m/courses/93 The five number summary of a dataset was found to be: -18, 6, 10, 11, 23 a) What is the IQR? b) Find the lower limit (ie: an observation is considered an outlier if it is below this). c) Find the upper limit (ie, an observation is considered an outlier if it is above this). d) Do we have any outliers? O no O yes
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![### Five Number Summary: Understanding Outliers and IQR
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**The five number summary of a dataset was found to be:**
\-18, 6, 10, 11, 23
---
**Questions:**
1. **What is the IQR?**
_Answer:_ `__________`
2. **Find the lower limit** (ie: an observation is considered an outlier if it is below this).
_Answer:_ `__________`
3. **Find the upper limit** (ie: an observation is considered an outlier if it is above this).
_Answer:_ `__________`
4. **Do we have any outliers?**
- o No
- o Yes
_Answer:_ `__________`
---
**Explanation of Terms:**
- **IQR (Interquartile Range)**: A measure of statistical dispersion, or how spread out the data points are in a dataset. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
- **Lower Limit**: To determine if a data point is an outlier on the lower end, we use the formula: Q1 - 1.5 * IQR.
- **Upper Limit**: To determine if a data point is an outlier on the upper end, we use the formula: Q3 + 1.5 * IQR.
- **Outliers**: Data points that fall below the lower limit or above the upper limit.
By understanding and applying these concepts, you can accurately identify outliers and gain more insights from your data analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9364916e-ff41-4b95-a11d-57a67c815768%2Fb17412f6-c50d-47fc-a5a8-a3b491539d4e%2Fy0nvliq_processed.jpeg&w=3840&q=75)
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