# Left-Skewed Box Plot: How to Read Skewness in Box Plots

A left skewed box plot has a longer whisker on the left side and a median that sits closer to the top of the box (near the third quartile). The data has a tail of unusually small values pulling the distribution toward the low end. This article shows you how to read that shape from the five-number summary, how to confirm it with a skewness number, and where the visual cue can mislead you.

## Quick Answer

- A left skewed box plot (also called a box and whisker plot skewed left) has a longer left whisker than right whisker.
- The median line sits closer to Q3 (the top of the box) than to Q1 (the bottom).
- The mean is usually smaller than the median, because low outliers pull the mean down.
- A negative skewness value confirms it. Values below zero mean left skew, values above zero mean right skew [1].
- The opposite pattern, a longer right whisker with the median near Q1, is a box and whisker plot skewed right.

## What a Left Skewed Box Plot Means

A box plot is a picture of the five-number summary: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum [2]. When you look at one, you are not seeing every data point. You are seeing where the middle half of the data lives and how far the tails stretch.

In plain terms, a left skewed box plot means most of your values are bunched at the high end, with a few small values trailing off to the left. Think of exam scores where most students scored in the 80s and 90s but a handful scored in the 30s and 40s. The bulk sits high, and the low scores form the tail.

The precise statistical definition: a distribution is skewed left when its left tail is longer or more drawn out than its right tail [1]. In a box plot, that longer tail shows up as a longer left whisker and a median positioned above the center of the box.

## How It Works

The box plot encodes skewness in two places: whisker length and median position within the box.

The interquartile range is the width of the box:

$$IQR = Q3 - Q1$$

Whiskers extend to the most extreme values still inside the fences, using the standard 1.5 times IQR rule [3]:

$$\text{lower fence} = Q1 - 1.5 \times IQR$$
$$\text{upper fence} = Q3 + 1.5 \times IQR$$

Here is what each symbol means:

- $Q1$ is the 25th percentile, the value below which a quarter of the data falls.
- $Q3$ is the 75th percentile.
- $IQR$ is the spread of the middle 50 percent of the data.
- The lower fence and upper fence mark the boundary beyond which a point is flagged as a potential outlier.

For a left skewed box plot, the lower whisker (from Q1 down to the smallest value inside the lower fence) is longer than the upper whisker. The median sits closer to Q3.

You can also measure skewness directly. A common sample formula is:

$$g_1 = \frac{n}{(n-1)(n-2)} \sum \left( \frac{x_i - \bar{x}}{s} \right)^3$$

where $n$ is the sample size, $x_i$ is each value, $\bar{x}$ is the mean, and $s$ is the sample standard deviation. A negative result means left skew.

## Worked Example

Take 30 exam scores and 30 reaction times in milliseconds. The exam scores are left skewed, and the reaction times are right skewed, so you can compare the two shapes side by side.

| Exam score | Reaction time (ms) |
|---|---|
| 98 | 210 |
| 96 | 215 |
| 95 | 220 |
| 94 | 225 |
| 93 | 230 |
| 92 | 235 |
| 91 | 240 |
| 90 | 245 |
| 89 | 250 |
| 88 | 255 |
| 87 | 260 |
| 86 | 265 |
| 85 | 270 |
| 84 | 275 |
| 83 | 280 |
| 82 | 285 |
| 81 | 290 |
| 80 | 295 |
| 78 | 300 |
| 76 | 310 |
| 74 | 320 |
| 72 | 330 |
| 70 | 345 |
| 68 | 360 |
| 65 | 380 |
| 62 | 405 |
| 58 | 430 |
| 52 | 460 |
| 45 | 500 |
| 30 | 560 |

**Step 1: Sort the exam scores.** The sorted values run from 30 up to 98.

**Step 2: Find the quartiles.** Using linear interpolation (the QUARTILE.INC method), Q1 = 70.5000, the median Q2 = 82.5000, and Q3 = 89.7500.

**Step 3: Compute the IQR.** IQR = 89.7500 - 70.5000 = 19.2500.

**Step 4: Find the fences.** Lower fence = 70.5000 - 1.5 × 19.2500 = 41.6250. Upper fence = 89.7500 + 1.5 × 19.2500 = 118.6250.

**Step 5: Set the whiskers.** The smallest value inside the lower fence is 45, and the largest inside the upper fence is 98.

