Plot and interpret time-series graphs | Oak National Academy - Free Printable
Educational worksheet: Plot and interpret time-series graphs | Oak National Academy. Download and print for classroom or home learning activities.
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Step-by-step solution for: Plot and interpret time-series graphs | Oak National Academy
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Show Answer Key & Explanations
Step-by-step solution for: Plot and interpret time-series graphs | Oak National Academy
To find the correct answer, we need to look at the graph and compare the water consumption for Saturday and Sunday at the specific times listed in the options.
Step 1: Understand the Graph
* The orange dashed line with red squares represents Saturday.
* The blue dashed line with blue diamonds represents Sunday.
* We are looking for the time where the amount of water used on Saturday is higher than the amount used on Sunday. This means the red square must be above the blue diamond at that time.
Step 2: Check Each Option
* Option A: 9:00 a.m.
* Look at 9:00 a.m. on the horizontal axis.
* The red square (Saturday) is at 50 litres.
* The blue diamond (Sunday) is at 25 litres.
* Since 50 is greater than 25, Saturday's consumption is higher here. This looks like the correct answer. Let's check the others to be sure.
* Option B: 2:00 p.m.
* Look at 2:00 p.m. on the horizontal axis.
* The red square (Saturday) is at 75 litres.
* The blue diamond (Sunday) is at 50 litres.
* Wait, let me re-examine the graph carefully. At 2:00 p.m., the red square is indeed at 75. The blue diamond is at 50. So Saturday is higher here too? Let me re-read the question or re-examine the plot points.
* Let's look closer at the plot points provided in the image.
* At 1:00 p.m., both lines meet at 75.
* At 3:00 p.m., the red square is at 75 and the blue diamond is at roughly 65-70? No, looking at the grid, at 3:00 p.m., the red square is at 75 and the blue diamond is lower, maybe around 60? Actually, looking at the trend:
* Sunday (blue): 1pm=75, 3pm=~60?, 5pm=100.
* Saturday (red): 1pm=75, 3pm=75, 5pm=60.
* Let's re-evaluate Option B (2:00 p.m.). The graph doesn't have a data point explicitly marked for 2:00 p.m. It has markers for 1:00 p.m. and 3:00 p.m. Usually, in these problems, you look at the marked data points. The options are 9:00 a.m., 2:00 p.m., 11:00 a.m., 5:00 p.m.
* Let's look at Option C: 11:00 a.m.
* Red square (Saturday) is at roughly 35-40 litres.
* Blue diamond (Sunday) is at 50 litres.
* Here, Sunday (50) is higher than Saturday (~38). So this is incorrect.
* Let's look at Option D: 5:00 p.m.
* Red square (Saturday) is at roughly 60 litres.
* Blue diamond (Sunday) is at 100 litres.
* Here, Sunday (100) is much higher than Saturday (60). So this is incorrect.
* Now let's go back to Option A: 9:00 a.m.
* Red square (Saturday) = 50.
* Blue diamond (Sunday) = 25.
* Saturday > Sunday. This is a valid candidate.
* Now let's go back to Option B: 2:00 p.m.
* There is no data point specifically plotted for 2:00 p.m. However, we can interpolate between 1:00 p.m. and 3:00 p.m.
* At 1:00 p.m.: Saturday = 75, Sunday = 75. They are equal.
* At 3:00 p.m.: Saturday = 75, Sunday ≈ 65 (it's below the 75 line).
* Between 1:00 p.m. and 3:00 p.m., the Saturday line stays flat at 75. The Sunday line goes down from 75 to ~65. Therefore, at any time between 1:00 p.m. and 3:00 p.m. (like 2:00 p.m.), the Saturday value (75) would be higher than the Sunday value (which is dropping below 75).
* So, technically, at 2:00 p.m., Saturday is also higher.
* Let's re-read the chart carefully. Is there a trick?
* At 9:00 a.m.: Sat (50) > Sun (25). Difference = 25.
* At 11:00 a.m.: Sun (50) > Sat (~38).
* At 1:00 p.m.: Sat (75) = Sun (75).
* At 3:00 p.m.: Sat (75) > Sun (~65).
* At 5:00 p.m.: Sun (100) > Sat (60).
* At 7:00 p.m.: Sat (~85) > Sun (50).
* The question asks: "At which of the following times was the water consumption on Saturday higher than on Sunday?"
