Q1: A line plot shows the number of hours students spent reading last week. The data points are at 2, 3, 3, 4, 4, 4, 5, and 6 hours. How many students read for 4 hours? (a) 2 students (b) 3 students (c) 4 students (d) 5 students
Solution:
Ans: (b) Explanation: On a line plot, each X or dot represents one data value. Looking at the data, the number 4 appears three times (4, 4, 4), which means 3 students read for 4 hours. Option (a) might be chosen if counting only two marks, (c) confuses the number of hours with the count, and (d) is too high.
Q2: Which of the following data sets would be best displayed on a line plot? (a) The favorite colors of students in a class (b) The lengths of pencils measured to the nearest 1/4 inch (c) The names of different types of animals (d) The addresses of students
Solution:
Ans: (b) Explanation: A line plot is best used for numerical data that can be measured and often has repeated values. Pencil lengths measured to the nearest 1/4 inch are numerical measurements that can be plotted on a number line. Options (a), (c), and (d) involve categorical data (colors, names, addresses) which are better shown using bar graphs or tables.
Q3: On a line plot showing the weights of apples in pounds, there are 2 Xs above 1/4, 3 Xs above 1/2, and 1 X above 3/4. What is the total number of apples weighed? (a) 3 apples (b) 5 apples (c) 6 apples (d) 9 apples
Solution:
Ans: (c) Explanation: Each X on a line plot represents one data point (one apple). To find the total number of apples, add all the Xs: \(2 + 3 + 1 = 6\) apples. Option (a) counts only the number of different values, (b) miscounts the Xs, and (d) incorrectly multiplies instead of adding.
Q4: A line plot shows the amounts of rainfall in inches over 10 days: 1/8, 1/4, 1/4, 1/2, 1/2, 1/2, 1/2, 3/4, 3/4, 1. What is the most common amount of rainfall? (a) 1/8 inch (b) 1/4 inch (c) 1/2 inch (d) 3/4 inch
Solution:
Ans: (c) Explanation: The most common value is called the mode. Looking at the data, 1/2 inch appears 4 times, which is more than any other value (1/8 appears once, 1/4 appears twice, and 3/4 appears twice). Therefore, 1/2 inch is the mode.
Q5: On a line plot, the data values range from 2 to 8. What would be the most appropriate scale to use on the number line? (a) 0 to 5 (b) 1 to 10 (c) 5 to 15 (d) 10 to 20
Solution:
Ans: (b) Explanation: The scale on a line plot should include all data values. Since the data ranges from 2 to 8, the scale needs to include both these numbers. Option (b) from 1 to 10 includes all values and provides some space on both ends. Option (a) doesn't reach 8, while (c) and (d) start too high and waste space.
Q6: A line plot shows the lengths of caterpillars in inches: 1 1/4, 1 1/2, 1 1/2, 1 3/4, 2, 2, 2 1/4. How many caterpillars were measured? (a) 4 caterpillars (b) 5 caterpillars (c) 6 caterpillars (d) 7 caterpillars
Solution:
Ans: (d) Explanation: Count each data value in the list: 1 1/4, 1 1/2, 1 1/2, 1 3/4, 2, 2, 2 1/4. There are 7 measurements, so 7 caterpillars were measured. Each measurement represents one caterpillar. Miscounting the values would lead to incorrect answers.
Q7: Which statement is true about a line plot? (a) It uses bars to show data (b) It shows data along a number line using Xs or dots (c) It can only show whole numbers (d) It is best for comparing different categories
Solution:
Ans: (b) Explanation: A line plot displays data by placing Xs or dots above a number line to show the frequency of each value. Option (a) describes a bar graph, (c) is incorrect because line plots can show fractions and decimals, and (d) describes categorical graphs like bar graphs.
Q8: Students measured the width of their hands to the nearest 1/2 inch. The measurements were: 3, 3 1/2, 3 1/2, 3 1/2, 4, 4, 4 1/2. What is the range of the data? (a) 1 inch (b) 1 1/2 inches (c) 2 inches (d) 3 inches
Solution:
Ans: (b) Explanation: The range is the difference between the largest and smallest values. The largest value is 4 1/2 inches and the smallest is 3 inches. \(4\frac{1}{2} - 3 = 1\frac{1}{2}\) inches. So the range is 1 1/2 inches. Other options result from calculation errors.
Section B: Fill in the Blanks
Q9: A __________ is a graph that shows data along a number line using Xs or dots.
Solution:
Ans: line plot Explanation: A line plot (also called a dot plot) is specifically designed to display numerical data along a number line, with each X or dot representing one data value.
Q10: On a line plot, each X or dot represents one __________.
Solution:
Ans: data point (or data value) Explanation: In a line plot, every X or dot stands for one piece of data or one observation from the data set. This allows us to see both individual values and their frequency.
Q11: The difference between the greatest and least values in a data set is called the __________.
