Mean, Median, Mode: What They Are, How to Find Them

Averages are measures of central tendency and the work can mean different things, this it is, or at least it can be, a source of ambiguity.  There are different kinds of measures or averages. Consider, for instance, the claim that “The average cost of a new house in your area is \$210,000.”

But what does that “the average cost” mean?  It might mean one of three distinct things: mean, median or mode.

Average, Mean, Median and Mode (They are not all the same thing.)

·         If that is the mean cost, then it is the sum total of the sales prices of houses (presumably sold within a given period of time, say the last 24 months) divided by the number of houses sold.

·         If that is the median, that is the “halfway” price.  It indicates that half the houses sold cost more and half cost less.

·         If that is the mode, it is the most common sales price.

So imagine that ten homes were sold in the neighborhood with the last 24 month at these prices.

 1 \$150,000 2 \$155,000 3 \$159,000 4 \$250,000 5 \$250,000 6 \$300,000 7 \$300,000 8 \$300,000 9 \$400,000 10 \$2,500,000 Sum \$4,764,000.00

The Mean is:               \$476,400

The Median is:            \$275,000

The Mode is:               \$300,000

If there are likely to be large or dramatic variations in what is measured, one must be cautious of figures that represent an unspecific "average."  Without greater specificity as to what is being claimed by the “average home price,” you cannot know whether to accept the claim as true, reject it as false or suspend judgement because you literally do not know what is being asserted (and so what facts would be relevant).

https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/mean-median-mode/#mode

·         The mean is the average of a data set.

o   Of these three, the mean is the only one that requires a formula. E.g. [(A+B+C)/3)]

·         The median is the middle point for a set of numbers.

·         The mode is the most common number in a data set.

Having trouble remembering the difference between the mean, median and mode? Here’s a couple of hints that can help.

Mean:

The “Mean” requires you do arithmetic (adding all the numbers and dividing).  So that’s the “mean” one (unpleasant one 😊).

Median:

The word “Median” has the same number of letters as the word “Middle”.  The mean is whatever the middle value of a set of numbers is.

Mode:

“A la mode” is a French phrase that means fashionable; It also refers to a popular way of serving pie with ice cream. (Apple Pie a la mode)  So “Mode” is the most popular or fashionable (numerous) member of a set of numbers.

Mean vs Average: What’s the Difference?

The answer is that they have the same meaning. They are synonyms.  That said, technically, the word “mean” is short for the “arithmetic mean.”  Statisticians use different words because there are multiple types of means, which all do different things.

For example:

·         Mean of the sampling distribution

·         Weighted mean.

·         Harmonic mean.

·         Geometric mean.

·         Arithmetic-Geometric mean.

·         Root-Mean Square mean.

·         Heronian mean.

·         Graphic Mean

·         Weighted Mean

Mean vs Median

Both are measures of where the “center” of a data set lies (called “Central Tendency” in stats), but they are usually different numbers. For example, take this list of numbers: 10, 10, 20, 40, 70.

The mean (informally, the “average“) is found by adding all of the numbers together (150) and dividing by the number of values in the set (5):

(10 + 10 + 20 + 40 + 70) / 5 = 30

The median is found by ordering the set of values from lowest to highest and finding the exact middle. The median is just whatever value occupies the space midway between to first and the last in the series of values.:

10 + 10 + 20 + 40 + 70

Thus, the median of the data set is 20.

Note: If you have an even set of numbers such that no one number is exactly in the middle, then to find the median must average the middle two values.

For example, take the data set: 23, 24, 26, 26, 28, 29, 30, 31, 33, 34

 1 2 3 4 5 6 7 8 9 10 23 24 26 26 28 29 30 31 33 34

The median of this set of numbers is the average of the two middle values “28”  and “29.”

That is, the median is [(28+ 29) / 2] or 28.5.

Sometimes the Mean and the Median can be the same number.  For example:

For the data set 1, 2, 4, 6, 7

The mean is (1 + 2 + 4 + 6 + 7) / 5 = 4

The median (middle)  of 1 + 2 + 4 + 6 + 7 is also 4.

Mode:

What is the Mode?

“A la mode” is a French phrase that means fashionable; It also refers to a popular way of serving pie with ice cream. (Apple Pit A la Mode)  So “Mode” is the most popular or fashionable member of a set of numbers.

The word MOde is also like MOst.

The mode is the most common number in a set. For example, the mode in this set of numbers is 21:

21, 21, 21, 23, 24, 26, 26, 28, 29, 30, 31, 33

How to find the mean, median and mode: MODE

Step 1: Put the value in order so that you can clearly see patterns.

For example, lets say we have 2, 19, 44, 44, 44, 51, 56, 78, 86, 99, 99. The mode is the number that appears the most often.  In this case: 44.  It appear three time. “ 99” appears twice, fewer times than “44”

Tip:  You can have more than one mode. For example, for the data set “1, 1, 5, 5, 6, 6,” there are three modes (e.g. 1, 5, and 6).

Exercise:

Below is a list of the heights of the top highest building in a large US city.  Find the mean, median and mode for these heights.  The heights, (in feet) are:

1250, 1200, 1046, 1046, 952, 927, 915, 861, 850, 814, 813, 809, 808, 806, 792, 778, 757, 755, 752, and 750.

Answer:

 Values 750 752 755 757 778 792 806 808 809 813 Median 814 813.5 850 861 915 927 952 1046 Mode 1046 1046 1200 1250 Mean 17681 (Total) 884.05