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Skewness (CIE A Level Maths: Probability & Statistics 1)
Revision Note
Skewness
The distribution of a data set is either symmetrical or it has skewness.
What is skewness?
- Skewness describes the way in which data in a non – symmetrical distribution is leaning
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- A distribution that has its tail on the right side has positive skew
- A distribution that has its tail on the left side has negative skew
- If the distribution is shown on a box plot looking at the difference between the quartiles can help decide how it is skewed
- If the median is closer to the lower quartile then the distribution has positive skew
- Q3 - Q2 > Q2- Q1
- If the median is closer to the upper quartile then the distribution has negative skew
- Q3 - Q2 < Q2 - Q1
- If the median is closer to the lower quartile then the distribution has positive skew
- Looking at the values of the statistics can help you decide whether distribution is positively skewed or negatively skewed
- In a positively skewed distribution
- Mode < median < mean
- In a negatively skewed distribution
- Mean < median < mode
- In a positively skewed distribution
Examiner Tip
- You only need to be able to recognise the different types of skewness
- It can help to comment on skewness when asked to compare distributions
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