Median Finder

Use data set 4, 12, 27, 26, 38, 45, 66, 78, 85 as an example:

Median(x~) 38
Mean(x) 42.333333333333
Geometric Mean 30.836864592792
Mode 4, 12, 26, 27, 38, 45, 66, 78, 85
Range 81
Largest value 85
Smallest value 4
Sum 381
Count 9
Sorted 4, 12, 26, 27, 38, 45, 66, 78, 85

About Median Finder

The median is the number located in the middle of a set of data arranged in order; Mode is a statistical term that represents the general level of data and has a significant concentrated trend point in statistical distribution; The mean refers to the sum of all data in a set of data and divided by the number of data.

If you are looking for an median finder, mean finder, or mode finder, this tool can perfectly assist you. We have designed and produced this median finder, which is very simple, convenient, and easy to operate. The current page displays the mean, median, mode, range, sum, and other numerical values of datasets 4, 12, 27, 26, 38, 45, 66, 78, and 85. You only need to enter a set of data in the input box, separated by commas (if you enter a space, it will automatically convert to commas), and click the "find" button to find the median, mean, mode, range, etc of this dataset. If your data is unordered, the dataset will also be displayed in ascending order.

What are the median, mode, and mean?

  1. Median: Arrange a set of data from small to large, and the middle number is the median.
  2. Mode: The number with the highest number of occurrences in a set of data, and the mode can be multiple.
  3. Mean: The sum of a set of data divided by the number of numbers in that set yields the average.

The role of median, mode, and mean.

Median: Refers to the average level of data. The median is related to the arrangement of data, and changes in certain data have no effect on it; It is a representative value at the middle position of a set of data, unaffected by extreme values of the data. For example, the median of 1, 2, 3, 4, 5 is 3.

Mode: represents the general situation of data. It is related to the frequency of data occurrence, focusing on the examination of the frequency of each data occurrence. Its size is only related to a portion of the data in this group and is not affected by extreme values. Its disadvantage is that it has no uniqueness. For example, the mode of 1, 2, 3, 3, 4, 4, 4, 5, 5 is 4.

Mean: represents the overall level of data. It is related to every data, and any change in the data will cause a corresponding change in the mean. The main disadvantage is that it is susceptible to the influence of extreme values, which refer to values that are too large or too small.

When there is a large number, the mean will be raised, and when there is a small number, the mean will be lowered.

How to find the median, mode, and mean?

  1. Median: Arrange data in ascending order or ascending order. If the number of data is odd, the number in the middle position is the median of the set of data; If the number of data is even, the average of the middle two data is the median of this set of data. Its calculation does not require or only requires simple calculations.
  2. Mode: The number that appears the most frequently in a set of data, which can be calculated without the need for calculation.
  3. Mean: Divide the total sum of all data by the number of data, which requires calculation to obtain. For example, the average of 1, 2, 3, 4, and 5 is (1+2+3+4+5)/5=3. The average is the most commonly used method for measuring trends in a dataset. (In the statistics of contestant competition results, the highest and lowest scores are usually removed to show fairness)

Obviously, there is a significant difference between the median, mode, and mean, so how should these values be used? Let's take a look at some examples.

For example, a quick way to get rich is to become a professional football player. In 2015, the average income of National Football League stars in the United States was $2.2 million.

Which value best illustrates the problem in this example? Please consider the comparison between the income of top players in professional sports and that of regular players. The most famous football stars, such as football star quarterbacks, earn much more than most other players on the team. In fact, the highest-paid rugby player in 2015 had an annual income of over $35 million - much higher than the average. Such high income will sharply increase the average, but it will have little impact on the median or mode.

For example, the average salary of players in the National Football League of the United States in 2015 was $2.2 million, but their median salary was only $830000. Therefore, for most professional sports, the average salary of athletes is much higher than the median or mode. So, if someone wants their salary level to appear very, very high, they will choose the mean as the average.

Let's take another example: in order to achieve good grades in university, students need to put in less and less effort. According to a recent survey, the average amount of time college students spend on studying per week is 12.8 hours, which is about half of the study time spent by college students 20 years ago.

In this example, if the average values listed here are median or mode, we may have underestimated the average learning time. Some students are likely to spend a lot of time studying, such as 30 or 40 hours a week, which can increase the average value but does not affect the median or mode value. The mode value of learning time may be much lower or higher than the median, mainly depending on how much learning time is most common for students.

When you see the mean, be sure to ask, "Is this the mean, median, or mode? Does the different meanings of the mean have any impact?" When answering these questions, think about how the different meanings of the mean can change the meaning of the information.