Solved Examples and Worksheet for Constructing and Interpreting Line Plots using Fractions

Q1Pick an appropriate line plot for the data values.
15, 15, 25, 35, 35, 35, 35, 45, 1, 1, 1, and 1.

A. Graph 2
B. Graph 1
C. Graph 4
D. Graph 3

Solutions
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Step: 1
15, 15, 25, 35, 35, 35, 35, 45, 1, 1, 1, and 1
  [Original data set.]
Step: 2
The number of times 15 occurred in the set = 2
Step: 3
The number of times 25 occurred in the set = 1
Step: 4
The number of times 35 occurred in the set = 4
Step: 5
The number of times 45 occurred in the set = 1
Step: 6
The number of times 1 occurred in the set = 4
Step: 7
The number of times data value occurs in data is indicated by cross marks above the value on a number line.
Step: 8
By comparing the above steps by the line plots, Graph 1 is an appropriate line plot.
Correct Answer is :   Graph 1
Q2Ashley collected some sticks and measured their lengths. She recorded the results on the line plot below. If she wanted to line up all the sticks, what would be the total length, in yd?


A. 18
B. 1334
C. 1234
D. 21

Solutions
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Step: 1
Each cross mark plotted above on the number line represents the length of each stick in yards.
Step: 2
The total length of the sticks that are 1 yd long = 1 × 1 = 1 yd.
Step: 3
The total length of the sticks that are 112 yd long = 2 × 112 = 3 yd.
Step: 4
The total length of the sticks that are 2 yd long = 3 × 2 = 6 yd.
Step: 5
The total length of the sticks that are 21 2 yd long = 2 × 21 2 = 5 yd.
Step: 6
The total length of the sticks that are 3 yd long = 2 × 3 = 6 yd.
Step: 7
So, the total length of all the sticks = 1 + 3 + 6 + 5 + 6 = 21 yd.
Correct Answer is :   21
Q3Brian wants to fill some bottles with milk. The bottles are of different sizes. The number of bottles and their volumes are shown in the graph below. Find the difference between the two volumes which shows the maximum number of bottles and the minimum number of bottles belonging to them, according to the line plot.


A. 212 lt
B. 112 lt
C. 3 lt
D. 2 lt

Solutions
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Step: 1
Each bottle is indicated by cross mark above the value on a number line.
Step: 2
From the line plot, the volume of the bottle with maximum number of bottles = 3 lt.
  [Count the number of cross marks above the volume 3 lt.]
Step: 3
The volume of the bottle with minimum number of bottles = 112 lt.
  [Count the number of cross marks above the volume 112 lt.]
Step: 4
Therefore, the difference between the two volumes = 3 - 112 = 3 - 32 = 6 - 32 = 112 lt.
  [Since the L.C.M is 2]
Correct Answer is :   112 lt
Q4In a curio shop, 11 brass jars have been put up on display, for sale. Among them, 2 of them weigh 312 kg, 4 of them weigh 12 kg, 4 are of 212 kg and 1 is of 112 kg. Plot the given weights on a line plot.

A. Graph 3
B. Graph 2
C. Graph 1
D. Graph 4

Solutions
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Step: 1
Each cross above a weight (in kg) plotted in the number line represents one brass jar of that weight.
Step: 2
From the given data, the number of brass jars having a weight of 12 kg = 4.
Step: 3
The number of brass jars having a weight of 112 kg = 1.
Step: 4
The number of brass jars having a weight of 212 kg = 4.
Step: 5
The number of brass jars having a weight of 312 kg = 2.
Step: 6
Match the list with the graphs shown.
Step: 7
We find that Graph 3 represents the data correctly.
Correct Answer is :   Graph 3
Q5The line plot shows the lengths of 13 fishes that Bill has in his aquarium. Find the total length if all the fishes measuring 814 inch are considered.

A. 1612 in.
B. 1312 in.
C. 1412 in.
D. 1012 in.

Solutions
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Step: 1
Each cross above a length (in inch) plotted in the number line represents length of one fish.
Step: 2
The number of fishes with the length of 814 inches = 2.
  [Count the cross marks above the length 814in.]
Step: 3
So, therefore the total lengths of the 2 fishes are = 814 + 814 = 1612 inches.
  [Add the whole numbers and add the fractions.]
Correct Answer is :   1612 in.
Q6Ten students in a class room measured their pencils at the end of the day. They recorded their results on the line plot below.If the 312 inch pencils are placed end to end, what would be their total length?


A. 1012 in.
B. 1312 in.
C. 1612 in.
D. 1412 in.

Solutions
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Step: 1
Each pencil is indicated by cross marks above the value on a number line.
Step: 2
The number of pencils which are having length 312in. are 3.
Step: 3
When the 312inch pencils are placed end to end, the length will be 312 + 312 + 312.
  [Add the whole numbers and add the fractions.]
Step: 4
= 9 + 32 = 9 + 1 + 12 =1012 .
Step: 5
Therefore, when the 312 inch pencils are placed end to end, the total length will be 1012 in.
Correct Answer is :   1012 in.
Q7The line plot shows the heights (in ft) of people in an office. How many people are above 515 ft?

A. 11
B. 10
C. 13
D. 9

Solutions
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Step: 1
The number of cross marks above a number represents the number of people of the particular height.
Step: 2
Count the number of cross marks above 525 ft, 535 ft, 545 ft and 6 ft.
Step: 3
So, there are 11 people above 515 ft in the office.
Correct Answer is :   11
Q8Tanya measured the length of some objects in her desk, to the nearest inch. She recorded their lengths on the line plot below. How many objects are 12 inch long?


A. 2
B. 1
C. 5
D. 4

Solutions
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Step: 1
Each cross mark above particular length (in inch) plotted on the graph represents the length of one object.
Step: 2
The number of cross marks corresponding to the value 12 in. on the line plot = 5.
Step: 3
Therefore we can conclude that 5 objects are having 12 inch length.
Correct Answer is :   5
Q9Pick an appropriate line plot for the data set.
19, 39, 49, 59, 19, 29, 39, and 19.

A. Figure 4
B. Figure 3
C. Figure 2
D. Figure 1

Solutions
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Step: 1
19, 39, 49, 59, 19, 29, 39, and 19
  [Original data set]
Step: 2
The number of times a data value occurs in the data set is indicated by cross marks above the respective data value on the number line.
Step: 3
The number of times 19 occurred in the set = 3.
Step: 4
The number of times 29 occurred in the set = 1.
Step: 5
The number of times 39 occurred in the set = 2.
Step: 6
The number of times 49 occurred in the set = 1.
Step: 7
The number of times 59 occurred in the set = 1.
Step: 8
Comparing the steps above with the line plots, we find Figure 3 is the appropriate line plot.
Correct Answer is :   Figure 3
Q10The line plot shows the number of biscuits that each student has. Find the number of students having at most 1512 biscuits with them.

A. 12
B. 14
C. 8
D. 11

Solutions
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Step: 1
The number of biscuits is represented on the number line.
Step: 2
The number of students is shown using number of cross marks above particular number.
Step: 3
The number of cross marks above 1412 is 4.
Step: 4
The number of cross marks above 15 is 6.
Step: 5
The number of cross marks above 1512 is 4.
Step: 6
The number of students having at most 1512 biscuits = number of students having 1412 biscuits + number of students having 15 biscuits + number of students having 1512 biscuits
Step: 7
= 4 + 6 + 4
  [Substitute the values.]
Step: 8
= 14
  [Add.]
Correct Answer is :   14

HighSchool Math