷ count.
2. It is also called the average.

Question 2. Define the median of a data set.
Answer:
The median is the middle value of the data arranged in order; for an even number of values it is the mean of the two middle values.

Teacher's Note:
1. Sort first, then find the middle.
2. The median depends on position, not on extreme values.

Question 3. Find the mean of 12, 15, 18 and 19.
Answer:
Sum = 12 + 15 + 18 + 19 = 64, so mean = 64 ÷ 4 = 16.

Teacher's Note:
1. Divide by the number of values, here 4.
2. 16 lies between 12 and 19, as it should.

Question 4. Find the median of 23, 16, 8, 19 and 12.
Answer:
In order: 8, 12, 16, 19, 23. With 5 values the median is the 3rd value, 16.

Teacher's Note:
1. Do not take the middle of the unsorted list (that would be 8).
2. For 5 values, the median is the 3rd.

Question 5. The mean is described as the balance point of the data. State what is equal on its two sides.
Answer:
The total of the distances of the values below the mean equals the total of the distances of the values above it.

Teacher's Note:
1. It is the distances that balance, not the number of values.
2. Think of a see-saw.

Question 6. Can a collection of data have two different balance points? Answer in one line.
Answer:
No. Any other point makes the distances on one side larger and on the other side smaller, so there is only one balance point.

Teacher's Note:
1. The mean of a data set is unique.
2. Moving the point upsets the balance.

Question 7. Which type of graph is best suited to show how a quantity changes over time?
Answer:
A line graph, because its joined points show clearly how the quantity rises or falls with time.

Teacher's Note:
1. Time goes along the horizontal axis.
2. Steep parts show fast changes.

Question 8. Name the two steps the chapter uses to read and understand a graph.
Answer:
Step 1: Identify what is given (organisation, axes, scale, patterns). Step 2: Infer and interpret what is given.

Teacher's Note:
1. Read the graph first; draw conclusions after.
2. Both steps are needed for a correct reading.

Question 9. Write the spreadsheet formula that gives the average of the numbers in the cells D2 to D23.
Answer:
=AVERAGE(D2:D23)

Teacher's Note:
1. The colon gives the whole range D2 to D23.
2. Every formula begins with an = sign.

Question 10. In a spreadsheet, name the cell that lies in column E and row 5.
Answer:
The cell is E5; the column letter is written before the row number.

Teacher's Note:
1. Letter for the column, number for the row.
2. This is like a grid reference.

Question 11. The median of a data set is 15. A new value of 6 is now included in it. Will the median increase or decrease?
Answer:
It will decrease (or at most stay the same), because 6 is below 15 and the middle position shifts towards the smaller values.

Teacher's Note:
1. A value below the median pulls the median down or leaves it unchanged.
2. It can never push the median up.

Question 12. Manoj records a whole day on a paper strip of 48 equal boxes. What length of time does each box stand for?
Answer:
A day has 24 × 60 = 1440 minutes and 1440 ÷ 48 = 30, so each box stands for 30 minutes.

Teacher's Note:
1. Change hours into minutes first.
2. Two boxes make one hour.

Question 13. The mean of 9 numbers is 14. Find the sum of these numbers.
Answer:
Sum = mean × number of values = 14 × 9 = 126.

Teacher's Note:
1. Knowing the mean and the count gives the total.
2. This is the key step in 'missing value' problems.

Question 14. The mean of 10 numbers is 32.4. Every number is increased by 7. Write the new mean.
Answer:
The total rises by 7 × 10 = 70, so the mean rises by 7. New mean = 32.4 + 7 = 39.4.

Teacher's Note:
1. Adding k to every value adds k to the mean.
2. The whole dot plot just shifts right.

Question 15. The mean of 6 numbers is 8.5. Every number is multiplied by 4. Write the new mean.
Answer:
The total becomes 4 times as large, so the mean does too: 8.5 × 4 = 34.

Teacher's Note:
1. Multiplying every value by k multiplies the mean by k.
2. Do not add 4; multiply by 4.

Question 16. If the mean of 5, 9, x and 16 is 10.5, find x.
Answer:
Total = 10.5 × 4 = 42 and 5 + 9 + 16 = 30, so x = 42 − 30 = 12.

Teacher's Note:
1. Total minus known values gives the unknown.
2. Check: (5 + 9 + 12 + 16) ÷ 4 = 10.5.