**Step 6: Compare whisker lengths.** Lower whisker = 70.5000 - 45 = 25.5000. Upper whisker = 98 - 89.7500 = 8.2500. The left whisker is more than three times longer.

**Step 7: Check the median position.** The median 82.5000 sits much closer to Q3 (89.7500) than to Q1 (70.5000). Both cues point left.

**Step 8: Confirm with skewness.** The mean is 78.1333, the sample standard deviation is 16.2114, and the skewness is -1.2661. Negative, so left skewed.

For contrast, the reaction times give Q1 = 246.2500, median = 282.5000, Q3 = 341.2500, IQR = 95.0000. The lower whisker is 36.2500 and the upper whisker is 118.7500, so the right side is far longer. The skewness is 1.3324, positive, so right skewed.

Here is the code that produces these numbers:

```python
import numpy as np
exam = [98,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,78,76,74,72,70,68,65,62,58,52,45,30]
q1, q2, q3 = np.percentile(exam, [25, 50, 75])  # linear interpolation (QUARTILE.INC)
iqr = q3 - q1
lower_fence = q1 - 1.5 * iqr
upper_fence = q3 + 1.5 * iqr
import pandas as pd
skew = pd.Series(exam).skew()  # negative => left-skewed
print(q1, q2, q3, iqr, lower_fence, upper_fence, round(skew, 4))
```

Output:

```
70.5 82.5 89.75 19.25 41.625 118.625 -1.2661
```

## How to Interpret It

Read a box plot in this order:

1. **Look at the whiskers.** Which one is longer? A longer left whisker is the first sign of left skew.
2. **Look at the median line.** Is it above or below the middle of the box? Above the middle means the data is concentrated at higher values.
3. **Compare the mean and median.** In a left skewed distribution, the mean is typically less than the median because the small tail values drag it down. In the example, the mean 78.1333 is below the median 82.5000.
4. **Check for outliers.** Points plotted beyond the whiskers on the left side reinforce the skew. See how to read those points in [box plot outliers](/blog/data-analysis/box-plot-outliers).

The practical meaning: a typical value is best described by the median, not the mean, because the mean is pulled toward the tail. If you report the mean of a left skewed variable, you may overstate or understate the typical case depending on which direction the tail runs.

## When to Use It (and when not to)

Use a box plot to check skew when you want a quick, distribution-free read of shape from the five-number summary [2]. It works well for comparing several groups at once, which is the whole point of [side-by-side boxplots](/blog/data-analysis/side-by-side-boxplots-guide).

Do not rely on a box plot alone when:

- You need to see whether the distribution has more than one peak. A box plot cannot show bimodality.
- Your sample is very small. With fewer than about 10 values, quartiles are unstable and whisker lengths can flip direction by chance.
- You need the exact shape. Pair the box plot with a histogram or density plot.

If you want to build one from your own numbers, the [Box Plot Maker](/tools/box-plot-maker) will compute the quartiles and draw it for you.

## Left Skew vs Right Skew

The two shapes are mirror images. This table summarizes the differences.

| Feature | Left skewed | Right skewed |
|---|---|---|
| Longer whisker | Left | Right |
| Median position | Near Q3 (top) | Near Q1 (bottom) |
| Mean vs median | Mean < median | Mean > median |
| Sign of skewness | Negative | Positive |
| Example here | Exam scores, skew -1.2661 | Reaction times, skew 1.3324 |

For a fuller comparison of the two directions, see [skew to the left vs skewed right](/blog/data-analysis/skew-to-the-left-vs-skewed-right).

## Common Mistakes

- **Judging skew from the box alone.** The box shows the middle 50 percent, and the median position inside it reflects only the shape of that middle half. Skew lives in the whiskers. Fix: always compare whisker lengths before deciding.
- **Assuming a long whisker means outliers.** Whiskers stop at the fence, so a long whisker just means spread. Fix: look for separately plotted points beyond the whisker caps.
- **Reading the median position backwards.** A median near the top of the box means the data is bunched high, which is left skew. Fix: ask where the tail is, not where the line is.
- **Using the mean as the typical value.** In skewed data the mean is pulled toward the tail. Fix: report the median for skewed variables.
- **Trusting skewness on tiny samples.** The skewness formula divides by $(n-1)(n-2)$, so small $n$ makes it unstable. Fix: treat skewness as descriptive only when $n$ is reasonably large.
- **Mixing up the direction of the sign.** Negative skewness means the tail is on the left. Fix: remember that the sign points toward the tail.

