- Refer to the following double bar graph comparing test scores for two classes. What is the difference between the number of students who scored 90-100 in Class A versus Class B?
Answer: Class B had 2 more
From the double bar graph: Class A has 5 students in the 90-100 range, Class B has 7 students in the 90-100 range. Difference = 7-5 = 2 more for Class B. Choice A reverses the classes. Choice B uses the wrong difference amount. Choice D uses wrong difference and wrong direction. Choice E is incorrect as the numbers are different.
- A town recorded 7 inches of rain in June, 5 inches in July, 6 inches in August, and 7 inches in September. What was the average monthly rainfall from June through September?
Answer: 6.25 inches was the average monthly rainfall from June through September
To find an average, add the values and divide by how many there are.
The four monthly amounts are 7, 5, 6, and 7 inches. Their sum is 7+5+6+7=25 inches.
There are 4 months, so the average is 425=6.25 inches.
An answer of 7.0 inches is the mode, the value that appears most often, not the average. An answer of 6.5 inches is the median, the middle of 5, 6, 7, 7. An answer of 6.0 inches comes from counting the repeated 7 only once (35+6+7=6). An answer of 5.5 inches is too low; it is below every month except July.
Check that the average makes sense: it must fall between the smallest value (5) and the largest value (7). - Refer to the following graph showing monthly rainfall in Riverside City. During which month did Riverside City receive exactly twice as much rainfall as it received in March?
Answer: August received exactly twice as much rainfall as March
From the bar graph, March received 3 inches of rainfall. Twice that amount would be 6 inches. Looking at all months: April=4, May=5, June=7, July=8, August=6, September=4, October=5, November=3, December=2. Only August has exactly 6 inches, which is twice March's 3 inches. The other choices show months with different amounts.
- Refers to the following table showing the results of a coin-flipping experiment conducted by four students. Which student had the greatest difference between their number of heads and number of tails?
Answer: David
Calculate the absolute difference |heads - tails| for each student: Amy: |22-18| = 4, Ben: |15-25| = 10, Carla: |28-12| = 16, David: |8-32| = 24. David has the greatest difference of 24. Students might make calculation errors or forget to find the absolute value of the differences.
- Refer to the following pictograph showing books read by students during summer reading month. Each book symbol represents 4 books. How many more books did the 7th graders read than the 5th graders?
Answer: 20
From the pictograph: 5th graders have 7 book symbols = 7×4 = 28 books. 7th graders have 12 book symbols = 12×4 = 48 books. Difference = 48-28 = 20 books. Choice A (8) forgets to multiply by 4. Choice B (12) is the difference in symbols, not books. Choice C (16) comes from calculation errors. Choice E (24) comes from misreading the pictograph.
- Refer to the following bar graph showing cars sold by five salespeople in January. If Maria's sales in February increased by 25% compared to January, how many cars did she sell in February?
Answer: 25
From the graph, Maria sold 20 cars in January. A 25% increase means: 20 + (0.25 × 20) = 20 + 5 = 25 cars. Choice A (15) comes from a 25% decrease instead of increase. Choice B (18) comes from calculation errors. Choice C (20) is January's amount (no change). Choice D (22) comes from using a 10% increase.
- The line graph shows the temperature throughout one day. Between which consecutive hours did the temperature increase by the greatest amount?
Answer: The greatest increase occurred between 8 AM and 9 AM
Temperature changes per hour: 6-7 AM: 52°-48°=4°, 7-8 AM: 58°-52°=6°, 8-9 AM: 66°-58°=8°, 9-10 AM: 72°-66°=6°, 10-11 AM: 76°-72°=4°. The greatest increase is 8° between 8-9 AM. Students might choose B or D (both 6° increases) if they miscalculate.
- Refer to the following chart showing student enrollment in after-school activities. What fraction of students enrolled in Drama are also enrolled in Music?
Answer: Two-fifths of Drama students are also enrolled in Music
From the chart: Total Drama students = 25, Drama students also in Music = 10. Fraction = 10/25 = 2/5. Choice A (1/3) might come from misreading numbers. Choice C (1/2) comes from using 12.5 instead of 10. Choice D (3/5) comes from using 15 instead of 10. Choice E (2/3) comes from calculation errors.
