Reading Graphs & Estimation — Practice
A graph is an argument. Read the scale before the shape, or you will believe whatever it wants you to believe.
What these questions cover
These questions use 8 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Rate — A ratio of two different units, like miles per hour or dollars per pound.
- Percent — Parts per hundred. 37% = 37100 = 0.37.
- Area — Space inside, measured in square units.
- Bar graph — Compares separate categories.
- Line graph — Shows change over time.
- Circle graph — Shows parts of one whole, as percentages summing to 100%.
- Dimensions — Rows × columns. A 2 × 3 matrix has two rows and three columns.
- Height — The perpendicular distance from the base to the opposite corner.
Problem 1
Which graph best shows how temperature changes over a day?
- Bar graph
- Line graph
- Circle graph
Worked answer
Line graph
A line graph shows a quantity changing over time.
Problem 2
Which graph best shows how a budget splits into categories?
- Bar graph
- Line graph
- Circle graph
Worked answer
Circle graph
A circle graph shows parts of a whole, summing to 100%.
Problem 3
A circle graph shows 25% of 800 students walk to school. How many is that?
Worked answer
200
0.25 × 800 = 200
Problem 4
Estimate 487 × 21.
- About 1,000
- About 10,000
- About 100,000
Worked answer
About 10,000
500 × 20 = 10,000
The exact value is 10,227.
Problem 5
Which graph best compares the populations of five different towns?
- Bar graph
- Line graph
- Circle graph
Worked answer
Bar graph
A bar graph compares separate categories.
Problem 6
A circle graph of a $2,400 budget shows housing at 35% and food at 20%. How much more goes on housing?
Worked answer
360
35% - 20% = 15%
0.15 × 2400 = 360
Problem 7
Estimate 6,13829 to the nearest hundred.
Worked answer
200
6000 ÷ 30 = 200
The exact value is about 211.7.
Problem 8
A bar chart has a vertical axis starting at 70. One bar reaches 74 and another 78, so the second looks twice as tall. What is the actual difference?
Worked answer
4
78 - 74 = 4
Only the part above 70 is drawn — 4 against 8 — which is why one looks double.
Problem 9
A circle graph shows sections of 30%, 25%, 20% and 15%. What percent is the remaining section?
Worked answer
10
30 + 25 + 20 + 15 = 90
100 - 90 = 10%
Problem 10
Estimate 8.9 × 31.
Worked answer
270
9 × 30 = 270
The exact value is 275.9.
Problem 11
A line graph shows temperature rising from 12° to 20° over 4 hours. What is the rate of increase per hour?
Worked answer
2
20 - 12 = 8 degrees
8 ÷ 4 = 2 degrees per hour
Problem 12
Estimate 1,997 + 4,085 to the nearest thousand.
Worked answer
6000
2000 + 4000 = 6000
The exact value is 6,082.
Problem 13
The sections of a circle graph must add up to what percent?
Worked answer
100
A circle graph shows parts of a single whole, so the sections total 100%.
If they do not, the graph is wrong.
Problem 14
A pictogram doubles both the height and the width of an icon to show a doubled value. How many times bigger does the icon LOOK?
Worked answer
4
Doubling both dimensions multiplies the area by 2 × 2 = 4
The value doubled but the picture looks four times bigger — a classic distortion.
Problem 15
Estimate 39.7 × 20.4.
Worked answer
800
40 × 20 = 800
The exact value is about 809.9.
Problem 16
A survey of 250 students found 18% prefer science. How many students is that?
Worked answer
45
0.18 × 250 = 45