Esther wants to know if the number of words on a page in her language arts book is generally more than the number of words on a page in her social studies book. She takes a random sample of 25 pages in each book and then calculates the mean, median, and mean absolute deviation for the 25 samples of each book. Book Mean Median Mean Absolute Deviation Language arts 78.5 60 14.2 Social studies 68.7 65 9.8 She claims that because the mean number of words on each page of the language arts book is greater than the mean number of words on each page of the social studies book, the language arts book has more words per page. Based on the data, is this a valid inference? Yes, because there is a lot of variability in the language arts book data No, because there is a lot of variability in the language arts book data Yes, because the mean is larger in the language arts book No, because the mean is larger in the social studies book

The data that Esther took shows that the answer to the inference being valid is No, because there is a lot of variability in the language arts book data.

What does Esther's data show?

The number of words on the pages in the language arts book seems to average to be more than the number of words in the Social studies text book as Esther inferred.

However, the variabillity in the language arts book shown as the absolute deviation of 14.2 means that sometimes the words in the language art book will be less than its mean. The inference is therefore not valid.

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