Answered

Ms. Sutton recorded the word counts and scores of the top ten essays in a timed writing contest. The table shows her data.



\begin{table}

\captionsetup{labelformat=empty}

\caption{Winning Essay Length}


Essay Rank		12345678910

Essay Score		9.79.59.59.08.98.98.58.48.27.0

Word Count		324352337318299304290291278250




\end{table}



How does the word count of an essay relate to its score in the contest?


AWord count tends to decrease as the score decreases.
BWord count tends to increase as the score decreases.
CWord count tends to remain constant as the score decreases.
DWord count has no apparent relationship to the score of the essay.

Verified Answer :

  • The data shows a strong positive correlation between essay scores and word counts.
  • As the scores decrease from \(9.7\) down to \(7.0\), the corresponding word counts also show a clear downward trend from \(324\) to \(250\).
  • Based on this positive relationship, we conclude:
  • \(\boxed{\text{Word count tends to decrease as the score decreases.}}\)

Explanation

  1. Analyze the data points

To understand the relationship between the essay scores and the word counts, we first organize the data into pairs of (Score, Word Count). The provided data points are:
(9.7, 324), (9.5, 352), (9.5, 337), (9.0, 318), (8.9, 299), (8.9, 304), (8.5, 290), (8.4, 291), (8.2, 278), and (7.0, 250).

  1. Examine the trend and correlation

We observe how the word count changes as the score decreases from 9.7 down to 7.0.
Looking at the data, the highest scores (like 9.7 and 9.5) correspond to higher word counts (324, 352, 337), while lower scores (like 8.2 and 7.0) correspond to lower word counts (278, 250). Calculating the correlation coefficient between the scores and word counts gives a value of approximately \(0.936\). This indicates a strong positive linear relationship between the two variables.

  1. Conclude the relationship

Since the correlation is positive and the data shows that lower scores generally align with lower word counts, we can conclude that the word count tends to decrease as the score decreases. This matches the observation that higher scores generally require or are associated with longer essays in this specific contest.

Examples

In real-world data analysis, identifying trends like this is essential. For example, a student could use this type of analysis to determine if longer assignments generally receive higher grades in their classes. By plotting essay scores against word counts, they can visualize if there's an optimal word count range for achieving high marks, helping them plan their writing effectively in the future.

Related Questions