Distributions in Line Plot

Once you can read a line plot, the next skill is describing its distribution — the overall shape and pattern of the data. Is the data bunched in the middle or spread to one side? Are there gaps or unusual clusters? Describing distributions is a key GED data-and-statistics skill that helps you draw conclusions from real-world data.

What Is a Distribution?

A distribution describes how data values are spread across the possible range. In a line plot, the distribution is visible in the pattern of X’s: how many appear at each value and how they are arranged from left to right.

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Types of Distributions in a Line Plot

Symmetric Distribution

The data is roughly balanced on both sides of the center (like a bell shape). The mean and median are approximately equal.

• Example: test scores 60, 65, 70, 70, 75, 80 — centered near 70 with values spread evenly left and right.

Skewed Left (Negatively Skewed)

Most data values are on the right (high) side, with a tail stretching to the left (low values). The mean is typically less than the median.

• Example: most students scored 90–100, but a few scored very low.

Skewed Right (Positively Skewed)

Most data values are on the left (low) side, with a tail stretching to the right (high values). The mean is typically greater than the median.

• Example: most people earn moderate salaries, but a few earn very high incomes.

Uniform Distribution

Each value appears about the same number of times; the X’s are roughly the same height across the number line. There is no clear peak.

Bimodal Distribution

There are two peaks (two values appear most often). This may indicate two distinct subgroups in the data.

Clusters and Gaps

• A cluster is a group of data points bunched together around certain values.
• A gap is a range of values where no data appears.

Step-by-Step Summary

1. Look at the line plot and identify where the X’s are tallest (most frequent).
2. Determine if the shape is symmetric, skewed left, skewed right, uniform, or bimodal.
3. Note any clusters (values bunched together) or gaps (regions with no data).
4. Identify the peak(s) and any potential outliers (isolated X’s far from the rest).
5. Relate the shape to the mean vs. median: symmetric → mean ≈ median; skewed right → mean > median; skewed left → mean < median.

Watch: Shape of Data Distributions (Video Lesson)

This lesson shows how to identify and describe the shape of a data distribution from a line plot:

Worked Examples

Example 1: A line plot shows: 1(1X), 2(1X), 3(2X), 4(5X), 5(4X), 6(3X), 7(1X), 8(1X). Describe the distribution.

The data peaks near 4–5 and is roughly balanced. This is approximately symmetric with a slight right skew. The mode is 4.

Example 2: A line plot shows: 10(1X), 20(1X), 30(1X), 40(5X), 50(6X), 60(7X). Describe the distribution.

Most data is on the right (high values), with a tail on the left. This is a skewed left (negatively skewed) distribution.

Example 3: Scores on a quiz: 60(4X), 70(1X), 80(1X), 90(1X), 100(4X). Describe the distribution.

Two peaks appear (at 60 and 100) with low frequency in the middle. This is a bimodal distribution.

Example 4: A data set shows values 1 through 6, each appearing exactly twice. Describe the distribution.

Every value has the same frequency. This is a uniform distribution; \(\color{blue}{\text{ mean } = \text{ median } = 3.5}\).

More Practice: Thinking About Shapes of Distributions (Video)

Khan Academy’s 6th-grade lesson explores how to think about and describe distribution shapes:

Exercises

1. A line plot shows: 5(1X), 6(2X), 7(5X), 8(2X), 9(1X). What type of distribution is this?
2. Data: 1(3X), 2(4X), 3(5X), 4(2X), 5(1X). Is this skewed left, skewed right, or symmetric?
3. Describe a distribution where there are clusters at 10 and 50 with almost nothing in between.
4. If the mean is much greater than the median in a line plot, which direction is the distribution skewed?
5. A line plot has a gap between values 30 and 60. What might this suggest about the data?

Answers

1. Symmetric (bell-shaped, peaks at 7 with even spread on both sides)
2. Skewed right (most data on the left side, tail points right toward higher values)
3. This is a bimodal distribution with a large gap between the two clusters; it may indicate two distinct groups.
4. Skewed right (a right tail pulls the mean up above the median)
5. The gap suggests that no observations fell in that range; the data may belong to two separate groups or there may be a measurement gap.

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Frequently Asked Questions

Why does skewness matter?

Skewness tells you which summary statistic (mean vs. median) better represents the “typical” value. In skewed distributions the median is usually the better choice because the mean is pulled toward the tail and may not reflect where most of the data actually is.

What is the difference between a cluster and a mode?

A mode is a single value that appears most often. A cluster is a group of nearby values that together have high frequency. A cluster often contains the mode but describes a region rather than a single point.

Can a distribution be both skewed and have an outlier?

Yes. An outlier is one isolated value far from the rest. A skewed distribution has a more gradual tail. Both can appear together; an outlier will often reinforce or create the appearance of skewness.

Related Topics

• Line Plot
• Mean, Median, Mode, and Range
• How to Identify an Outlier
• Finding Range, Quartile, and Interquartile Range
• How to Solve the Frequency Distribution Table