Ms. Sutton recorded the word counts and scores of the top ten essays in a timed writing contest. The table shows her data.
Winning Essay Length
| Essay Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| ---------- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Essay Score| 9.7 | 9.5 | 9.5 | 9.0 | 8.9 | 8.9 | 8.5 | 8.4 | 8.2 | 7.0 |
| Word Count | 324 | 352 | 337 | 318 | 299 | 304 | 290 | 291 | 278 | 250 |
How does the word count of an essay relate to its score in the contest?
A. Word count tends to decrease as the score decreases.
B. Word count tends to increase as the score decreases.
C. Word count tends to remain constant as the score decreases.
D. Word count has no apparent relationship to the score of the essay.
Answer (2)
The analysis of the essay scores and word counts shows that higher scores are generally associated with higher word counts. As we observe the scores and corresponding word counts, it becomes clear that as essay scores decrease, the word count tends to decrease as well. Therefore, the answer is A: Word count tends to decrease as the score decreases.
;
Calculate the correlation coefficient between essay scores and word counts.
The correlation coefficient is approximately 0.936, indicating a strong positive correlation.
A positive correlation suggests that as the score increases, the word count tends to increase.
Therefore, word count tends to decrease as the score decreases. Word count tends to decrease as the score decreases.
Explanation
Analyzing the Problem We are given a table of essay scores and word counts for the top ten essays in a contest. We want to determine the relationship between the word count of an essay and its score. To do this, we can analyze the data to see if there is a trend. A positive correlation would suggest that as the score increases, the word count also tends to increase. A negative correlation would suggest that as the score increases, the word count tends to decrease. A correlation close to zero would suggest there is no apparent relationship.
Calculating the Correlation Coefficient To quantify the relationship, we can calculate the correlation coefficient between the essay scores and the word counts. The correlation coefficient ranges from -1 to 1. A value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates a weak or no correlation.
Interpreting the Correlation Coefficient Using the provided data, the correlation coefficient between the essay scores and word counts is approximately 0.936. This value is close to 1, indicating a strong positive correlation.
Determining the Relationship Since the correlation coefficient is positive and close to 1, we can conclude that as the essay score increases, the word count tends to increase. Conversely, as the score decreases, the word count tends to decrease.
Examples
Understanding the relationship between essay length and score can be useful in various real-life scenarios. For example, if you are a teacher grading essays, knowing this relationship can help you set expectations for essay length based on the desired score range. Similarly, if you are a student preparing for a writing contest, understanding this relationship can guide you in determining the optimal word count to aim for to achieve a high score. In data analysis, the correlation coefficient is a valuable tool for understanding the strength and direction of linear relationships between variables. In this case, we found a strong positive correlation (approximately 0.936) between essay scores and word counts, indicating that longer essays tend to receive higher scores.