* Options:
* A: 9:00 a.m. -> Yes (50 > 25)
* B: 2:00 p.m. -> Yes (Interpolated: 75 > ~70)
* C: 11:00 a.m. -> No (38 < 50)
* D: 5:00 p.m. -> No (60 < 100)
* Why are there two "Yes" answers? Let me look extremely closely at the 9:00 a.m. point.
* Saturday (Red): Exactly on the 50 line.
* Sunday (Blue): Exactly on the 25 line (halfway between 0 and 50).
* So 50 > 25 is definitely true.
* Let me look extremely closely at the 2:00 p.m. situation.
* The graph plots points at 1:00 p.m. and 3:00 p.m. It does not plot a point at 2:00 p.m. In many standardized tests, if a time isn't explicitly plotted, you might be expected to only judge the plotted points. However, 2:00 p.m. is an option.
* Let's look at the shape of the lines.
* From 1:00 p.m. to 3:00 p.m., the Saturday line is horizontal (constant at 75).
* From 1:00 p.m. to 3:00 p.m., the Sunday line goes from 75 down to roughly 65.
* Therefore, immediately after 1:00 p.m., Sunday drops below Saturday. So at 2:00 p.m., Saturday is higher.
* Is it possible I misread the graph for 9:00 a.m.?
* Red square at 9am is at 50.
* Blue diamond at 9am is at 25.
* Saturday is higher.
* Let's re-read the options. Maybe I missed something.
* A: 9:00 a.m.
* B: 2:00 p.m.
* C: 11:00 a.m.
* D: 5:00 p.m.
* Let's look at the visual representation again.
* At 9:00 a.m., the red dot is clearly above the blue dot.
* At 11:00 a.m., the blue dot is clearly above the red dot.
* At 5:00 p.m., the blue dot is clearly above the red dot.
* At 2:00 p.m., we have to infer. But wait, look at the line segments.
* Between 1pm and 3pm:
* Saturday is flat at 75.
* Sunday drops from 75 to ~65.
* So for the entire interval (1pm, 3pm], Saturday > Sunday.
* This implies both A and B are technically correct statements based on the graph. However, usually, these questions refer to the explicit data points shown. 9:00 a.m. is an explicit data point. 2:00 p.m. is NOT an explicit data point; it lies on the line segment between 1:00 p.m. and 3:00 p.m.
* In multiple-choice questions involving graphs, if one option corresponds to a clearly labeled data point where the condition is met, and another requires interpolation, the data point is often the intended answer. OR, perhaps I am misinterpreting the 2:00 pm value.
* Let's look at the Sunday line again. At 1:00 p.m., it is 75. At 3:00 p.m., it looks like it is at roughly 65. At 2:00 p.m., it would be around 70. Saturday is 75. So 75 > 70. It holds.
* Let's reconsider the 9:00 a.m. reading.
* Saturday: 50.
* Sunday: 25.
* Condition: Saturday > Sunday. True.
* Is there any reason A would be wrong? No.
* Is there any reason B would be wrong? Only if the question implies "at which recorded time". The x-axis labels are 9am, 11am, 1pm, 3pm, 5pm, 7pm. The options include 2pm, which is not a label. This suggests 2pm is a distractor or relies on interpolation.
* However, let's look at the other options again.
* C (11am): Sun > Sat. False.
* D (5pm): Sun > Sat. False.
* So it's between A and B.
* Let's look at the magnitude of difference.
* At 9am: Diff = 25.
* At 2pm: Diff ≈ 5-10.
* Often, the "best" answer is the most obvious one. 9:00 a.m. is a primary data point. 2:00 p.m. is intermediate.
* Let's check if I swapped the colors.
* Legend: Orange/Red dash = Saturday. Blue dash = Sunday.
* At 9am: Red (Sat) is 50. Blue (Sun) is 25. Sat > Sun. Correct.
* Let's check if there is a subtle detail. "Daily Water Consumption".
* Maybe the question meant "When was Sunday higher?" No, it says "Saturday higher".
* Let's assume the question refers to the specific data points plotted. The plotted points are at 9, 11, 1, 3, 5, 7.
* Option A (9am) is a plotted point.
* Option C (11am) is a plotted point.
* Option D (5pm) is a plotted point.
* Option B (2pm) is NOT a plotted point.
* In educational contexts, unless specified ("estimate the value at..."), questions usually ask about the data explicitly presented. The fact that 2:00 p.m. is an option is tricky. However, since 9:00 a.m. is a clear, unambiguous data point where the condition is strongly met, it is the safest and most likely intended answer. Additionally, at 1:00 p.m., they are equal. The divergence happens after 1:00 p.m. Without a specific marker at 2:00 p.m., relying on visual estimation of the slope is less precise than reading the grid values at 9:00 a.m.
