The median is defined as the center data value of the data set. This data set is already set in numerical order: 

\(\displaystyle \small 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 , 100\).

Since there is an odd number of data values, \(\displaystyle \small 11\), we subtract one, \(\displaystyle \small 11-1=10\), and then divide ten in half, \(\displaystyle \small 5\). This means that there must be five data values on either side of the median. To satisfy this requirement, the median must be at the sixth spot.

Thus for this data set: 

\(\displaystyle \small 1, 2, 3, 4, 5, \textbf{6}, 7, 8, 9, 10 , 100\), the median is \(\displaystyle \small 6\). 

To find the median of a data set, we must find the center of the data. If the data set has an odd number of data values, simply subtract one, and then divide in half. Your result will be the amount of values that lie on each side of the median.

However, when there is an even amount of data values, there is no definite center of the data set. The most commonly used method of finding the median given an even amount of data values is to simply cross off data values on either ends of the set until we are left with two numbers in the center:

 \(\displaystyle \small \small \small 2, 2, \textbf{3,4}, 5, 6\). In this set \(\displaystyle \small 3\) and \(\displaystyle \small 4\) are the center numbers.

Now we can find the average of these two values: 

\(\displaystyle \small 3 + 4 = 7, 7\div2 = 3. 5.\) 

Thus, our true center of the data set lies between the numbers \(\displaystyle \small 3\) and \(\displaystyle \small 4\), \(\displaystyle \small 3.5\). 

The median is defined as the center number of the data. To find this value, the first step is to place the numbers in numerical order. 

\(\displaystyle \small 12, 22, 23, 42, 53, 55, 56\).

Since there are 7 pieces of data, and odd number, we can subtract one, and then divide the answer in half. 

\(\displaystyle \small 7- 1 = 6 , 6 \div2 = 3.\) 

This means that the median has to have 3 data values on either side of it.

\(\displaystyle \small 12, 22, 23, {\color{Red} 42}, 53, 55, 56\)

To satisfy this requirement, our median must be \(\displaystyle \small 42.\)

To find the median, we first must put the numbers in numerical order: 

\(\displaystyle \small 6,6,9,10,15,16,20,30,48.\) 

Since there are 9 pieces of data, we subtract one and then divide in half. 

\(\displaystyle \small 9-1 = 8 \div2 = 4\).

This means that there must be 4 pieces of data on either side of the number that is the median.

To satisfy this requirement, \(\displaystyle \small 15\) must be the median. 

The median is the numer that, when put in numerical order, appears in the direct center of the group.

To find this value, we must first put the numbers in numerical order: 

\(\displaystyle \small 1,1,2,2,3,3,9\).

In this set of data we have seven pieces of data, we subtract one, then divide the result in half, 

\(\displaystyle \small 7-1=6\div2 = 3\).

This means that there must be three numbers on either side of the median.

To satisfy this requirement, our median must be \(\displaystyle \small 2\). 

Median means the middle of a sorted set of numbers. That is, it is the exact middle of a set of numbers. 

In order to solve for median, we must allign the numbers in order in increasing value.

\(\displaystyle 48,46,56,53,44,38,39,42,44,47,51,49,60,25\)

This number set will become:

\(\displaystyle 25,38,39,42,44,44,46,47,48,49,51,53,56,60\)

As you cross out one number from each side, you will eventually be left with the remaining number if there is an odd number of numbers. If there is an even number of numbers, the median will be the average of the last two remaining numbers. 

\(\displaystyle {\color{red} 25},38,39,42,44,44,46,47,48,49,51,53,56,{\color{Red} 60}\)\(\displaystyle {\color{Red} 25,38},39,42,44,44,46,47,48,49,51,53,{\color{Red} 56,60}\)\(\displaystyle {\color{Red} 25,38,39,}42,44,44,46,47,48,49,51,{\color{Red} 53,56,60}\)\(\displaystyle {\color{Red} 25,38,39,42},44,44,46,47,48,49{\color{Red},51,53,56,60}\)\(\displaystyle {\color{Red} 25,38,39,42,44},44,46,47,48,{\color{Red} 49,51,53,56,60}\)\(\displaystyle {\color{Red} 25,38,39,42,44,44},46,47,{\color{Red} 48,49,51,53,56,60}\)

Because we're left with two numbers, we must take their mean (average) to solve for the median of the data set.

\(\displaystyle \frac{46+47}{2}=\frac{93}{2}={\color{Blue} 46.5}\)

The median is the middle number of a set of numbers listed in ascending order.

Start by listing out how many hot dogs Bob ate, in ascending order.

\(\displaystyle 1,2,3,9,9,12,13\)

\(\displaystyle 9\) is the number right in the middle of the set, so it must be the median.

The mode is the number that appears most often in a set of numbers.

\(\displaystyle 89, 88, 88, 100, 75, 88, 78, 91, 92, 82\)

If we order our number set we get the following:

\(\displaystyle 75, 78, 82, 88, 88, 88, 89, 91, 92, 100\)

In this case, because Henry scored 88 three times, that is the mode.

The mode is the number that occurs the most in a group.

Rearranging our numbers we get:

\(\displaystyle 2, 2, 2, 3, 4, 6, 6, 7, 8, 10\)

While \(\displaystyle 6\) does occur twice, \(\displaystyle 2\) occurs three times, and no other number does, so \(\displaystyle 2\) must be the mode.

The correct answer is 6.

If we reorganize our set in ascending order we get the following:

\(\displaystyle 1, 1, 2, 2, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7\)

The mode is the number in a set that appears the most often.

In this particular number set, 6 appears four times and no other number appears more than three times.