Question

How to identify a right or left skewed histogram

Answer 1

To identify whether a histogram is right-skewed or left-skewed, you should look at the shape of the distribution of the data represented in the histogram. Here’s how to differentiate between the two:

### Right-Skewed Histogram (Positive Skew)
- **Shape**: The bulk of the data points (the larger bars) are concentrated on the left side of the histogram, and the tail extends towards the right.
- **Mean and Median**: In a right-skewed distribution, the mean is typically greater than the median.
- **Example**: Income distribution is often right-skewed, where a majority of people earn below average, and a few people earn a significantly higher amount, creating a long tail on the right.

### Left-Skewed Histogram (Negative Skew)
- **Shape**: The bulk of the data points are concentrated on the right side of the histogram, and the tail extends towards the left.
- **Mean and Median**: In a left-skewed distribution, the mean is typically less than the median.
- **Example**: Age at retirement might be a left-skewed distribution because most people retire around the same age, but a few retire much earlier, creating a tail on the left.

### Steps to Analyze a Histogram:
1. **Examine the Bars**: Look at where the longest bars are located (the peak) and where the tail is pointing.
2. **Check for Tails**: If the tail is longer on the right, it is right-skewed; if it is longer on the left, it is left-skewed.
3. **Consider the Mean and Median**: If you have access to these statistics, use them to confirm your visual assessment.
4. **Look for Gaps**: In some cases, gaps in the histogram can also indicate skewness, but the shape is usually a more telling indicator.

By following these observations, you can effectively determine whether a histogram is right or left skewed.