Graphs

Line graph and trend-based data questions

31 practice questionsPage updated 25 Sept 2026Reviewed by AISEA Editorial DeskPractice questions

Line graphs show how a quantity changes across an ordered sequence, most often time. In aptitude exams, the points may represent temperature, rainfall, prices, usage, production, savings or revenue. Read the title, axes, scale, units and time intervals first. Then separate the question's required operation from the visual trend: a rising line does not by itself give a percentage increase, average or rate.

Key formulas and rules

6 rules

Percentage change: $\%\Delta = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100$

Average value: $\bar{x} = \frac{\sum x_i}{n}$

Average rate of change (slope): $\text{Rate} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\Delta y}{\Delta t}$

Range: $\text{Range} = \text{Maximum Value} - \text{Minimum Value}$

Percentage-point change: $\Delta\text{pp} = \text{New Percentage} - \text{Old Percentage}$

Cumulative total: $\text{Total} = \sum_{i=1}^n x_i$ across all observed periods

Key concepts

Read the graph metadata

Start with the title, horizontal axis, vertical axis, scale intervals and unit. A point at 50 may mean 50 people, 50 thousand users or 50 millimetres. Check whether the periods are days, months, quarters or years, and whether the values are counts, rates, percentages or cumulative totals.

Worked examples

Example 1

A line graph gives daily temperatures in degrees Celsius: Monday 28, Tuesday 32, Wednesday 35, Thursday 30, Friday 29, Saturday 33 and Sunday 31. What is the average temperature?

Solution

Step 1: Sum the seven observations = 28 + 32 + 35 + 30 + 29 + 33 + 31 = 218.
Step 2: Average = 218 / 7 = 31.142857... degrees Celsius.
Answer: Approximately 31.14 degrees Celsius, or 31 degrees Celsius to the nearest whole degree.

Example 2

Monthly rainfall is 50, 40, 30, 20, 60, 120, 200, 180, 100, 80, 60 and 40 millimetres from January to December. What is the ratio of the wettest month to the driest month?

Solution

Step 1: The maximum is 200 millimetres in July.
Step 2: The minimum is 20 millimetres in April.
Step 3: Ratio = 200 : 20 = 10 : 1.
Answer: 10 : 1.

Example 3

A line graph shows a stock price of 100, 120, 110, 130, 125 and 140 rupees over six months. What is the largest percentage drop from one month to the next?

Solution

Step 1: The only drops are 120 to 110 and 130 to 125.
Step 2: Drop after 120 = (10 / 120) × 100 = 8.333...%.
Step 3: Drop after 130 = (5 / 130) × 100 = 3.846...%.
Step 4: Compare the percentages, not just the absolute drops.
Answer: Approximately 8.33%, from the second month to the third.

Example 4

Electricity bills for May, June and July are ₹900, ₹1,200 and ₹1,400. What is the average bill for these three months?

Solution

Step 1: Total = ₹900 + ₹1,200 + ₹1,400 = ₹3,500.
Step 2: Number of months = 3.
Step 3: Average = ₹3,500 / 3 = ₹1,166.666... .
Answer: Approximately ₹1,166.67, or ₹1,167 to the nearest rupee.

Example 5

A stock index moves from 15,000 on Day 1 to 15,900 on Day 5. What is the percentage return from Day 1 to Day 5?

Solution

Step 1: Increase = 15,900 − 15,000 = 900.
Step 2: Percentage return = (900 / 15,000) × 100 = 6%.
Answer: 6%.

Example 6

Daily active users rise from 50 thousand in Week 1 to 95 thousand in Week 6. What is the percentage increase?

Solution

Step 1: Increase = 95 − 50 = 45 thousand users.
Step 2: Use the starting value as the denominator: (45 / 50) × 100 = 90%.
Answer: 90%.

Example 7

A line graph gives daily sales revenue in thousands of rupees: Monday 25, Tuesday 30, Wednesday 28, Thursday 35, Friday 32, Saturday 40 and Sunday 38. What is the total revenue for the week?

Solution

Step 1: Add the seven separate daily amounts: 25 + 30 + 28 + 35 + 32 + 40 + 38 = 228.
Step 2: The unit is thousand rupees.
Answer: ₹228 thousand, or ₹228,000.

Example 8

A website's bounce rate falls from 60% in Week 1 to 35% in Week 6. Find the reduction in percentage points and the relative percentage reduction.

Solution

Step 1: Percentage-point reduction = 60% − 35% = 25 percentage points.
Step 2: Relative reduction uses the original 60% as the denominator: (25 / 60) × 100 = 41.666...%.
Answer: 25 percentage points, which is a relative reduction of approximately 41.67%.

Histograms, Frequency Polygons, and Time Series GraphsOpenStax · Checked 1 Sep 2026Supports: time-series ordering, trend interpretation and graph construction

Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar GraphsOpenStax · Checked 1 Sep 2026Supports: line graphs, axes and using graphs to identify trends

Measures of the Center of the DataOpenStax · Checked 1 Sep 2026Supports: arithmetic mean, median and frequency-aware averages

Graphs

Key formulas and rules

Key concepts

Read the graph metadata

Time order creates the trend

Describe trends precisely

Absolute change versus percentage change

Averages and totals

Rates and slopes

Compare drops, returns and ratios

Check scale, rounding and missing context

Worked examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Sources and review notes

Ready to test your understanding?

Key formulas and rules

Key concepts

Read the graph metadata

Time order creates the trend

Describe trends precisely

Absolute change versus percentage change

Averages and totals

Rates and slopes

Compare drops, returns and ratios

Check scale, rounding and missing context

Worked examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Sources and review notes

Ready to test your understanding?

Keep building the same skill family.