Question

a librarian was trying to figure out the number of books in the nonfiction section. the values represent the numbers of books on each shelf of a corner bookcase. 27, 15, 23, 15, 22, 18, 16, 14, 23, 25, 13, 29 which measure of central tendency should the librarian use? the mean neither the mean nor median because there is too much variability the median either the mean or median since they are the same

Explanation:

Step1: Calculate the mean

The mean is calculated by summing all the values and dividing by the number of values.
Sum of values: \(27 + 15+23 + 15+22+18+16+14+23+25+13+29=240\)
Number of values \(n = 12\)
Mean \(\bar{x}=\frac{240}{12}=20\)

Step2: Calculate the median

First, order the data: \(13,14,15,15,16,18,22,23,23,25,27,29\)
Since \(n = 12\) (even), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th values.
\(\frac{n}{2}=6\) and \(\frac{n}{2}+1 = 7\)
Median \(M=\frac{18 + 22}{2}=\frac{40}{2}=20\)

Answer:

either the mean or median since they are the same