Let's analyze the dot plots provided in the image.

Part (a): Compare the shapes of the plots.

• Fourth Grade Plot: The distribution is slightly skewed to the right. Most of the word lengths cluster around 2 to 6 characters, with a peak at 4 characters. There are fewer longer words, with some outliers around 10 to 14 characters.
• Seventh Grade Plot: This distribution also has a peak but is more spread out across different word lengths. The words range more evenly from 2 to 12 characters, with a slight peak around 4 to 6 characters. The distribution seems less skewed and more uniform compared to the fourth-grade plot.

Part (b): Compare the ranges of the plots.

• Range of Fourth Grade Plot: The data points span from 1 to 14, giving a range of 13 characters.
• Range of Seventh Grade Plot: The data points span from 0 to 14, giving a range of 14 characters.

Explanation: The range for both grades is quite similar, suggesting that the variation in word lengths is not drastically different between the fourth-grade and seventh-grade books. However, the shape comparison indicates that while fourth-grade books have a concentration of shorter words, seventh-grade books have a more even distribution of word lengths. This could imply that books for older students use a more diverse vocabulary with varying word lengths.

Would you like further details on any part of this analysis?

Related Questions:

1. How does the median word length compare between the two grades?
2. What does the skewness of each plot suggest about word length in the respective grades?
3. How would you describe the mode of each plot, and what does it indicate about word length frequency?
4. What can we infer about the difficulty level of the books from the distribution of word lengths?
5. If the data set included more grades, how might the word length distribution change as the grade level increases?

Tip: When analyzing distributions, consider both the shape and spread to understand the data's underlying patterns.