To understand how the word count of an essay relates to its score in the contest, we need to analyze the relationship between the two variables: word count and essay score.
Given the word counts and scores for the top ten essays:
Word counts: [tex]\(324, 352, 337, 318, 299, 280, 270, 260, 278, 250\)[/tex]
Scores: [tex]\(9.7, 9.5, 9.5, 9.0, 8.9, 8.9, 8.5, 8.4, 8.2, 7.0\)[/tex]
To find the relationship between these two sets of data, we calculate the correlation coefficient. The correlation coefficient is a statistical measure that describes the extent to which two variables are linearly related. It ranges from -1 to 1, where:
- 1 indicates a perfect positive linear relationship,
- -1 indicates a perfect negative linear relationship,
- 0 indicates no linear relationship.
In this case, the correlation coefficient between the word counts and scores is approximately [tex]\(0.859\)[/tex].
Since the correlation coefficient is positive and quite close to 1, this implies a strong positive linear relationship between word count and essay score. Thus, as the word count increases, the essay score also tends to increase.
Therefore, based on this analysis, we can conclude:
- Word count tends to increase as the score increases.
This means that higher word counts are generally associated with higher essay scores in this data set.
