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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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What is a Line Plot? A line plot is a graph that displays data along a number line. Visually, it consists of a horizontal line with marks at equal intervals, where an 'X' or a dot is placed above a number for each time that value occurs. This helps show the frequency and distribution of data points in a clear, vertical stack.

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Title and Axis Labels: Every line plot must have a title to explain the data being presented. There should also be a label below the number line to describe what the data represents, such as 'Pencil Length' or 'Weight in Kilograms', including any units used.

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Scale and Fractional Intervals: The scale is the range of numbers on the line plot. In Grade 4, these intervals often include fractions like 14\frac{1}{4}, 12\frac{1}{2}, or 34\frac{3}{4}. Visually, these are represented by small, evenly spaced tick marks placed between the whole numbers on the horizontal axis.

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Understanding Data Frequency: Frequency refers to how many times a specific value appears in a dataset. On a line plot, frequency is visually shown by the height of the 'X' marks stacked above a number. If one number has more 'X' marks than others, it has a higher frequency.

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Identifying the Mode: The mode is the value that appears most often in a set of data. On a line plot, the mode is easily identified as the tallest column of 'X' marks or dots, representing the most common measurement or count.

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Determining the Range: The range is the spread of the data from the smallest to the largest value with a recorded data point. Visually, it is the distance along the number line between the first 'X' on the left and the last 'X' on the right. It is calculated as: Range=Greatest Value−Least ValueRange = \text{Greatest Value} - \text{Least Value}.

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Outliers in Data: An outlier is a value that is much larger or much smaller than the rest of the data. Visually, an outlier appears as a single 'X' mark that is far away from the main cluster of data, separated by a noticeable empty gap on the number line.

📐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.