Create Line Plots From Measurements
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2nd Grade Math › Create Line Plots From Measurements
Emma measured how many jumping jacks she could do in 10 seconds each day for 6 days. Her counts were: 15, 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?
No number will have the same count, because 17 appears more often than any other number
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
18, because 18 is one more than 17, so it should have the same number of X's
Explanation
Looking at the frequency count: 15 appears 2 times, 16 appears 2 times, and 17 appears 2 times. Since 17 appears 2 times, we need another number that also appears 2 times. The number 16 also appears exactly 2 times in the data. Choice A suggests 14 which doesn't appear in the data at all. Choice C incorrectly suggests 18 (which doesn't appear in the data) would have X's. Choice D is wrong because 17 doesn't appear more than others - three values (15, 16, and 17) each appear twice.
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, because 5 is the largest number of books that any student read
Above 7, because there were 7 students total who read books for this data collection
Above 4, because 4 is in the middle between the smallest and largest numbers
Above 3, because 3 books appears 4 times in the data, more than any other number
Explanation
When you're making a line plot, you need to count how often each number appears in your data set. A line plot shows frequency - how many times each value occurs - by stacking X's above each number on a horizontal scale.
Let's count how many times each number of books appears in the data: 3 books, 4 books, 3 books, 5 books, 4 books, 3 books, 3 books. The number 3 appears 4 times, the number 4 appears 2 times, and the number 5 appears 1 time. Since 3 books appears most frequently (4 times), you would put the most X's above the number 3 on your line plot - specifically, you'd stack 4 X's there.
Choice A is wrong because even though 5 is the largest number, it only appears once in the data, so it gets the fewest X's. Choice B incorrectly focuses on finding a middle value rather than counting frequency - the number 4 only appears twice, not the most. Choice C confuses the total number of students (7) with the actual data values we're plotting. We plot the number of books each student read, not how many students there were total.
Remember this key rule for line plots: the column with the most X's always goes above the number that appears most often in your data set. Always count carefully how many times each value appears - don't get distracted by which number is biggest, smallest, or in the middle.
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 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
Numbers from 4 to 7, because the shortest name had 4 letters and longest had 7 letters
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.
A teacher had students measure the width of their hands. The measurements were: 4 inches, 5 inches, 4 inches, 4 inches, 6 inches, 5 inches. If a student makes a line plot and then counts all the X's above numbers that are 5 or less, how many X's should they count?
6 X's, because all measurements except the 6-inch measurement are 5 or less, so 6-1=5 X's
4 X's, because the number 4 appears most often and 4 is less than 5
2 X's, because there are 2 different numbers (4 and 5) that are 5 or less in the data
5 X's, because there are 5 measurements of 5 inches or less in the original data
Explanation
When you see a line plot question, you need to understand that each measurement from the data becomes one X on the plot. You're looking at data about hand measurements and need to count how many X's represent measurements of 5 inches or less.
Let's work through the data: 4 inches, 5 inches, 4 inches, 4 inches, 6 inches, 5 inches. To find measurements that are 5 or less, check each one: 4 ≤ 5? Yes. 5 ≤ 5? Yes. 4 ≤ 5? Yes. 4 ≤ 5? Yes. 6 ≤ 5? No. 5 ≤ 5? Yes. That's five measurements total that are 5 inches or less. Since each measurement becomes one X on the line plot, you'll count 5 X's.
Choice A is correct because it properly counts each individual measurement that meets the criteria. Choice B incorrectly focuses only on the most frequent number (4) rather than counting all qualifying measurements. Choice C makes the mistake of counting different number values instead of individual measurements - while only two different numbers (4 and 5) are 5 or less, there are actually five total measurements with those values. Choice D has the right idea about excluding the 6-inch measurement but makes an error in the final calculation.
Remember: in line plot problems, always count individual data points (measurements), not just the different number values. Each piece of original data becomes exactly one X on your plot, so count every measurement that meets your criteria.
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?
4 X's total, because the longest pencil minus the shortest pencil is 7 - 5 = 2, plus 2 more
6 X's total, because he found 6 different pencils in his drawer that he could measure
3 X's total, because there are 3 different pencil lengths he measured
7 X's total, because he measured 7 pencils and each measurement gets one X mark
Explanation
Each individual measurement gets represented by one X on a line plot. Tim made 7 measurements total (even though some lengths were repeated), so there will be 7 X's total on his line plot. Choice A confuses the number of different values with the total frequency. Choice B uses an incorrect calculation that doesn't relate to line plot construction. Choice D incorrectly focuses on the number of physical pencils rather than the number of measurements recorded.