## Limitations

A box plot compresses your data into five numbers, so it hides everything between them. Two datasets with identical quartiles and whiskers can have completely different shapes, including one that is bimodal and one that is not. Skewness read from a box plot is a visual impression, not a test.

The whisker rule also depends on the software. Some tools use 1.5 times the IQR, others let you change the multiplier, and some draw whiskers to the minimum and maximum regardless of outliers [3]. If you compare plots made in different tools, check the whisker convention first. And remember that skewness is a property of the sample you drew, not proof about the population. A negative value in one sample does not guarantee the underlying distribution is left skewed.

## Frequently Asked Questions

### What does a left skewed box plot look like?

It has a longer whisker on the left and the median line sits closer to the top of the box. The bulk of the data is at higher values, with a tail of small values stretching left. If you also plot the mean, it usually appears below the median.

### How do I tell left skew from right skew in a box plot?

Compare the two whiskers. If the left whisker is longer, the plot is skewed left. If the right whisker is longer, it is skewed right. Confirm with the median position: near Q3 means left skew, near Q1 means right skew.

### Is a left skewed box plot the same as negative skewness?

Yes. Left skew and negative skewness describe the same shape. The skewness value is negative because the cubed deviations of the small tail values dominate the sum. In the worked example, the exam scores had a skewness of -1.2661.

### Can a box plot be skewed left with no outliers?

Yes. Skewness comes from the length of the whiskers and the position of the median, not from flagged outliers. A dataset can be clearly left skewed with every point inside the fences, as long as the left whisker is longer than the right one.

### Why is the mean lower than the median in a left skewed distribution?

The few very small values in the left tail pull the mean downward, while the median only depends on position in the sorted order. That gap between mean and median is one of the most reliable signs of left skew, and it is why the median is the better summary for skewed data.

## References

1. [1.3.3.14.6. Histogram Interpretation: Skewed (Non-Normal) Right](https://www.itl.nist.gov/div898/handbook/eda/section3/eda33e6.htm)
2. [9.5: Box Plots - Statistics LibreTexts](https://stats.libretexts.org/Courses/Compton_College/Pre-Statistics/09%3A_Descriptive_Statistics/9.05%3A_Box_Plots)
3. [1.3: Basic summary statistics, histograms, and boxplots using R - Statistics LibreTexts](https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Intermediate_Statistics_with_R_(Greenwood)/01%3A_Preface/1.03%3A_Basic_summary_statistics_histograms_and_boxplots_using_R)

## Further Reading

- [2.3: Box Plots - Mathematics LibreTexts](https://math.libretexts.org/Courses/Heartland_Community_College/HCC%3A_Introduction_to_Statistics_(Lathrop)/02%3A_Visualizing_Data/2.3%3A_Box_Plots)
- [3.E: Descriptive Statistics (Optional Exercises) - Statistics LibreTexts](https://stats.libretexts.org/Courses/Las_Positas_College/Math_40%3A_Statistics_and_Probability/03%3A_Data_Description/3.E%3A_Descriptive_Statistics_(Optional_Exercises))
- [matplotlib.pyplot.boxplot, Matplotlib 3.11.2 documentation](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.boxplot.html)
- [Weissgerber TL, Milic NM, Winham SJ et al. (2015). Beyond Bar and Line Graphs: Time for a New Data Presentation Paradigm. PLOS Biology](https://doi.org/10.1371/journal.pbio.1002128)

## Related Articles

- [Skew to the Left vs Skewed Right: How to Tell the Difference](/blog/data-analysis/skew-to-the-left-vs-skewed-right)
- [Box Plot Outliers: How to Identify and Interpret Them](/blog/data-analysis/box-plot-outliers)
- [Side-by-Side Boxplots: How to Read and Create Them](/blog/data-analysis/side-by-side-boxplots-guide)
- [Left Skewed Distribution: Meaning and Examples](/blog/data-analysis/left-skewed-distribution-meaning)
- [Residual Plots: How to Interpret Them with Examples](/blog/data-analysis/residual-plots-how-to-interpret)
- [How to Make and Read a Box Plot: Quartiles, Whiskers and Outliers](/blog/research-skills/how-to-make-a-box-plot)