# Min mode and median relationship

### Mode (statistics) - Wikipedia

Any traditional introductory statistics course will teach students the definitions of modes, medians and means. But, because introductory. Suppose we have a set of numbers, say 3,6,4,3,7,2,8,5,9,6,3,3. We arrange them in ascending order: 2,3,3,3,3, 4,5, 6,6,7,8, The sum of the 12 numbers is = 2. Explains how to compute the mean, median, mode, and range of a list of numbers. What is the minimum grade he must get on the last test in order to achieve.

An example of a mode is presented below: Normally, the mode is used for categorical data where we wish to know which is the most common category, as illustrated below: We can see above that the most common form of transport, in this particular data set, is the bus.

However, one of the problems with the mode is that it is not unique, so it leaves us with problems when we have two or more values that share the highest frequency, such as below: We are now stuck as to which mode best describes the central tendency of the data. This is particularly problematic when we have continuous data because we are more likely not to have any one value that is more frequent than the other.

For example, consider measuring 30 peoples' weight to the nearest 0. How likely is it that we will find two or more people with exactly the same weight e. The answer, is probably very unlikely - many people might be close, but with such a small sample 30 people and a large range of possible weights, you are unlikely to find two people with exactly the same weight; that is, to the nearest 0.

This is why the mode is very rarely used with continuous data. For a data sample it is the "halfway" value when the list of values is ordered in increasing value, where usually for a list of even length the numerical average is taken of the two values closest to "halfway". Finally, as said before, the mode is not necessarily unique.

## Measures of Central Tendency

Certain pathological distributions for example, the Cantor distribution have no defined mode at all. Properties[ edit ] Assuming definedness, and for simplicity uniqueness, the following are some of the most interesting properties. All three measures have the following property: Except for extremely small samples, the mode is insensitive to " outliers " such as occasional, rare, false experimental readings.

The median is also very robust in the presence of outliers, while the mean is rather sensitive. In continuous unimodal distributions the median often lies between the mean and the mode, about one third of the way going from mean to mode. This rule, due to Karl Pearsonoften applies to slightly non-symmetric distributions that resemble a normal distribution, but it is not always true and in general the three statistics can appear in any order.

If we have an even number of events we take the average of the two middles.

### Mean Median Mode

The median is better for describing the typical value. It is often used for income and home prices. Example Suppose you randomly selected 10 house prices in the South Lake Tahoe area.

Your are interested in the typical house price. Although this number is true, it does not reflect the price for available housing in South Lake Tahoe.

### Modes, Medians and Means: A Unifying Perspective

A closer look at the data shows that the house valued at Instead, we use the median. Since there is an even number of outcomes, we take the average of the middle two 3. This better reflects what house shoppers should expect to spend. There is an alternative value that also is resistant to outliers. We can also use the trimmed mean if we are concerned with outliers skewing the data, however the median is used more often since more people understand it.

At a ski rental shop data was collected on the number of rentals on each of ten consecutive Saturdays: To find the sample mean, add them and divide by To find the median, first sort the data: