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: Calculate the mean

First, find the sum of the numbers: $6 + 14+6 + 18+9 + 9+12+10+11+15=110$. There are $n = 10$ data - points. The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{110}{10}=11$.

Step2: Calculate the median

Arrange the data in ascending order: $6,6,9,9,10,11,12,14,15,18$. Since $n = 10$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The 5th value is $10$ and the 6th value is $11$. The median $M=\frac{10 + 11}{2}=10.5$.

Answer:

The mean number of books to a box is 11.