MathsCBSE Class 8 · Tales by Dots and Lines

Spreadsheets and Line Graphs for Class 8

Q: What is the difference between a column graph and a line graph?

A column graph draws separate columns for each value; a line graph joins the points to show how the quantity changes in time. For many data points a line graph is lighter and clearer.

Q: How can I find a total in a spreadsheet without typing each cell?

Use =SUM(first:last) with the range of cells.

Q: Why might the lines of countries not add up to the world total?

Because other countries are not shown in the graph.

Q: Can I read exact values from a line graph?

Only approximately unless values are marked; say "about" when you estimate.

Updated 17 October 2026 · Fact-checked

A spreadsheet is a grid of cells named by column letter and row number (E5), where a formula such as =SUM(B3:G3) or =AVERAGE(B7:D7) works on a range Start:End. A line graph connects data points taken over time, so its steepness shows how fast the quantity changes. Read a graph in two steps: observe the organisation, scale and patterns, then infer and interpret.

Cells are named by column then row, a range like B3:D3 feeds a formula, and a steeper line segment means faster change.

Illustration drawn for QuestionBuddy.

Understand Spreadsheets and Line Graphs

Spreadsheets. A spreadsheet is like a digital notebook of rows and columns of boxes called cells. A cell can hold text, numbers or a formula.

Cells are named with the column header (A, B, C, ...) and row header (1, 2, 3, ...): the cell in column E, row 5 is E5.
A row or column range is written Start:End. In a marks sheet, one student's marks across six subjects in row 3 may be B3:G3; marks in three subjects of row 7 may be B7:D7; a column range looks like C2:C9.
Formulas begin with $=$ and compute on a range: =SUM(B3:G3) gives the total of the cells B3 to G3 and =AVERAGE(B7:D7) gives their average. A formula typed once can be copied to other rows or columns to get all totals and averages quickly.

Spreadsheets save time with large tables, such as the marks of a whole class.

Line graphs. In a line graph, points for successive values (for example the months of a year) are marked and connected by line segments. Line graphs are generally used to visualise data across time, and they show trends. Compare a clustered-column graph (separate columns for each state each month) with a line graph of the same data: the line graph shows the changes more directly. When there are very many data points, a smooth-looking line graph (like a graph of average sleep time from age 6 to 75, with 70 points) is lighter and clearer than 70 columns.

Two steps to read a graph.
1. *Observe what is given:* how the graph is organised (axes, units, the colours and marks for each series, the scale), and what patterns it shows (rises, falls, flat parts, peaks, lows).
2. *Infer and interpret:* turn each observation into a statement, check what the data does and does not say, and summarise.

Steepness. The steeper a line segment, the greater the change in that interval: for the USA, an increase that looks steeper between 2022 and 2023 than between 2023 and 2024 was bigger. A flat segment shows no change. Compare two lines by the size of the rise over the same time.

Where does the data come from? Knowing how the data is collected helps in understanding its scope and limits. For example, the monthly maximum temperature for a state is the maximum of the readings from several weather stations. A line that does not add up to a total shows that some groups are missing from the graph.

Other displays. The chapter also shows an infographic (a coloured map where shade shows how much rice or wheat is preferred, on a scale from -100 to +100) and a 48-box day strip (each box is a 30-minute interval from midnight to midnight) to record activities.

The mean and median of data are on the previous topic page of this chapter.

Spreadsheets and Line Graphs: formulas to remember

Cell reference: $column letter + row number, e.g. E 5$; The cell in column E, row 5.
Range: $Start:End, e.g. B 3 : G 3$; Cells from B3 to G3 along row 3.
Sum formula: $= SUM(B3:G3)$; Total of the cells in the range.
Average formula: $= AVERAGE(B7:D7)$; Mean of the cells in the range.
Rate of change: $\frac{change in value}{change in time}$; Steeper segment means a larger rate.

How to solve Spreadsheets and Line Graphs questions

Follow these steps for spreadsheet and line graph questions.

