Find the median of the following number set:

\(\displaystyle 14,15,76,345,222,976,300,117,236,426\)

Recall that the median is the middle value of a number set when it is arranged in ascending order. So we must begin by arranging the set in ascending order.

\(\displaystyle 14,15,76,117,{\color{DarkOrange} 222,236},300,345,426,976\)

In this case, because we have an even number of terms, we do not have a single middle number. This means we need to take the average of the middle two terms to find our median.

\(\displaystyle Median=\frac{222+236}{2}=229\)

So our answer is 229.

First regroup all numbers in chronological order.

\(\displaystyle a=[-5,-1-1,0,-2,-9] = [-9,-5,-2,-1,-1,0]\)

Since there is an even amount of numbers in the dataset, 6 numbers total, the median will be the average of the third and fourth numbers.

Find the mean of the two numbers.

\(\displaystyle \frac{-2-1}{2}= -\frac{3}{2}\)

Find the median of the following data set:

\(\displaystyle 1,43,117,42,2952,54,18,97,112,23,117\)

To find the median, we should first put our numbers in increasing order:

\(\displaystyle 1,18,23,42,43,54,97,112,117,117,2952\)

Next, the median will simply be the number in the middle. 

We have 11 terms, so our median will be the 6th term in the sequence:

\(\displaystyle 1,18,23,42,43,{\color{DarkBlue} 54},97,112,117,117,2952\)

So 54 is our median

Find the median of this data set:

\(\displaystyle 145,57,223,76,453,123,979,57,76,233,435,76\)

To begin, let's put our numbers in increasing order:

\(\displaystyle 57,57,76,76,76,123,145,223,233,435,453,979\)

Next, find the median by finding the number in the middle of  the data set. If there are two numbers in the middle, then find their average:

\(\displaystyle 57,57,76,76,76,{\color{Blue} 123,145},223,233,435,453,979\)

So, the median will be:

\(\displaystyle \frac{123+145}{2}=\frac{268}{2}=134\)

Find the median of the following data set:

\(\displaystyle 66,123,44,78,99,67,143,44,107,12,578,12,67,367,44\)

Let's begin by putting our data in increasing order:

\(\displaystyle 12,12,44,44,44,66,67,67,78,99,107,123,143,367,578\)

Now, the median should be pretty straightforward to find.

The median will simply be the number in the middle of all the terms. 

In this case, it is the number in red below

\(\displaystyle 12,12,44,44,44,66,67,{\color{Red} 67},78,99,107,123,143,367,578\)

So our answer is 67.

The key to solving this problem is to first write the numbers in ascending order. 

77, 80, 35, 76, 99, 95, 86, 65, 72, 56, 21

21, 35, 56, 65, 72, 76, 77, 80, 86, 95, 99

After this you will find the middle number of the set which turns out to be \(\displaystyle \small 76\).

21, 35, 56, 65, 72, 76, 77, 80, 86, 95, 99

We first plug each of the \(\displaystyle x\) values into the function:

\(\displaystyle f(-6)=(-6)^2 - 1 = 35\)

\(\displaystyle f(-1)=(-1)^2 - 1 = 0\)

\(\displaystyle f(0)=(0)^2 - 1 = -1\)

\(\displaystyle f(2)=(2)^2 - 1 = 3\)

\(\displaystyle f(4)=(4)^2 - 1 = 15\)

Next, we put the answers in order from least to greatest:

\(\displaystyle -1, 0, 3, 15, 35\)

Now, to find the median, we find the value that is in the middle of the data set. Since our data set has an odd number of entries the median will be the value that have an equal number of values to either side of it. In this particular case that value lies at the third entry which is 3.

Step 1: Define median...

The median of a set is the middle number, if the amount of numbers in a given set is odd. The median of a set with an even amount of numbers is the average of the two middle numbers in the set.

Step 2: Find the median of this set..

There is an odd number of numbers...

So, we take the middle number...

The middle number is \(\displaystyle 7\).

So, \(\displaystyle 7\) is the median. 

To find the median, find the number that is in the middle of the set when all of the numbers are ordered from smallest to largest.

\(\displaystyle 12, 5, 7, 15,21,17,16,13,12\)

First order the numbers from smallest to largest:

\(\displaystyle 5,7,12,12,13,15,16,17,21\)

In this case, the number in the middle of the set and our answer is: \(\displaystyle 13\)

To find the median, find the number that is in the middle of the set when all of the numbers are ordered from smallest to largest.

\(\displaystyle 41,38,27,42,35,38,44\)

First order the numbers in the set from smallest to largest:

\(\displaystyle 27,35,38,38,41,42,44\)

In this case, our answer and the middle number of the set is: \(\displaystyle 38\)