Question

Two students look at the books on their personal bookshelves.Books on BookshelvesFiction10 12 14 15 15 19Nonfiction 13 13 13 17 18 18Which statement is true?Based on the averages, more fictions books are usually found than nonfiction books.Half a book is the difference in the medians for nonfiction and fiction.The difference in the medians is 1.1.For both fiction and nonfiction books, the mean is greater than the median.

Answer 1

Answer:

Step 1:

Calculate the mean for the fiction books

The data is given below as

$\begin{gathered} 10,12,14,15,15,19 \\ \operatorname{mean}=\frac{\text{total value of numbers}}{nu\text{mber of items}} \\ \operatorname{mean}=\frac{10+12+14+15+15+19}{6} \\ \operatorname{mean}=\frac{85}{6} \\ \operatorname{mean}=14.2 \end{gathered}$

Calculate the median.

The median of a set of numbers is the number that is the middle when arranged in order of magnitude

$\begin{gathered} \operatorname{median}=\frac{14+15}{2} \\ \operatorname{median}=\frac{29}{2}=14.5 \end{gathered}$

Step 2:

Calculate the mean

The values are given below as

$\begin{gathered} 13,13,13,17,18,18 \\ \operatorname{mean}=\frac{\text{total value of numbers}}{nu\text{mber of items}} \\ \operatorname{mean}=\frac{13+13+13+17+18+18}{2} \\ \operatorname{mean}=\frac{92}{6} \\ \operatorname{mean}=15.3 \end{gathered}$

Calculate the median

The median of a set of numbers is the number that is the middle when arranged in order of magnitude

$\begin{gathered} \operatorname{median}=\frac{13+17}{2} \\ \operatorname{median}=\frac{30}{2} \\ \operatorname{median}=15 \end{gathered}$

Hence,

From the values above,

Based on the averages, fewer fictions books are usually found than nonfiction books.

The difference between the medians is 15-14.5=0.5

Hence,

The final answer is

Half a book is the difference in the medians for nonfiction and fiction.