1For a spreadsheet, locate the row and column; name the cell by column letter then row number.
2Write the range as Start:End and the formula with an equals sign, such as =SUM(...) or =AVERAGE(...).
3Compute the value by hand to check the formula, adding and dividing carefully.
4For a line graph, note the title, the axes, the unit and the scale before reading any values.
5Read values at the marked points and compute differences between consecutive points to find the largest rise or fall.
6Describe the trend in words (rising, falling, flat, peak, low), then give an interpretation, noting limits of the data.
7Compare lines by the change over the same interval, not only by the final value.

Spreadsheets and Line Graphs in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Spreadsheet formulas

Suppose a sheet records one student's marks in four subjects in cells B2, C2, D2 and E2 as 62, 75, 58 and 80.

Write the formulas for the total and the average and give their values.

Try it first, then show the solutionSolution

Total: =SUM(B2:E2) $= 62 + 75 + 58 + 80 = 275$ .
Average: =AVERAGE(B2:E2) $= 275 \div 4 = 68.75$ .

Answer: =SUM(B2:E2) gives 275; =AVERAGE(B2:E2) gives 68.75

Memory hook: A range runs from the first cell to the last cell of the row or column.

Reading a trend

Imagine a shop that records its monthly sales (in thousands of rupees) as January 40, February 48, March 45, April 60, May 72, June 66 and plots them on a line graph.

In which interval is the line steepest, and what is the percentage rise in that interval?

Try it first, then show the solutionSolution

Changes: $+ 8, - 3, + 15, + 12, - 6$ .
The steepest rise is March to April, $+ 15$ thousand.
Percentage rise $= \frac{15}{45} \times 100 \approx 33.3%$ .

Answer: March to April; about 33.3%

Memory hook: Steepness is the change between neighbouring points.

Tricks to remember Spreadsheets and Line Graphs

Short memory aids. Say each one aloud once, then use it on a question the same day.

Letter then number
Cells are named column letter first, then row number: E5 is column E, row 5.
Use it when: Reading and writing cell references.
Start colon End
A range goes from its first cell to its last cell, with a colon between.
Use it when: SUM and AVERAGE formulas.
Lines show time
Use a line graph when the quantity changes over time and you want to see the trend.
Use it when: Choosing a graph.
Steeper means faster
The steeper the line, the larger the change in that time interval.
Use it when: Comparing intervals.

Spreadsheets and Line Graphs: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Writing a formula · 1 mark · MCQBoard level

In a spreadsheet, the total marks of the student whose marks are in cells B4 to F4 can be found by typing: (a) =SUM(B4:F4) (b) =B4+F4 (c) SUM(B4,F4) (d) =AVERAGE(B4:F4)

Try it first, then show the solutionSolution

A total over a range needs the sum function and the range B4:F4, starting with an equals sign.

Answer: (a) =SUM(B4:F4)

Example 2: Evaluating formulas · 2 marks · Short answerBoard level

A student's marks in cells B2, C2, D2 and E2 are 62, 75, 58 and 80. State the formulas for the total and the average of her marks and the values they give.

Try it first, then show the solutionSolution

=SUM(B2:E2) $= 62 + 75 + 58 + 80 = 275$ . (1 mark)
=AVERAGE(B2:E2) $= 275 \div 4 = 68.75$ . (1 mark)

Answer: =SUM(B2:E2) = 275; =AVERAGE(B2:E2) = 68.75

Example 3: Reading a sales line graph · 3 marks · Short answerHarder board level

Monthly sales of a shop (in thousands of rupees) were: January 40, February 48, March 45, April 60, May 72, June 66. Find the interval of the largest rise, the percentage rise in it, and the average monthly sales.

Try it first, then show the solutionSolution

Changes between months: $+ 8, - 3, + 15, + 12, - 6$ . The largest rise is from March to April, $+ 15$ . (1 mark)
Percentage rise $= \frac{15}{45} \times 100 \approx 33.3%$ . (1 mark)
Average $= \frac{40 + 48 + 45 + 60 + 72 + 66}{6} = \frac{331}{6} \approx 55.17$ thousand rupees. (1 mark)

Answer: March to April; about 33.3%; average about 55.17 thousand rupees

Example 4: Comparing two lines · 3 marks · Short answerHarder board level

The average monthly temperatures (in degrees Celsius) from January to April are 12, 17, 24, 31 for city P and 24, 25, 27, 28 for city Q. Which graph is steeper overall, what is the average rise per month for each, and in which month is the biggest one-month rise for P?

