All questions
Question 1
Emma measured how many jumping jacks she could do in 10 seconds each day for 6 days. Her counts were: 14, 17, 15, 16, 17, 16. When she makes her line plot, which number on the horizontal scale will have exactly the same number of X's above it as the number 17?
- 14, because it's one less than 15 and would balance the data
- 16, because both 16 and 17 appear exactly 2 times in her data list (correct answer)
- 18, because 18 is one more than 17, so it should have the same number of X's
- No number will have the same count, because 17 appears more often than any other number
Explanation: Emma's data set is 14, 17, 15, 16, 17, 16, so 14 appears once, 15 appears once, 16 appears twice, and 17 appears twice. Since 16 and 17 both appear exactly two times, 16 will have the same number of X's as 17. Choice A is incorrect because being one less than 15 has no bearing on how many times a number appears in the data. Choice C is incorrect because 18 does not appear in the data set at all. Choice D is incorrect because 16 ties with 17 for the highest count, so a matching number does exist.
Question 2
A class measured the number of letters in their first names. The data collected was: 5 letters, 6 letters, 4 letters, 5 letters, 6 letters, 4 letters, 7 letters, 5 letters. If they want to make a line plot, what should the horizontal scale show?
- Numbers from 1 to 8, because there were 8 students who provided name length data
- Numbers from 4 to 7, because the shortest name had 4 letters and longest had 7 letters (correct answer)
- Numbers from 0 to 10, because line plots always need to start at 0 and go to 10
- Numbers from 5 to 6, because those are the name lengths that appeared most frequently
Explanation: The horizontal scale of a line plot should include all the values in the data set. The data ranges from 4 letters (minimum) to 7 letters (maximum), so the scale needs to include 4, 5, 6, and 7. Choice A confuses the number of data points with the data values themselves. Choice C applies a nonexistent rule about line plot scales. Choice D only includes the most frequent values but excludes 4 and 7, which also appear in the data.
Question 3
Maria measured the heights of 8 sunflowers in her garden, in inches: 24, 26, 24, 25, 26, 24, 27, 25. If she made a line plot of this data, how many X's should appear above 24 inches?
- 4 X's above 24
- 3 X's above 24 (correct answer)
- 2 X's above 24
- 1 X above 24
Explanation: The number 24 appears 3 times in Maria's data, so the line plot should show 3 X's above 24. Choosing 4 X's counts one extra measurement that is not in the data. Choosing 2 X's misses one of the three 24-inch measurements. Choosing 1 X only counts one of the three times 24 appears in the data.
Question 4
Refer to the line plot below. Which statement is true based on the plot?
- There are more 4-inch crayons than 5-inch crayons.
- There are exactly 3 crayons that are 5 inches long.
- The shortest crayon measured is 4 inches long. (correct answer)
- There are more 3-inch crayons than 6-inch crayons.
Explanation: The line plot has no X's above 2 or 3 inches, so the shortest crayon measured is 4 inches. There are 3 X's above 4, 4 X's above 5, and 2 X's above 6, so 5-inch is the most common (not 4-inch), and there are 4 (not 3) five-inch crayons. There are zero 3-inch crayons, so A, B, and D are false.
Question 5
Tim measured the lengths of pencils in his desk drawer. He found pencils that were 5 inches, 6 inches, 5 inches, 7 inches, 6 inches, 5 inches, and 6 inches long. If Tim makes a line plot correctly, what will be the total number of X's on his entire line plot?
- 3
- 4
- 7 (correct answer)
- 6
Explanation: A line plot places one X for every single measurement taken, and Tim measured 7 pencils in total, so there are 7 X's. Three is the number of different lengths recorded, not the total number of measurements. Four comes from subtracting the shortest length from the longest and adding extra, which does not represent counting individual data points. Six undercounts the measurements, missing one of the seven pencils Tim measured.
Question 6
Jake measured the heights of plants in his garden and recorded: 12 inches, 14 inches, 13 inches, 12 inches, 14 inches, 13 inches, 13 inches. What is the difference between how many times 13 inches was recorded and how many times 14 inches was recorded?
- 1 (correct answer)
- 2
- 0
- 3
Explanation: The height 13 inches appears 3 times and 14 inches appears 2 times in the list, so the difference is 3 minus 2, which is 1. Choice B would only be true if 14 inches appeared just once, but it appears twice. Choice C would only be true if both heights appeared the same number of times, which they do not. Choice D counts the number of different heights recorded instead of the difference between two specific counts.
Question 7
Refer to the line plot below. How many more worms are 4 cm long than are 6 cm long?
- 2 (correct answer)
- 4
- 10
- 6
Explanation: There are 6 X's above 4 and 4 X's above 6. 6−4=2. Choice B is the count at 6 cm. Choice C adds instead of subtracts. Choice D is the count at 4 cm. Question 8
Refer to the line plot below. How many pencils are longer than 4 inches?
- 3
- 8
- 11
- 5 (correct answer)
Explanation: 'Longer than 4' means 5, 6, or 7 inches — do not include 4. Count X's above 5, 6, and 7: 2+2+1=5. Choice A counts only pencils at 4 inches. Choice B includes the 4-inch pencils (3+2+2+1). Choice C is the total number of pencils. Question 9
Two sticker amounts were each reported by exactly 2 students: 2 stickers and 4 stickers.
What is the sum of 2 and 4?
- 4
- 6 (correct answer)
- 8
- 10
Explanation: Adding 2 and 4 gives a sum of 6. Choice A, 4, is just one of the two numbers by itself. Choice C, 8, is too large for this sum. Choice D, 10, does not match adding 2 and 4.
Question 10
Sarah measured how long it took her to walk to school each day for one week. Her times were: 8 minutes, 9 minutes, 8 minutes, 10 minutes, 9 minutes. Based on the line plot shown, what mistake did Sarah make when creating her line plot?
- She put too many X's above 8 minutes - there should only be 1 X there instead of 2
- She put too many X's above 9 minutes - there should only be 1 X there instead of 3
- She forgot to put any X's above 10 minutes even though she measured 10 minutes one time (correct answer)
- She used the wrong scale - her horizontal axis should go from 1 to 5 instead of 8 to 10
Explanation: Looking at Sarah's data (8, 9, 8, 10, 9), there should be 2 X's above 8, 2 X's above 9, and 1 X above 10. If the line plot is missing the X above 10, that would be a mistake since 10 minutes appears once in her data. Choice A is wrong because 8 minutes appears twice, so 2 X's is correct. Choice B is wrong because 9 minutes appears twice, not three times, so having 3 X's there would indeed be wrong but the choice incorrectly states there should be only 1. Choice D is wrong because the horizontal scale should match the range of data values (8-10), not the count of measurements.
Question 11
Look at this data that shows how many books different students read: 3 books, 4 books, 3 books, 5 books, 4 books, 3 books, 3 books. When making a line plot from this data, above which number on the horizontal scale should you put the most X's?
- Above 5
- Above 4
- Above 7
- Above 3 (correct answer)
Explanation: The number 3 appears four times in the data, more often than any other number, so the line plot should have the most X's above 3, matching D. A is incorrect because 5 is the largest number in the data, but that does not mean it appears most often. B is incorrect because being in the middle of the range does not determine how many times a number appears. C is incorrect because there were 7 pieces of data total, not 7 students, and that total does not tell you which number repeats most.