Question

A textbook publisher wants to estimate the number of sentences per paragraph in a history textbook. The publisher counts the number of sentences in 150 randorly selected paragraphs. The results areshown in the tableBased on the data, what is the mean number of sentences per paragraph in the textbook?

Answer 1

In order to calculate the number of sentences per paragraph, we need to calculate the weighted mean of the number of sentences using the number of paragraphs as a weight of each number of sentences:

`\mu=\frac{\sum ^{}_{}(wx)}{\sum ^{}_{}(w)}_{}`

So we have:

`\begin{gathered} \mu=(0\cdot1+3\cdot2+20\cdot3+43\cdot4+36\cdot5+25\cdot6+10\cdot7+8\cdot8+2\cdot9+3\cdot10)/(0+3+20+43+36+25+10+8+2+3) \\ \mu=(0+6+60+172+180+150+70+64+18+30)/(150) \\ \mu=(750)/(150) \\ \mu=5 \end{gathered}`

Therefore the mean number of sentences per paragraph is 5.