Try it first, then show the solutionSolution

P rises $31 - 12 = 19$ over 3 monthly intervals: $\frac{19}{3} \approx 6.3$ per month. Q rises $28 - 24 = 4$ : $\frac{4}{3} \approx 1.3$ per month. (1 mark)
P's line is much steeper. (1 mark)
P's monthly rises are $5, 7, 7$ ; the biggest one-month rise is 7, from February to March (and again March to April, equal). (1 mark)

Answer: P is steeper: about 6.3 against 1.3 degrees per month; the biggest one-month rise for P is 7 degrees.

Example 5: A class marks sheet · 4 marks · Long answerHarder board level

Marks of 4 students in 5 subjects are in cells B2:F5. Row 2: 45, 38, 50, 41, 36; row 3: 40, 44, 35, 47, 42; row 4: 33, 29, 41, 38, 30; row 5: 49, 46, 44, 40, 45. (i) Write the formula for the total of the student in row 3 and its value. (ii) Write the formula for the class average in the subject in column D and its value. (iii) Find the average total score of the four students.

Try it first, then show the solutionSolution

(i) =SUM(B3:F3) $= 40 + 44 + 35 + 47 + 42 = 208$ . (1 mark)
(ii) =AVERAGE(D2:D5) $= \frac{50 + 35 + 41 + 44}{4} = \frac{170}{4} = 42.5$ . (1 mark)
(iii) Totals of rows 2 to 5: $210, 208, 171, 224$ (sum $813$ ). (1 mark)
Average total $= 813 \div 4 = 203.25$ . (1 mark)

Answer: (i) =SUM(B3:F3) = 208; (ii) =AVERAGE(D2:D5) = 42.5; (iii) 203.25

Where students lose marks in Spreadsheets and Line Graphs

The slips examiners see most often, and what to write instead.

Mistake: Writing a cell as row then column
Cells are named column letter first, then row number.
Wrong working
"Farooq's Mathematics score is in cell 5E."
Right working
The cell is E5.
Do this: Say the letter first.
Usually costs: 1 mark.
Mistake: Forgetting the equals sign in a formula
A formula must start with = or the spreadsheet treats it as text.
Wrong working
"SUM(B3:G3)"
Right working
=SUM(B3:G3).
Do this: Begin every formula with =.
Usually costs: 1 mark.
Mistake: Reading the final value instead of the change
Steepness depends on the change over an interval, not on how high the end is.
Wrong working
"City P is steeper because it ends at 31."
Right working
P rises by 19 in three months, Q by 4: P is steeper.
Do this: Subtract the start from the end for the same interval.
Usually costs: 1 to 2 marks.
Mistake: Giving conclusions the data cannot support
The graph shows what happened, not why, and may leave groups out.
Wrong working
"Sales rose because of the festival."
Right working
"Sales rose from 45 to 60 thousand between March and April." (Say what could be checked next.)
Do this: Separate the observation from the possible explanation.
Usually costs: 1 mark.

Exam tips

Name the axes and units at the start of an interpretation.
Use numbers in every statement (rose from 45 to 60 thousand), not just words like increased.
Compute differences between neighbouring points to compare steepness.
Write formulas with the equals sign and a Start:End range.
Mention one limit of the data, such as groups not shown, when asked for a conclusion.

