Start with the recap, study the fully worked examples, then use the practice problems to
check your understanding of Line Graph.
This page combines explanation, solved examples, and follow-up practice so you can move
from recognition to confident problem-solving in Statistics.
Concept Recap
A line graph is a chart that uses points connected by straight line segments to show how a quantity changes over time or across a continuous variable. The horizontal axis typically represents time, and the vertical axis represents the measured value.
Line graphs are like following a hiking trail on a map - they show the journey of a number over time. Going up means increasing, going down means decreasing. The steeper the line, the faster the change.
Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:Line Graph organizes data so the right pattern is visible without distorting the counts or scale.
Common stuck point:Students often know a procedure related to line graph but skip the recognition step: Am I choosing or interpreting a display that matches the type of data and the question being asked? That leads to a calculation or graph that looks reasonable but answers a different question.
Sense of Study hint:Ask: Am I choosing or interpreting a display that matches the type of data and the question being asked?
Worked Examples
Example 1
medium
A line graph shows weekly weight: 80,78,77,75,74 kg. Walk through finding total weight lost.
Answer
6 kg
First step
1
Start: 80 kg, end: 74 kg.
See the full worked solution + why-it-works coaching
Setup·Key insight·Why it works·Common pitfall·Connection
A line graph shows a chemical's concentration each minute: 100,80,64,51.2,41.0. What is the constant decay factor per minute?
Example 3
easy
The table shows the temperature at noon each day for five days: Monday 12°C, Tuesday 14°C, Wednesday 11°C, Thursday 15°C, Friday 13°C. Describe how you would draw a line graph to display this data.
Example 4
medium
A shop recorded weekly sales (in units) over 6 weeks: 40, 55, 50, 65, 60, 75. From the line graph of this data, identify (a) the overall trend and (b) the week with the largest increase in sales.
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
A line graph shows a plant's height: Day 1 = 4 cm, Day 2 = 7 cm. How much did it grow from Day 1 to Day 2?How much did the plant grow from Day 1 to Day 2?
Example 2
easy
On a line graph, sales were 20 units in Week 1 and 20 units in Week 2. Is the line segment rising, falling, or flat?Is the segment rising, falling, or flat?
Example 3
easy
A line graph of temperature reads 10 deg at noon and 6 deg at 1 PM. Did the temperature rise or fall?Did the temperature rise or fall?
Example 4
easy
A line graph shows website visits: Mon 50, Tue 80, Wed 80, Thu 110. On how many days did visits increase from the previous day?On how many days did visits increase from the previous day?
Example 5
easy
A line graph plots distance every hour: 0, 5, 10, 15 km. By how much does the distance increase each hour?By how much does the distance increase each hour?
Example 6
easy
Which data is best shown by a line graph: (A) favorite fruit of 30 students, (B) a city's population each year from 2000 to 2010?
Example 7
easy
A line graph shows profit: Jan 200,Feb350. What was the total profit over the two months?What was the total profit over the two months?
Example 8
easy
A line graph rises steeply from Week 1 to Week 2, then rises gently from Week 2 to Week 3. In which interval did the value grow faster?
Example 9
medium
A line graph shows a runner's distance: 0 min = 0 km, 10 min = 2 km, 20 min = 6 km, 30 min = 6 km. What was the average speed over the first 20 minutes in km per minute?What was the average speed over the first 20 minutes?
Example 10
medium
A line graph of account balance reads: Day 0 = 100,Day1=130, Day 2 = 90,Day3=120. What is the net change from Day 0 to Day 3?What is the net change from Day 0 to Day 3?
Example 11
medium
A line graph shows monthly rainfall (cm): Jan 4, Feb 6, Mar 3, Apr 7, May 5. What is the mean monthly rainfall?What is the mean monthly rainfall?
Example 12
medium
A line graph of stock price peaks at 80inMarchandbottomsat50 in June. What is the percent decrease from peak to bottom?What is the percent decrease from peak to bottom?
Example 13
medium
Two line graphs are drawn on the same axes. Line A is at 30 in Week 1 and 60 in Week 4. Line B is at 50 in Week 1 and 50 in Week 4. In which week do the two lines cross if A rises steadily and B is flat?
Example 14
medium
A line graph shows energy use (kWh): Mon 12, Tue 15, Wed 9, Thu 18, Fri 6. What is the range of daily energy use?What is the range of daily energy use?
Example 15
medium
A line graph shows quarterly revenue (\$1000s): Q1 40, Q2 50, Q3 45, Q4 65. Which quarter-to-quarter change was the largest in size?Which quarter-to-quarter change was the largest in size?
