Question

Question #f9e8f

Answer 1

See a solution process below:

Explanation:

The median is the middle number (in a sorted list of numbers).

There are 11 occurrences of hours of sleep less than 6 hours:

5 times at 4 hours and 6 times at 5 hours.

There are 7 occurrences of 6 hours of sleep.

Therefore the last occurrence of 6 hours of sleep is in the 18th position.

Therefore, there are 17 sorted numbers prior to the last occurrence.

So, to find the largest number for `x`, the sum of the occurrences must equal 17.

So we can write and solve for `x`:

`2 + x + 6 = 17`

`x + 8 = 17`

`x + 8 - color(red)(8) = 17 - color(red)(8)`

`x = 9`

The largest value `x` can have and still have a median of `6` is `color(red)(8)`

Answer 2

The maximum value of `x` is `7`. See explanation.

Explanation:

The median is the middle value of an ordered data set. In the given set there are 18 values not higher than `6`. So if the median is `6`, then the median is somewhere between `12` and `18` term.

If the median is the `18th` term, then the total number of data is `2xx17+1=35`. Given the total number of data we have:

`28+x=35`

`x=7`

Answer 3

9

Explanation:

For the median, it has to be six. That means the 17 numbers before the last 6 (the five 4's, the six 5's, and the remaining six 6's) has to be equal to the number of 7's, 8's, and 9's. So `17 = 2 + x + 6`. Therefore, `x=9`.