What are right-skewed and left-skewed distributions?
Statistics Interview Questions: Part 2
Hello, welcome back to Statistics Interview Questions series. In this article, we will go through the right-skewed and left-skewed distributions. Before moving to the left and right-skewed distribution, it is important to know the normal distribution.
The normal distribution is a bell-shaped distribution. If we cut the bell in two shapes from the middle, both parts will be the same in shape, i.e left part would be identical to the right part. The mean, median, and mode all three are represented by this middle point. In a normal distribution, the mean, median, and mode all are equal. The normal distribution is also known as no-skew or zero-skew or symmetrical distribution as both left and right parts are symmetrical to each other.
But when the left and right parts are not symmetrical then there is skewness in the distribution. Skewness describes the shape of data. To know the skewness, look at the shape of the distribution to know which side of the distribution has a long tail.
Question: Explain right-skewed and left-skewed distributions. Where are the mean and median values in these cases compared to normal symmetrical bell shapes?
Skewness distribution can be of three types:
- Right-skewed Distribution:
When the distribution has a long tail towards the right side, then it is known as a right-skewed or positive-skewed distribution. In the right-skewed distribution, the concentration of data points towards the right tail is more than the left tail.
In the right-skewed distribution: Mean > Median> Mode.
2. Left-skewed Distribution:
When the distribution has a long tail towards the left side, then it is known as a left-skewed or negative-skewed distribution. In the negative-skewed distribution, the concentration of data points towards the left tail is more than the right tail.
In the left-skewed distribution: Mode > Median > Mean
3. Zero-skewed Distribution:
When the distribution’s left side is symmetrical to the right side then it is known as a zero-skewed or normal distribution. In the zero-skewed distribution, the concentration of data points toward the left tails is the same as toward the right tail.
In the zero-skewed distribution: Mode = Median = Mean
Some additional points: Skewness with Box and Whisker Plots
A box and whisker plot is a graph that exhibits data from a five-number summary (Q0, Q1, Q2, Q3, Q4), including one of the measures of central tendency median Q2.
The skew of a distribution can be determined by a number of different methods. Using quartiles is one method for doing this.
If (Q 2 -Q 1) > (Q 3 -Q 2), we can say that a distribution is left-skewed, whereas (Q 2 -Q 1) < (Q 3 - Q 2) indicates that a distribution is right-skewed.
Remembering that distribution is left skewed if the left rectangle is larger than the right and is right skewed if the right rectangle is larger than the left can help you to remember this rule.
Here are some broad guidelines for figuring out a distribution’s skew: — To determine skew :
- If you receive a distribution graph, look for the graph’s tail.
- If you receive a box plot, find the larger rectangle to determine the skew.
- Try creating a box plot or graph and using that to calculate skew if all you have is the data.
- If none of these techniques are successful, find the skew by comparing the mean, median, and mode.
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