Question 17. Find the mean and the median of 3, 7, 7, 10, 12 and 15.
Answer:
Sum = 54, so mean = 54 ÷ 6 = 9. Median = \( \frac{7 + 10}{2} \) = 8.5.

Teacher's Note:
1. Six values: average the 3rd and 4th.
2. Mean and median need not be equal.

Teacher's Note:
1. Multiply each value by its frequency.
2. Divide by the total frequency, 20.

Teacher's Note:
1. Running totals locate the middle positions quickly.
2. No need to write out all 26 values.

Question 20. The mean marks of 20 students in a test were worked out as 36.5. Later it was found that one student’s marks had been entered 4 more than the marks actually scored. Find the correct mean.
Answer:
Recorded total = 36.5 × 20 = 730; true total = 730 − 4 = 726.
Correct mean = 726 ÷ 20 = 36.3 marks.

Teacher's Note:
1. Correct the total, then divide again.
2. The mean falls by 4 ÷ 20 = 0.2.

Question 21. Why is a line graph a better choice than a clustered-column graph for showing thirteen years of data for four different groups?
Answer:
A clustered-column graph would need 13 × 4 = 52 bars, which is crowded and hard to read; four lines show each group’s trend clearly.

Teacher's Note:
1. Fewer marks on the page means an easier read.
2. Lines make trends and crossings easy to see.

Question 22. In the 2023 monthly maximum temperature graph, which of the two states had the flatter trend, and what was that state’s peak monthly maximum temperature?
Answer:
Kerala had the flatter trend; its peak monthly maximum was about 33°C, in April.

Teacher's Note:
1. A flat line means little change through the year.
2. Punjab's line rises and falls much more.

Question 23. Why are differently shaped markers used for the different lines of a line graph?
Answer:
So that the lines can still be told apart when the graph is printed in black and white, and by readers who find it hard to distinguish colours.

Teacher's Note:
1. Shapes work even when colours do not.
2. This makes graphs accessible to everyone.

Question 24. The line graph of sleep duration against age looks like a smooth curve instead of a few joined segments. Why?
Answer:
It is drawn from about 80 closely spaced points, so the many short segments joining them look like one smooth curve.

Teacher's Note:
1. More points make a line graph look smoother.
2. It is still made of straight segments.

Question 25. A value smaller than the mean is removed from a collection. What happens to the mean? Give a reason.
Answer:
The mean increases. The removed value was pulling the balance point down, so the remaining values balance at a higher point.

Teacher's Note:
1. Removing a small value works like adding a large one.
2. Removing a large value lowers the mean.

Question 26. Using algebra, show in one or two lines that adding 3 to every one of n values raises the mean by 3.
Answer:
If \( \frac{x_1 + x_2 + \cdots + x_n}{n} = a \), the new mean is \( \frac{(x_1 + 3) + \cdots + (x_n + 3)}{n} = \frac{x_1 + \cdots + x_n}{n} + \frac{3n}{n} = a + 3 \).

Teacher's Note:
1. Adding 3 to n values adds 3n to the total.
2. Dividing 3n by n gives 3.

Question 27. A collection of data has mean 10. Name two values that can be included in it without changing the mean, and say why they work.
Answer:
For example 7 and 13. Their total is 20 = 2 × 10, so the sum grows by twice the mean while the count grows by 2, leaving the mean at 10.

Teacher's Note:
1. Any pair that adds up to 20 will work.
2. One value is 3 below the mean, the other 3 above: they balance.

Question 28. The mean of 7, 12, 9, 5, 6, 18, y and 11 is 10.25. Find y.
Answer:
Total = 10.25 × 8 = 82; known values add to 7 + 12 + 9 + 5 + 6 + 18 + 11 = 68.
y = 82 − 68 = 14.

Teacher's Note:
1. There are 8 values including y.
2. Mean × count = total.

Question 29. On the rice-versus-wheat infographic, a state is shaded at +100. A student concludes that this state eats no wheat at all. Is the conclusion correct? Explain briefly.
Answer:
No. +100 only means that the difference between per capita rice and wheat consumption is the largest, in favour of rice; some wheat is still eaten.

Teacher's Note:
1. The scale shows a difference, not an amount.
2. Always read what the colour scale measures.

Question 30. Before drawing conclusions from a graph, why is it useful to find out how the data was collected?
Answer:
It tells us the scope of the data and shows up limitations such as bias or missing information, so we know how far a conclusion can be trusted.

Teacher's Note:
1. Data from a small or one-sided sample can mislead.
2. Good conclusions depend on good data.