Is finding the average value or the median value of a set of numbers more accurate?

Answer 1

Median Value:The Median is the "middle number" (in a sorted list of numbers). The median is the exact middle number in a sequence or set of numbers. When you're looking for the median in a sequence that has an odd amount of total numbers, the process is really easy. Finding the median in a sequence that has an even amount of total numbers is a bit harder. To find the median easily and successfully, read on. How to Find the Median Value?To find the Median, place the numbers in value order and find the middle number. Find the Median in an Odd Set of Numbers:-Sort your set of numbers from least to greatest. If they're scrambled, line them up, starting with the lowest number and ending with the highest number.

Find the number that is exactly in the middle. This means that median number has the same amount of numbers in front of it as it does behind it. Count them to make sure. There are two numbers in front of the 3, and two numbers behind it. This tells us that 3 is the number exactly in the middle

Finished. The median of an odd-numbered sequence is always a number in the sequence itself. It is never a number that is not in the sequence.

Find the Median in an Even Set of Numbers:-Sort out your set of numbers from least to greatest. Again, use the same first step as the first method. An even set of numbers is going to have two numbers exactly in the middle.

Find the average of the two numbers in the middle.2 and 3 are both in the middle, so you need to add 2 and 3, then divide the sum by 2. The formula for finding the average of two numbers is (the sum of the two middle numbers) ÷ 2.

Finished. The median of a sequence with even amount of numbers doesn't have to be a number in the sequence itself.

Example: find the Median of 12, 3 and 5Step 1:- Put them in order: 3, 5, 12Step 2:-Find the middle value:The middle number is 5, so the median is 5.Example:

3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

When we put those numbers in order we have:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56

There are fifteen numbers. Our middle number will be the eighth number:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56

The median value of this set of numbers is 23.

Two Numbers in the MiddleBUT, when there are an even amount of numbers things are slightly different.

In that case we need to find the middle pair of numbers, and then find the value that would be half way between them. This is easily done by adding them together and dividing by two.

Example:3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29

When we put those numbers in order we have:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56

There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56

In this example the middle numbers are 21 and 23.

To find the value half-way between them, add them together and divide by 2:

21 + 23 = 44

44 ÷ 2 = 22

So the Median in this example is 22.

Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all.

The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.

The "range" is just the difference between the largest and smallest values.

• Find the mean, median, mode, and range for the following list of values:

• 13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average, so:

(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

Note that the mean isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.

The median is the middle value, so I'll have to rewrite the list in order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

13, 13, 13, 13, 14, 14, 16, 18, 21

So the median is 14. Copyright © Elizabeth Stapel 2004-2011 All Rights Reserved

The mode is the number that is repeated more often than any other, so 13 is the mode.

The largest value in the list is 21, and the smallest is 13, so the range is 21 - 13 = 8.

mean: 15

median: 14

mode: 13

range: 8

Note: The formula for the place to find the median is "( [the number of data points] + 1) ÷ 2", but you don't have to use this formula. You can just count in from both ends of the list until you meet in the middle, if you prefer. Either way will work.

It's easy to get median, mode and mean confused, partly because they start with m. But they are also ways of describing a number which is somewhere in the middle of the set. The median is the middle number, but may be closer to the minimum than it is to the maximum (or vice versa), if most of the numbers are clustered round one end. The mode is the most common number in the set, so it could be anywhere in the set. However, many sets have a normal distribution, which means that the mode is is the middle. Since the mean is a calculation which uses every number in the set, it reflects the value of each number. But one high or low number may affect the mean (although not by much if there are a lot of numbers).