Question

garth is packing boxes with books. the list shows how many books are in each of 10 boxes. 6, 14, 6, 18, 9, 9, 12, 10, 11, 15 which statement is true about the number of books packed to a box? the median number of books to a box is 8. the median number of books to a box is 9. the mean number of books to a box is 11. the mean number of books to a box is 12.

Explanation:

Step1: Sort the data

Sort the number of books \(6,14,6,18,9,9,12,10,11,15\) in ascending order: \(6,6,9,9,10,11,12,14,15,18\)

Step2: Calculate the median

Since \(n = 10\) (even), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=5\), \(\frac{n}{2}+1 = 6\). The 5th value is \(10\) and the 6th value is \(11\). Median \(=\frac{10 + 11}{2}=\frac{21}{2}=10.5\)

Step3: Calculate the mean

Mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), \(\sum_{i=1}^{10}x_{i}=6+14+6+18+9+9+12+10+11+15=110\), \(n = 10\). Mean \(\bar{x}=\frac{110}{10}=11\)

Answer:

C. The mean number of books to a box is 11.