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Data Handling - Line Plots

Grade 4IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A line plot is a graph that shows the frequency of data along a number line. Each piece of data is represented by a symbol, usually an 'X', placed above the value on the line.

A simple line plot showing data points 1, 2, 2, and 3 represented by X marks above a number line.
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The horizontal scale on a line plot represents the categories or measurements being tracked (e.g., length, weight, or counts). It is important that the intervals between numbers are equal.

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The 'Mode' in a line plot is the value that has the highest column of 'X' marks, indicating it is the most frequent value in the data set.

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Line plots help in identifying the 'Outliers', which are data points that are located far away from the rest of the data clusters.

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To find the total number of items surveyed, simply count every 'X' mark displayed on the entire plot.

📐Formulae

Range=Greatest Value−Least ValueRange = \text{Greatest Value} - \text{Least Value}

Total Count=Sum of all symbols (X)Total\ Count = \text{Sum of all symbols (X)}

Frequency of x=Total number of marks above x\text{Frequency of } x = \text{Total number of marks above } x

💡Examples

Problem 1:

Students measured the lengths of their erasers to the nearest centimeter: 3,5,3,4,3,6,43, 5, 3, 4, 3, 6, 4. Create a line plot and find the range and mode.

Solution:

Step 1: Sort the data: 3,3,3,4,4,5,63, 3, 3, 4, 4, 5, 6. Step 2: Draw a number line from 33 to 66. Step 3: Place three 'X' marks above 33, two 'X's above 44, one 'X' above 55, and one 'X' above 66. Step 4: Range = 6−3=36 - 3 = 3. Step 5: Mode = 33.

Explanation:

The range is found by subtracting the minimum value (33) from the maximum value (66). The mode is 33 because it has the tallest stack of 'X' marks.

Problem 2:

A group of friends tracked how much juice they drank in liters: 12,14,12,12,34\frac{1}{2}, \frac{1}{4}, \frac{1}{2}, \frac{1}{2}, \frac{3}{4}. Find the most common amount of juice drank.

Solution:

Step 1: Identify the frequencies: 14\frac{1}{4} appears once, 12\frac{1}{2} appears three times, and 34\frac{3}{4} appears once. Step 2: On a line plot, the tallest stack would be above 12\frac{1}{2}.

Explanation:

The most common amount is the mode. Since 12\frac{1}{2} has the highest frequency (three times), it is the most common amount.

Problem 3:

Ms. Sarah recorded the number of books read by her students over the summer: 2,4,2,3,5,2,4,22, 4, 2, 3, 5, 2, 4, 2. Represent this data on a line plot and identify the number of books most students read.

Line plot showing 4 marks above 2, 1 mark above 3, 2 marks above 4, and 1 mark above 5.

Solution:

  1. Organize the data: 22 (4 times), 33 (1 time), 44 (2 times), 55 (1 time).
  2. Draw a number line from 22 to 55.
  3. Place 'X' marks for each occurrence.
  4. The most frequent value (mode) is 22 books.

Explanation:

By counting the 'X' marks, we see that the number 22 has the tallest stack (4 marks), making it the most common amount.

Problem 4:

A baker measured the weights of several bags of flour to the nearest quarter kg: 14\frac{1}{4} kg, 24\frac{2}{4} kg, 14\frac{1}{4} kg, 34\frac{3}{4} kg, 14\frac{1}{4} kg. Based on the line plot, what is the total number of bags and the range of weights?

Line plot for flour weights with three marks at 1/4, one mark at 2/4, and one mark at 3/4.

Solution:

  1. Plot the data: 14\frac{1}{4} (3 marks), 24\frac{2}{4} (1 mark), 34\frac{3}{4} (1 mark).
  2. Total count of bags = 3+1+1=53 + 1 + 1 = 5.
  3. Range = 34−14=24\frac{3}{4} - \frac{1}{4} = \frac{2}{4} or 12\frac{1}{2} kg.

Explanation:

The total number of bags is the sum of all 'X' marks. The range is the difference between the heaviest bag and the lightest bag.