Solution:
Ans: range Explanation: The range is a measure of spread that shows how far apart the data values are. It is calculated by subtracting the smallest value from the largest value.
Q12: The value that appears most often in a data set is called the __________.
Solution:
Ans: mode Explanation: The mode is the data value with the highest frequency. On a line plot, it's the value with the most Xs or dots above it.
Q13: If a line plot shows measurements in fractions of an inch, the number line should be divided into equal parts based on the __________ used in the data.
Solution:
Ans: denominator (or fractions) Explanation: When creating a line plot with fractional data, the number line intervals must match the fractions in the data. For example, if data includes fourths (1/4, 2/4, 3/4), the number line should be marked in fourths.
Q14: To find the total number of data points on a line plot, you __________ all the Xs or dots.
Solution:
Ans: count (or add) Explanation: Since each X or dot represents one data value, counting all the marks gives the total number of observations in the data set.
Section C: Word Problems
Q15: Mrs. Johnson measured the lengths of cucumbers from her garden to the nearest 1/4 inch. The lengths were: 5 1/4, 5 1/2, 5 1/2, 5 3/4, 6, 6, 6 1/4, 6 1/4, 6 1/2 inches. Create a line plot for this data and determine how many cucumbers measured exactly 6 inches.
Solution:
Ans: Final Answer: 2 cucumbers measured exactly 6 inches. Explanation: Looking at the data list, the value 6 appears twice. On a line plot, there would be 2 Xs above the 6 on the number line.
Q16: A group of students collected seashells at the beach. They measured the lengths to the nearest 1/2 inch and recorded: 1 1/2, 2, 2, 2 1/2, 2 1/2, 2 1/2, 3, 3, 3 1/2 inches. What is the range of the seashell lengths?
Solution:
Ans: Final Answer: 2 inches Explanation: The range is the difference between the largest and smallest values. Largest value: 3 1/2 inches Smallest value: 1 1/2 inches \(3\frac{1}{2} - 1\frac{1}{2} = 2\) inches
Q17: Tommy recorded the amount of time in hours he practiced piano each day for one week: 1/2, 3/4, 1, 1, 1/2, 3/4, 1 1/4. If he makes a line plot of this data, above which value will there be the most Xs?
Solution:
Ans: Final Answer: Both 1/2 hour and 1 hour (tie with 2 Xs each), or the mode values are 1/2 and 1 Explanation: Counting the frequencies: 1/2 hour appears 2 times 3/4 hour appears 2 times 1 hour appears 2 times 1 1/4 hour appears 1 time There is a three-way tie, but typically we look for the value(s) with the highest frequency. All three values (1/2, 3/4, and 1) have 2 Xs. Note: Upon recount, 3/4 appears twice, 1/2 appears twice, and 1 appears twice, creating a three-way tie.
Q18: A baker weighed batches of cookie dough to the nearest 1/4 pound. The weights were: 2 1/4, 2 1/2, 2 1/2, 2 3/4, 2 3/4, 2 3/4, 3, 3 pounds. How many batches weighed more than 2 1/2 pounds?
Solution:
Ans: Final Answer: 5 batches Explanation: Values more than 2 1/2 pounds are: 2 3/4, 2 3/4, 2 3/4, 3, 3. Counting these values: 5 batches weighed more than 2 1/2 pounds. Note: "More than" means we do not count the values equal to 2 1/2.
Q19: A science class measured the lengths of bean plants to the nearest 1/8 inch. The line plot showed: 3 plants at 4 1/4 inches, 5 plants at 4 1/2 inches, 2 plants at 4 5/8 inches, and 4 plants at 4 3/4 inches. What is the total number of plants measured?
Solution:
Ans: Final Answer: 14 plants Explanation: Add the number of plants at each measurement: \(3 + 5 + 2 + 4 = 14\) plants total.
Q20: A veterinarian recorded the weights of puppies in pounds to the nearest 1/4 pound: 3 1/4, 3 1/2, 3 1/2, 3 3/4, 4, 4, 4, 4 1/4. What is the difference between the mode and the smallest weight?
Solution:
Ans: Final Answer: 3/4 pound Explanation: First, find the mode (most common value): 4 pounds appears 3 times, which is more than any other value, so the mode is 4 pounds. The smallest weight is 3 1/4 pounds. Difference: \(4 - 3\frac{1}{4} = \frac{3}{4}\) pound.
The document Worksheet (with Solutions): Line Plots is a part of the Grade 5 Course Math Grade 5.
Free, MCQs, ppt, Summary, past year papers, Semester Notes, Previous Year Questions with Solutions, Worksheet (with Solutions): Line Plots, Viva Questions, practice quizzes, Extra Questions, Worksheet (with Solutions): Line Plots, video lectures, shortcuts and tricks, mock tests for examination, study material, pdf , Exam, Sample Paper, Important questions, Objective type Questions, Worksheet (with Solutions): Line Plots;
