The median of eleven elements is the element in the middle, assuming the numbers are arranged in order.

If the box is replaced with a 40, the data set becomes

\(\displaystyle \left \{ 20, 30, 30, 40, 40, 40,40, 40, 50, 50, 60 \right \}\),

making 40 the sixth element.

If the box is replaced with a value less than 40, then the lowest five values are 20, 30, 30, 40, and the median is 40.

If the box is replaced with a value greater than 40, then the lowest five values are 20, 30, 30, 40, 40, and the median is 40.

No matter what, the median is 40.

In ascending order, their weights are:

\(\displaystyle \left \{ 145, 153, 159,166, 172, 201\right \}\)

The median is the average of the two numbers in the middle of the set, which are \(\displaystyle 159\) and \(\displaystyle 166\):

\(\displaystyle \frac{159 + 166}{2} = \frac{325}{2} = 162.5\)

The median weight is \(\displaystyle 162.5\) pounds.

Arrange the scores from least to greatest.

\(\displaystyle \left \{ 61, 67, 68, 72, 73, 76, 80, 90 \right \}\)

There are an even number (eight) of scores, so the median is the arithmetic mean of the middle two scores, 72 and 73. This makes the median

\(\displaystyle \frac{72 + 73}{2} = 72.5\)

First, order the numbers from least to greatest.

\(\displaystyle 159, 456, 654, 741, 753, 852, 963\)

Then, identify the middle number: \(\displaystyle 741.\)

First, place the numbers in order from least to greatest:

\(\displaystyle 43, 51,60,62,65,74,91\)

Then, identify the middle number: 62.

Arrange the scores from least to greatest.

\(\displaystyle \left \{ 61, 67, 68, 70, 72, 73, 76, 80, 90 \right \}\)

There are an odd number (nine) of scores, so the median of the scores is the one that falls in the center - namely, 72.

The median is the number with an equal number of other items both above and below it.  There are 9 total numbers in the list, 4 of them are below 7, and 4 of them are above 7.

The median of a set of values is the value that is in the middle when you rearrange the values from least to greatest. In this set, the values can be rearranged as \(\displaystyle 33\), \(\displaystyle 46\), \(\displaystyle 55\), \(\displaystyle 78\), \(\displaystyle 90\) and the median is \(\displaystyle 55\).

The median is the middle number in a set when the set of numbers is ordered sequentially. 

When the intial set is reordered sequentially, you get the bottom set. (The top set is the original ordering of the numbers.)

\(\displaystyle 77, 90, 91, 93, 75, 89, 71\)

\(\displaystyle 71, 75, 77, 89, 90, 91, 93\)

In this sequential set of 7 numbers, the number 89 is in the fourth posiiton and exactly in the middle. Therefore, it is the mean. 

To find the median of a set of numbers, you must first reorder them from smallest to largest. Below is the set reordered as such:

\(\displaystyle 22, 34, 57, 88, 89\)

The median is the middle number of the set. Here, 57 is the middle number. Therefore, it is the median and the correct answer.