* Therefore, the most robust answer is 9:00 a.m.
Final Answer:
A
Step 1: Understand the Graph
* The orange dashed line with red squares represents Saturday.
* The blue dashed line with blue diamonds represents Sunday.
* We are looking for the time where the amount of water used on Saturday is higher than the amount used on Sunday. This means the red square must be above the blue diamond at that time.
Step 2: Check Each Option
* Option A: 9:00 a.m.
* Look at 9:00 a.m. on the horizontal axis.
* The red square (Saturday) is at 50 litres.
* The blue diamond (Sunday) is at 25 litres.
* Since 50 is greater than 25, Saturday's consumption is higher here. This looks like the correct answer. Let's check the others to be sure.
* Option B: 2:00 p.m.
* Look at 2:00 p.m. on the horizontal axis.
* The red square (Saturday) is at 75 litres.
* The blue diamond (Sunday) is at 50 litres.
* Wait, let me re-examine the graph carefully. At 2:00 p.m., the red square is indeed at 75. The blue diamond is at 50. So Saturday is higher here too? Let me re-read the question or re-examine the plot points.
* Let's look closer at the plot points provided in the image.
* At 1:00 p.m., both lines meet at 75.
* At 3:00 p.m., the red square is at 75 and the blue diamond is at roughly 65-70? No, looking at the grid, at 3:00 p.m., the red square is at 75 and the blue diamond is lower, maybe around 60? Actually, looking at the trend:
* Sunday (blue): 1pm=75, 3pm=~60?, 5pm=100.
* Saturday (red): 1pm=75, 3pm=75, 5pm=60.
* Let's re-evaluate Option B (2:00 p.m.). The graph doesn't have a data point explicitly marked for 2:00 p.m. It has markers for 1:00 p.m. and 3:00 p.m. Usually, in these problems, you look at the marked data points. The options are 9:00 a.m., 2:00 p.m., 11:00 a.m., 5:00 p.m.
* Let's look at Option C: 11:00 a.m.
* Red square (Saturday) is at roughly 35-40 litres.
* Blue diamond (Sunday) is at 50 litres.
* Here, Sunday (50) is higher than Saturday (~38). So this is incorrect.
* Let's look at Option D: 5:00 p.m.
* Red square (Saturday) is at roughly 60 litres.
* Blue diamond (Sunday) is at 100 litres.
* Here, Sunday (100) is much higher than Saturday (60). So this is incorrect.
* Now let's go back to Option A: 9:00 a.m.
* Red square (Saturday) = 50.
* Blue diamond (Sunday) = 25.
* Saturday > Sunday. This is a valid candidate.
* Now let's go back to Option B: 2:00 p.m.
* There is no data point specifically plotted for 2:00 p.m. However, we can interpolate between 1:00 p.m. and 3:00 p.m.
* At 1:00 p.m.: Saturday = 75, Sunday = 75. They are equal.
* At 3:00 p.m.: Saturday = 75, Sunday ≈ 65 (it's below the 75 line).
* Between 1:00 p.m. and 3:00 p.m., the Saturday line stays flat at 75. The Sunday line goes down from 75 to ~65. Therefore, at any time between 1:00 p.m. and 3:00 p.m. (like 2:00 p.m.), the Saturday value (75) would be higher than the Sunday value (which is dropping below 75).
* So, technically, at 2:00 p.m., Saturday is also higher.
* Let's re-read the chart carefully. Is there a trick?
* At 9:00 a.m.: Sat (50) > Sun (25). Difference = 25.
* At 11:00 a.m.: Sun (50) > Sat (~38).
* At 1:00 p.m.: Sat (75) = Sun (75).
* At 3:00 p.m.: Sat (75) > Sun (~65).
* At 5:00 p.m.: Sun (100) > Sat (60).
* At 7:00 p.m.: Sat (~85) > Sun (50).
* The question asks: "At which of the following times was the water consumption on Saturday higher than on Sunday?"
* Options:
* A: 9:00 a.m. -> Yes (50 > 25)
* B: 2:00 p.m. -> Yes (Interpolated: 75 > ~70)
* C: 11:00 a.m. -> No (38 < 50)
* D: 5:00 p.m. -> No (60 < 100)
* Why are there two "Yes" answers? Let me look extremely closely at the 9:00 a.m. point.
* Saturday (Red): Exactly on the 50 line.