Example 16
medium
A line graph tracks a balloon's altitude: it rises from 0 to 300 m in 5 min, then descends to 100 m over the next 5 min. What is the average rate of change over the full 10 minutes?What is the average rate of change over the full 10 minutes?
Example 17
medium
A line graph shows daily sales for a week and is described as 'trending upward overall.' Sales were: 10, 12, 11, 14, 13, 16, 15. Is the median greater than, less than, or equal to the first value?Is the median greater than, less than, or equal to the first value?
Example 18
challenge
A line graph shows distance vs time as three straight segments: 0 to 10 km over hour 1, flat at 10 km during hour 2, then 10 to 40 km over hour 3. Over which single hour was the average speed highest, and what was it?Over which single hour was the average speed highest?
Example 19
challenge
A line graph of a tank's water level (liters) is linear: at t=2 min it reads 30 L, at t=6 min it reads 50 L. Using the constant rate, what was the level at t=0?Using the constant rate, what was the level at t = 0 minutes?
Example 20
challenge
Two cities' temperatures are on one line graph. City X: 5, 8, 11, 14 deg over four days (slope steady). City Y starts at 20 deg and falls 2 deg per day. On which day do they first read the same temperature?
Example 21
easy
A line graph shows daily steps: Mon 5000, Tue 7000. By how many steps did Tuesday increase over Monday?
Example 22
easy
A line graph shows weights over 3 months: 50,48,47 kg. Is the overall trend rising or falling?
Example 23
easy
A line graph rises from 10 at t=0 to 25 at t=5. What is the change in value?
Example 24
easy
A line graph shows temperatures every hour: 20,22,25,25,23. How many hours had a temperature higher than 22?
Example 25
easy
A line graph plots earnings: Week 1 \$80, Week 2 \$100, Week 3 \$60. What was the average weekly earning?
Example 26
easy
A line graph of pages read: Day 1 = 10, Day 2 = 15, Day 3 = 25. In which interval did the slope (pages per day) double?
Example 27
medium
A line graph shows a car's distance: t=0: 0 km, t=2 h: 120 km. What is the average speed over the interval?
Example 28
medium
A line graph shows monthly visitors (thousands): 4,6,7,9,14. What is the percent increase from month 1 to month 5?
Example 29
medium
A line graph of cumulative donations: \$200, \$350, \$420, \$600. How much was donated between the second and fourth points?
Example 30
medium
A line graph plots monthly temperature (\degree C): 5,8,14,19,22,24. What is the mean monthly temperature?
Example 31
medium
A line graph shows a runner's speed (m/s) every 5 s: 0,2,4,6,8. What is the speed change per second?
Example 32
medium
A line graph dips: 50,40,30,50,60. What is the value at the lowest point?
Example 33
medium
A line graph shows two lines for sales of A and B over 5 months. Where A is above B, A outsells B. If A's values are 20,30,40,50,60 and B's are 25,30,50,45,55, in how many months does A outsell B (strictly above)?
Example 34
medium
A line graph shows house price ($ thousands) over years: 200,220,240,260. If the linear trend continues, what is the predicted value for the next year?
Example 35
hard
A line graph plots a population (thousands): 10 in year 0, doubling every 5 years. What is the value at year 20?
Example 36
hard
A line graph shows stock value: \$50 in Jan, peaks at \$80 in April, drops to \$40 in Sept. What is the percent change from peak to Sept?
Example 37
hard
A line graph shows temperatures: 10,12,15,13,14. What is the median? What is the mean (to one decimal)?
Example 38
hard
A line graph shows daily revenue ($): 200,250,220,260,270. What is the largest single-day percent increase (to nearest percent)?
Example 39
hard
A line graph plots cumulative distance over time: 0,5,12,20,30 km at t=0,1,2,3,4 hours. In which 1-hour interval was speed greatest?
Example 40
challenge
A line graph shows a balance: $1000 at month 0, growing 5% per month. What is the balance at month 3 (rounded to nearest dollar)?
Example 41
medium
A city recorded the average monthly rainfall (in mm) from January to June: 30, 25, 40, 55, 70, 85. Between which two consecutive months did rainfall increase the most?
Example 42
hard
Two towns recorded their noon temperatures (°C) over 4 days. Town A: 18, 22, 19, 25. Town B: 20, 21, 20, 21. Both are plotted on the same line graph. Which town shows greater variability and how can you tell from the graph?