To find the median you need to arrange the values in numerical order.

Starting with this:

Rearrange to look like this:

\(\displaystyle \small \small \left \{ 67,68,70,75,77,83,89,92\right \}\)

If there are an odd number of values, the median is the middle value. In this case there are 8 values so the median is the average (or mean) of the two middle values.

\(\displaystyle \small (75+77)\div2=76\)

The median of nine (an odd number) integers is the one in the middle when the numbers are arranged in ascending order; in this case, it is the fifth lowest. Since the nine integers are consecutive, the greatest integer is four more than the median, or \(\displaystyle 604 + 4 = 608\).

We know that the numbers should be arranged in ascending order to find the median. When the number of values is odd, the median is the single middle value. In this question we have \(\displaystyle 11\) consecutive integers with the median of \(\displaystyle 28\). So the median is the \(\displaystyle 6th\) number in the rearranged data set. Since the \(\displaystyle 11\) integers are consecutive, the smallest integer is five less than the median or it is equal to \(\displaystyle 28-5=23\).

There are \(\displaystyle 4+7+3+2=16\) data values altogether. When the number of values is even, the median is the mean of the two middle values. So in this problem the median is the mean of the \(\displaystyle 8th\) and \(\displaystyle 9th\) largest values. So we can write:

\(\displaystyle 8th\ largest \ value=14\)

\(\displaystyle 9th\ largest \ value=14\)

So:

\(\displaystyle Median=\frac{14+14}{2}=14\)

In order to find the median the data must first be ordered. So we have:

\(\displaystyle \left \{ 57,66,69,80,84,86,90,92 \right \}\)

In this problem the number of values is even. We know that when the number of values is even, the median is the mean of the two middle values. So we get:

\(\displaystyle Median=\frac{80+84}{2}=82\)

In order to find the median the data must first be ordered. So we have:

\(\displaystyle \left \{ 165,168,169,174,176,180,181,182,188 \right \}\)

When the number of values is odd, the median is the single middle value. In this problem we have nine values. So the median is th \(\displaystyle 5th\) value which is \(\displaystyle 176cm\).

In order to find the median, the data must first be ordered. So we should write:

\(\displaystyle \left \{ 1,2,2,3,3,3,4,4,4,7 \right \}\)

When the number of values is even, the median is the mean of the two middle values. In this problem we have \(\displaystyle 10\) values, so the median would be the mean of the \(\displaystyle 5th\) and \(\displaystyle 6th\) values:

\(\displaystyle Median=\frac{3+3}{2}=3\)

The data should first be ordered:

\(\displaystyle \left \{ t, t+1, t+2, t+4, t+5, t+8 \right \}\)

When the number of values is even, the median is the mean of the two middle values. So in this problem we need to find the mean of the \(\displaystyle 3th\) and \(\displaystyle 4th\) values:

\(\displaystyle Median=\frac{(t+2)+(t+4)}{2}=\frac{2t+6}{2}=t+3\)

The mean is the sum of the data values divided by the number of values or as a formula we have:

\(\displaystyle \bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}\)

Where:

\(\displaystyle \bar{x}\) is the mean of a data set, \(\displaystyle \sum\) indicates the sum of the data values \(\displaystyle x_{i}\) and \(\displaystyle n\) is the number of data values. So we can write:

\(\displaystyle \bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}=\frac{(64+78+76+80+82+83+75+x)}{8}\)

\(\displaystyle \Rightarrow \bar{x}=\frac{538+x}{8}=78\Rightarrow 538+x=78\times 8\)

\(\displaystyle \Rightarrow 538+x=624\Rightarrow x=624-538=86\ in\)

In order to find the median, the data must first be ordered:

\(\displaystyle \left \{ 64,75,76,78,80,82,83,86 \right \}\)

Since the number of values is even, the median is the mean of the two middle values. So we get:

\(\displaystyle Median=\frac{78+80}{2}=79\ in\)