The new data point for a child who is 6 years old and has a vocabulary of 900 words decreased the correlation coefficient. This means that the relationship between age and vocabulary became weaker.
Here's why:
The original correlation coefficient was 0.997, which is a very strong positive correlation.
This means that there was a strong tendency for older children to have larger vocabularies.
The new data point is for a child who is younger than the average child in the data set (6 years old compared to an average age of about 10 years old).
This child's vocabulary is also smaller than the average vocabulary for children in the data set.
Adding this new data point pulls the average age down and the average vocabulary down.
This has the effect of weakening the positive relationship between age and vocabulary, which is why the correlation coefficient decreased.
It is important to note that the effect of adding a new data point on the correlation coefficient will depend on the specific values of the new data point.
In some cases, adding a new data point can actually increase the correlation coefficient.
However, in the case of the data set you provided, adding the new data point had the effect of weakening the relationship between age and vocabulary.
Question
The ages (in years) of 11 children and the number of words in their vocabulary are shown in the attached data table with a sample correlation coefficient r of 0.975 A 12th data point was added to the end of the data set for a child who is 6 years old and has a vocabulary of 900 words. Describe how this affects the correlation coefficient r.