The following bivariate data set contains an outlier. y 69.5 -15.5 63.5 -653.4 72.1 -3212.9 94.2 191.8 102.7 2672.9 93 706.8 62 -1192.1 52.1 -2637 78.1 -1757.5 65.4 -1137.1 72.3 -1805 108.8 -5526.2 50.4 2520.6 61.1 4793.8 284 -1266.5 What is the correlation coefficient with the outlier? rw = [Round your answer to three decimal places.] What is the correlation coefficient without the outlier? wo = [Round your answer to three decimal places.]
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.
![### Bivariate Data Analysis with an Outlier
The following bivariate data set contains an outlier.
| x | y |
|-------|--------------|
| 69.5 | -15.5 |
| 63.5 | -653.4 |
| 72.1 | -3212.9 |
| 94.2 | 191.8 |
| 102.7 | 2672.9 |
| 93 | 706.8 |
| 62 | -1192.1 |
| 52.1 | -2637 |
| 78.1 | -1757.5 |
| 65.4 | -1137.1 |
| 72.3 | -1805 |
| 108.8 | -5526.2 |
| 50.4 | 2520.6 |
| 61.1 | 4793.8 |
| 284 | -1266.5 |
#### Analysis Questions
**1. What is the correlation coefficient with the outlier?**\
\( r_w = \) \_\_\_\_\_\_ [Round your answer to **three decimal places.**]
**2. What is the correlation coefficient without the outlier?**\
\( r_{wo} = \) \_\_\_\_\_\_ [Round your answer to **three decimal places.**]
#### Graph and Diagram Explanation
The provided table lists paired values for variables \( x \) and \( y \). It is observed that one of these pairs (specifically \( x = 284 \) and \( y = -1266.5 \)) displays a significantly different pattern compared to the others, indicating the presence of an outlier.
**Having an outlier in your data can drastically affect statistical measures such as the correlation coefficient.** The correlation coefficient quantifies the degree to which two variables are linearly related. The two questions above prompt an analysis of this relationship both in the presence of the outlier and with the outlier excluded, to understand the impact of the outlier on the data set.
**Note:** This bivariate data set is essential for learning about the robustness of correlation coefficients and the impact of anomal](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F443e45af-3927-4fd9-baca-290567a407b3%2F982f98a6-3c66-4d95-ab0e-eac19a2d81b8%2Flze533i_processed.png&w=3840&q=75)
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