Practice questions on Spreadsheets and Line Graphs

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · Assertion-reasonBoard level
Assertion (A): Line graphs are generally used to show how a quantity changes over time.
Reason (R): The points for successive times are joined by line segments, so the slope of each segment shows the rise or fall.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Hint
Why are the points joined?
Answer
(a). Joining the points makes each segment's steepness show the change between successive times.
Q2 · 2 marks · Very short answerBoard level
Write the spreadsheet formula for the average of the numbers in column C from row 2 to row 9. Also state what =SUM(B3:G3) computes.
Hint
Range is Start:End.
Answer
=AVERAGE(C2:C9). =SUM(B3:G3) gives the total of the cells B3, C3, D3, E3, F3 and G3 in row 3.
Q3 · 3 marks · Short answerHarder board level
The number of rainy days in a city in successive months is: April 2, May 4, June 12, July 20, August 18, September 11. (i) In which interval is the rise steepest? (ii) In which interval is the fall steepest? (iii) Find the total and the average number of rainy days per month.
Hint
Compute differences between neighbouring months.
Answer
Changes: $+ 2, + 8, + 8, - 2, - 7$ . (i) The rise is steepest from May to June and from June to July (both $+ 8$ ). (ii) The fall is steepest from August to September ( $- 7$ ). (iii) Total $= 2 + 4 + 12 + 20 + 18 + 11 = 67$ ; average $= 67 \div 6 \approx 11.17$ days.
Q4 · 4 marks · Long answerHOTS / competency
Two shops show yearly sales (in lakh rupees) for 5 years. Shop A: 100, 120, 140, 160, 180. Shop B: 100, 110, 121, 133.1, 146.41. (i) How much does each shop add each year? (ii) Find the percentage growth in each year for each shop. (iii) Describe how the two line graphs would look and what each trend means.
Hint
Shop B multiplies by 1.1 each year. Percentage growth uses the previous year as the base.
Answer
(i) A adds 20 every year. B adds 10, 11, 12.1 and 13.31 in successive years. (ii) A: $\frac{20}{100}, \frac{20}{120}, \frac{20}{140}, \frac{20}{160}$ , that is 20%, 16.7%, 14.3%, 12.5%. B: 10% every year. (iii) A's graph is a straight line (equal additions: linear growth), with its percentage growth slowing. B's graph curves upward (equal percentage growth: exponential growth), with the increases getting larger each year, and it ends below A after 4 years ( $146.41 < 180$ ) but would eventually overtake it.
Q5 · 4 marks · Case-basedHOTS / competency
Case study: a day strip has 48 boxes, each representing 30 minutes from midnight to midnight. A student records 15 boxes of sleep, 12 of school, 6 of study, 7 of play and 8 of other activities.
(i) Convert each activity to hours. (1 mark)
(ii) What percentage of the day is sleep? (1 mark)
(iii) Find the pie chart angles for sleep and school. (1 mark)
(iv) Which display, a pie chart or a line graph, suits this data and why? (1 mark)
Hint
Each box is half an hour; the whole day is 48 boxes.
Answer
(i) Sleep $7.5$ h, school $6$ h, study $3$ h, play $3.5$ h, other $4$ h (total 24 h). (ii) $\frac{15}{48} \times 100 = 31.25%$ . (iii) Sleep: $\frac{15}{48} \times 360 = 112. 5^{\circ}$ ; school: $\frac{12}{48} \times 360 = 9 0^{\circ}$ . (iv) A pie chart: the data shows how one whole day is shared among categories. A line graph shows change over time and is better for something like hourly activity level across the day.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.How is the cell in column E, row 5 written?Show answer
E5.
2.What does =SUM(B3:G3) do?Show answer
Adds the values in cells B3 to G3.
3.What are line graphs generally used for?Show answer
To show data across time.
4.What does a steep segment mean?Show answer
A large change in that time interval.
5.What are the two steps to read a graph?Show answer
Observe what is given; then infer and interpret.
6.What does each box of the day strip represent?Show answer
A 30-minute interval.

Spreadsheets and Line Graphs: frequently asked questions

What is the difference between a column graph and a line graph?

A column graph draws separate columns for each value; a line graph joins the points to show how the quantity changes in time. For many data points a line graph is lighter and clearer.

How can I find a total in a spreadsheet without typing each cell?

Use =SUM(first:last) with the range of cells.

Why might the lines of countries not add up to the world total?

Because other countries are not shown in the graph.

Can I read exact values from a line graph?

Only approximately unless values are marked; say "about" when you estimate.