Mean,+median+and+Mode

=Averages – Mean, Median, Mode and Range=

The Mean, Median, and Mode represent three different ways of finding the “Average” value for a group of numbers.

Often the “Median” or Middle value is used to express an Average for cases where there can be large variations in values at the high and low ends of the group. Typical Examples of this are Median Income, Median House Price, Median Car Price, and so on.

=How to Find the Mean= =The mean is just the **average** of the numbers.=

It is easy to calculate: **add up** all the numbers, then **divide by how many** numbers there are. In other words it is the **sum** divided by the **count**.

Example 1: What is the Mean of these numbers? 6,11,7

 * Add the numbers: **6 + 11 + 7 = 24**
 * Divide by //how many// numbers (there are 3 numbers): **24 / 3 = 8** **The Mean is 8**

The sum of these numbers is 330 There are fifteen numbers. The mean is equal to 330 / 15 = 22
 * Example 2:** 3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

Negative Numbers
How do you handle negative numbers? Adding a negative number is the same as subtracting the number (without the negative). For example 3 + (-2) = 3-2 = 1.

Example 3: Find the mean of these numbers:
3, -7, 5, 13, -2 =**The mean of the above numbers is 2.4**= = **The Mean**: To find the mean, you need to add up all the data, and then divide this total by the number of values in the data. = = = = The Median =
 * The sum of these numbers is **3 - 7 + 5 + 13 - 2 = 12**
 * There are **5** numbers.
 * The mean is equal to **12 ÷ 5 = 2.4**

If we have an odd number of items, and put them into order, there will only be one item in the ** middle for the Median. **
==

This halfway point average is the Median of the data.
=source:=

http://passyworldofmathematics.wordpress.com/2012/03/06/averages-mean-median-mode/
= = = = = **The Median**: To find the median, you need to put the values in order, then find the middle value. If there are two values in the middle then you find the mean of these two values. = = = = The Mode =

Remember: Mode means most of
= = = = ==


 * ====Example 1:==== || ====The following is the number of problems that Ms. Matty assigned for homework on 10 different days. What is the mode?==== ||  ||
 * || ====8, 11, 9, 14, 9, 15, 18, 6, 9, 10==== ||^  ||
 * ====[[image:http://www.mathgoodies.com/lessons/vol8/images/tab.gif width="1" height="3" caption=" "]]==== ||^   ||
 * ====Solution:==== || ====Ordering the data from least to greatest, we get:==== ||^  ||
 * || ====6, 8, 9, 9, 9, 10, 11 14, 15, 18==== ||^  ||
 * ====[[image:http://www.mathgoodies.com/lessons/vol8/images/tab.gif width="1" height="3" caption=" "]]==== ||
 * ====Answer:==== |||| ====The mode is 9.==== ||


 * ====Example 2:==== || ====In a crash test, 11 cars were tested to determine what impact speed was required to obtain minimal bumper damage. Find the mode of the speeds given in miles per hour below.==== || ====[[image:http://www.mathgoodies.com/lessons/vol8/images/tab.gif width="15" height="1" caption=" "]]==== ||
 * || ====24, 15, 18, 20, 18, 22, 24, 26, 18, 26, 24==== ||^  ||
 * ====[[image:http://www.mathgoodies.com/lessons/vol8/images/tab.gif width="1" height="3" caption=" "]]==== ||^   ||
 * ====Solution:==== || ====Ordering the data from least to greatest, we get:==== ||^  ||
 * || ====15, 18, 18, 18, 20, 22, 24, 24, 24, 26, 26==== ||^  ||
 * ====[[image:http://www.mathgoodies.com/lessons/vol8/images/tab.gif width="1" height="3" caption=" "]]==== ||
 * ====Answer:==== |||| ====Since both 18 and 24 occur three times, the modes are 18 and 24 miles per hour. This data set is .==== ||

||^  ||
 * ====Example 3:==== || ====A marathon race was completed by 5 participants. What is the mode of these times given in hours?==== ||  ||
 * || ====2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr, 4.9 hr==== ||^  ||
 * ====[[image:http://www.mathgoodies.com/lessons/vol8/images/tab.gif width="1" height="3" caption=" "]]==== ||^   ||
 * ====Solution:==== || ====Ordering the data from least to greatest, we get:==== ||^  ||
 * || ====2.7, 3.5, 4.9, 5.1, 8.3====
 * ====[[image:http://www.mathgoodies.com/lessons/vol8/images/tab.gif width="1" height="3" caption=" "]]==== ||
 * ====Answer:==== |||| ====Since each value occurs only once in the data set, there is //no mode// for this set of data.==== ||


 * ====Example 4:==== || ====On a cold winter day in January, the temperature for 9 North American cities is recorded in Fahrenheit. What is the mode of these temperatures?==== || ====[[image:http://www.mathgoodies.com/lessons/vol8/images/tab.gif width="15" height="1" caption=" "]]==== ||
 * || ====-8, 0, -3, 4, 12, 0, 5, -1, 0==== ||^  ||
 * ====[[image:http://www.mathgoodies.com/lessons/vol8/images/tab.gif width="1" height="3" caption=" "]]==== ||^   ||
 * ====Solution:==== || ====Ordering the data from least to greatest, we get:==== ||^  ||
 * || ====-8, -3, -1, 0, 0, 0, 4, 5, 12==== ||^  ||
 * ====[[image:http://www.mathgoodies.com/lessons/vol8/images/tab.gif width="1" height="3" caption=" "]]==== ||
 * ====Answer:==== |||| ====The mode of these temperatures is 0.==== ||

= **The Mode**: The mode is the value which appears the most often in the data. It is possible to have more = = than one mode if there is more than one value which appears the most. = media type="youtube" key="g4vbXvoQWf0" height="315" width="420"
 * ====Let's compare the results of the last two examples. In Example 3, each value occurs only once, so there is no mode. In Example 4, the mode is 0, since 0 occurs most often in the set. Do not confuse a mode of 0 with no mode.==== ||

= = =Range=

To work out the range:
> ====3 6 6 6 7 9 11 11 13==== > ====13 - 3 = 10==== > ====So the range of this set of numbers is 10==== = **The Range**:To find the range, you first need to find the lowest and highest values in the data. The range is found by subtracting the lowest value from the highest value. =
 * 1) ====Put the numbers in order:====
 * 1) ====Subtract the smallest number from the biggest number:====