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: Order the data

First, we order the number of books in each box from least to greatest: \(6, 6, 9, 9, 10, 11, 12, 14, 15, 18\).

Step2: Calculate the median

Since there are 10 (an even number) data points, the median is the average of the 5th and 6th values. The 5th value is \(10\) and the 6th value is \(11\). So the median is \(\frac{10 + 11}{2}=\frac{21}{2} = 10.5\). Wait, maybe I made a mistake. Wait, let's re - order: \(6,6,9,9,10,11,12,14,15,18\). Yes, 5th is 10, 6th is 11. So median is 10.5. Now let's calculate the mean.

Step3: Calculate the mean

The mean is the sum of all values divided by the number of values. The sum of the values: \(6+6 + 9+9+10+11+12+14+15+18\). Let's calculate step by step: \(6 + 6=12\); \(12+9 = 21\); \(21+9=30\); \(30 + 10=40\); \(40+11 = 51\); \(51+12=63\); \(63+14 = 77\); \(77+15=92\); \(92+18 = 110\). There are 10 values, so the mean is \(\frac{110}{10}=11\).

Now let's check the options:

• Option 1: Median is 8. Wrong, we calculated median as 10.5.
• Option 2: Median is 9. Wrong.
• Option 3: Mean is 11. Correct.
• Option 4: Mean is 12. Wrong.

Answer:

The mean number of books to a box is 11. (The option corresponding to this statement, e.g., if it's the third option in the list, we would write the option as per the original question's option numbering. Since the options are:

• 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.

So the correct option is: The mean number of books to a box is 11. (Or if we use the option identifier, assuming the third option is labeled as C, then C. The mean number of books to a box is 11.)