Calculate Average and Range
DetailsNumbersEnter Your Numbers to RightWith a Comma Between Each E.g: 3, 19, 9, 7, 27, 4, 8, 15, 3, 11 | |
Mean (Average): | |
Median (Middle): | |
Mode (Most Common): |
Range (Biggest – Smallest): | |
Total Numbers in Set: | |
Ascending Order: | |
Decending Order: | |
Even Numbers: | |
Odd Numbers: |
Math Definition
MeanThe average of all the data in a set.MedianThe value in a set which is most close to the middle of a range.ModeThe value which occures most frequently in a data set.RangeThe difference between the largest and smallest data in a data set.
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Example Calculation
Calculate the mean, median, mode and range for 3, 19, 9, 7, 27, 4, 8, 15, 3, 11.
How to Find the Mean (or Average Value)
To figure the mean, add up the numbers, 3+3+4+7+8+9+11+15+19+27=106 then divide it by the number of data points 106/10=10.6.
How to Find the Median
In ascending order the numbers are 3, 3, 4, 7, 8, 9, 11, 15, 19, 27. There are 10 total numbers, so the 5th and 6th numbers are used to figure the median. (8+9)/2 = 8.5
If there were 9 numbers in the series rather than 10 you would take the 5th number and would not need to average the 2 middle numbers. The 2 middle numbers only need to be averaged when the data set has an even number of data points in it.
How to Find the Mode
The only number which appears multiple times is 3, so it is the mode.
How to Find the Range
To figure the range subtract the smallest number from the largest number 27-3=24.
Mean, Median and Mode: Data Trends, Detecting Anomalies, and Uses in Sports
– Guide Authored by Corin B. Arenas, published on October 17, 2019
In school, we ask the average score for a test to know if wehave a good grade. When it comes to buying expensive products, we often ask theaverage price to look for the best deals.
These are just a few examples of how averages are used inreal life.
In this section, you’ll learn about the different types of averages and how they’re calculated and applied in various fields, especially in sports.
What Does the Term ‘Average’ Mean?
When people describe the ‘average’ of a group of numbers, they often refer to the arithmetic mean. This is one out of 3 different types of average, which include median and mode.
Types of AverageDescriptionMean | The average of numbers in a group. |
Median | The middle number in a set of numbers. |
Mode | The number that appears most often in a set of numbers. |
In conversational terms, most people just say ‘average’ whenthey’re really referring to the mean. Arithmetic mean and average aresynonymous words which are used interchangeably, according to Dictionary.com.
It’s calculated by adding the numbers in a set and dividing it by the total number in the set—which is what most people do when they’re finding the average. See the example below.
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Mean
Set: 8, 12, 9, 7, 13, 10Mean = (8 + 12 + 9 + 7 + 13 + 10) / 6= 59 / 6= 9.83The average or arithmetic mean in this example is 9.83.
Median
The median, on the other hand, is another type ofaverage that represents the middle number in an ordered sequence of numbers. Thisworks by ordering a sequence of numbers (in ascending order) then determiningthe number which occurs at the middle of the set. See the example below.
Average Median
Set: 22, 26, 29, 33, 39, 40, 42, 47, 53In this example, 39 is the median or middle value in the set.
Mode
The mode is basically the most frequent value thatrepeats itself in a set of values. For instance, if your set has 21, 9, 14, 3,11, 33, 5, 9, 16, 21, 5, 9, what is the mode?
The answer is 9 because this value is repeated 3 times.
In statistics, mean, median, and mode are all terms used tomeasure central tendency in a sample data. This is illustrated by the normaldistribution graph below.
The normal distribution graph is used to visualize standard deviation in data analysis. Distribution of statistical data shows how frequent the values in a data set occurs.
In the graph above, the percentages represent the amount of values that fall within each section. The highlighted percentages basically show how much of the data falls close to middle of the graph.
What is the Relationship Between Mean, Median and Mode?
At first glance, it would seem like no connection existsbetween mean, median, and mode. But there is an empiricalrelationship that exists in measuring the center of a data set.
Mathematicians have observed that there is usually adifference between the median and the mode, and it is 3 times the differencebetween the mean and the median.
The empirical relationship is expressed in the formula below:Mean – Mode = 3(Mean – Median)
Let’s take the example of population data based on 50 states.For instance, the mean of a population is 7 million, with a median of 4.8million and mode of 1.5 million.
Mean = 7 millionMedian = 4.8 millionMode = 1.5 million
Mean – Mode = 3(Mean – Median)7 million – 1.5 million = 3(7 million – 4.8 million)5.5 million = 3(2.2)5.5 million = 6.6 million
Take note: Mathematics professor Courtney Taylor, Ph.D. stated that it is not an exact relationship. When you do calculations, the numbers are not always precise. But the corresponding numbers will be relatively close.
Asymmetrical or Skewed Data
According to Microeconomicsnotes.com, when the values of the mean, median and mode are notequal, the distribution is asymmetrical or skewed. The degree of skewnessrepresents the extent to which a data set varies from the normal distribution.
When the mean is greater than themedian, and the median is greater than the mode (Mean > Median > Mode), itis a positively skewed distribution. It’s described as ‘skewed to theright’ because the long tail end of the curve is towards the right.
In the sample graph below, the median and mode are located to the left of the mean.
On the other hand, in a negativelyskewed distribution, the mean is less than the median, and the median is lessthan the mode (Mean
Varying Mean from Median: Resistant Numerical Summaries
In a data set, when the mean is high, a reader might assumethe median will also be high. However, this does not always follow.
The difference between mean and median becomes apparent whena data set has an outlying disparate value. This situation calls attention tothe concept of resistantnumerical summaries. A resistant statistic is a numerical summary whereinextreme numbers do not have a substantial impact on its value.
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Let’s show this by demonstrating how Bill Gates’ presence impacts mean and median wealth when he walks into a room.
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