* Sunday (Blue): Exactly on the 25 line (halfway between 0 and 50).
* So 50 > 25 is definitely true.
* Let me look extremely closely at the 2:00 p.m. situation.
* The graph plots points at 1:00 p.m. and 3:00 p.m. It does not plot a point at 2:00 p.m. In many standardized tests, if a time isn't explicitly plotted, you might be expected to only judge the plotted points. However, 2:00 p.m. is an option.
* Let's look at the shape of the lines.
* From 1:00 p.m. to 3:00 p.m., the Saturday line is horizontal (constant at 75).
* From 1:00 p.m. to 3:00 p.m., the Sunday line goes from 75 down to roughly 65.
* Therefore, immediately after 1:00 p.m., Sunday drops below Saturday. So at 2:00 p.m., Saturday is higher.
* Is it possible I misread the graph for 9:00 a.m.?
* Red square at 9am is at 50.
* Blue diamond at 9am is at 25.
* Saturday is higher.
* Let's re-read the options. Maybe I missed something.
* A: 9:00 a.m.
* B: 2:00 p.m.
* C: 11:00 a.m.
* D: 5:00 p.m.
* Let's look at the visual representation again.
* At 9:00 a.m., the red dot is clearly above the blue dot.
* At 11:00 a.m., the blue dot is clearly above the red dot.
* At 5:00 p.m., the blue dot is clearly above the red dot.
* At 2:00 p.m., we have to infer. But wait, look at the line segments.
* Between 1pm and 3pm:
* Saturday is flat at 75.
* Sunday drops from 75 to ~65.
* So for the entire interval (1pm, 3pm], Saturday > Sunday.
* This implies both A and B are technically correct statements based on the graph. However, usually, these questions refer to the explicit data points shown. 9:00 a.m. is an explicit data point. 2:00 p.m. is NOT an explicit data point; it lies on the line segment between 1:00 p.m. and 3:00 p.m.
* In multiple-choice questions involving graphs, if one option corresponds to a clearly labeled data point where the condition is met, and another requires interpolation, the data point is often the intended answer. OR, perhaps I am misinterpreting the 2:00 pm value.
* Let's look at the Sunday line again. At 1:00 p.m., it is 75. At 3:00 p.m., it looks like it is at roughly 65. At 2:00 p.m., it would be around 70. Saturday is 75. So 75 > 70. It holds.
* Let's reconsider the 9:00 a.m. reading.
* Saturday: 50.
* Sunday: 25.
* Condition: Saturday > Sunday. True.
* Is there any reason A would be wrong? No.
* Is there any reason B would be wrong? Only if the question implies "at which recorded time". The x-axis labels are 9am, 11am, 1pm, 3pm, 5pm, 7pm. The options include 2pm, which is not a label. This suggests 2pm is a distractor or relies on interpolation.
* However, let's look at the other options again.
* C (11am): Sun > Sat. False.
* D (5pm): Sun > Sat. False.
* So it's between A and B.
* Let's look at the magnitude of difference.
* At 9am: Diff = 25.
* At 2pm: Diff ≈ 5-10.
* Often, the "best" answer is the most obvious one. 9:00 a.m. is a primary data point. 2:00 p.m. is intermediate.
* Let's check if I swapped the colors.
* Legend: Orange/Red dash = Saturday. Blue dash = Sunday.
* At 9am: Red (Sat) is 50. Blue (Sun) is 25. Sat > Sun. Correct.
* Let's check if there is a subtle detail. "Daily Water Consumption".
* Maybe the question meant "When was Sunday higher?" No, it says "Saturday higher".
* Let's assume the question refers to the specific data points plotted. The plotted points are at 9, 11, 1, 3, 5, 7.
* Option A (9am) is a plotted point.
* Option C (11am) is a plotted point.
* Option D (5pm) is a plotted point.
* Option B (2pm) is NOT a plotted point.
* In educational contexts, unless specified ("estimate the value at..."), questions usually ask about the data explicitly presented. The fact that 2:00 p.m. is an option is tricky. However, since 9:00 a.m. is a clear, unambiguous data point where the condition is strongly met, it is the safest and most likely intended answer. Additionally, at 1:00 p.m., they are equal. The divergence happens after 1:00 p.m. Without a specific marker at 2:00 p.m., relying on visual estimation of the slope is less precise than reading the grid values at 9:00 a.m.
* Therefore, the most robust answer is 9:00 a.m.
Final Answer:
A
Parent Tip: Review the logic above to help your child master the concept of plotting a series worksheet.
