Median Mode

Topics: Arithmetic mean, Standard deviation, Mean Pages: 3 (487 words) Published: November 23, 2014
Statistics: Median, Mode and Frequency Distribution
Given a list of numbers,

The median is the “middle value” of a list. It is the smallest number such that at least half the numbers in the list are no greater than it. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two.

The mode is the most common (frequent) value. A list can have more than one mode.

Let’s have a look at an example:

In an experiment measuring the percentage shrinkage on drying, 30 plastic clay test specimens produced the following results (rounded to one decimal):

19.3 15.8 20.7 18.4 14.9 17.3 21.3 16.1 18.6 20.5
20.5 16.9 18.5 18.7 12.3 19.5 23.4 18.8 18.3 16.9
17.9 17.1 22.5 18.8 19.4 17.4 18.5 17.5 16.5 17.5

In order to determine the median and the mode, let’s sort the numbers in the list, starting with the smallest and ending with the biggest:

12.3 14.9 15.8 16.1 16.5 16.9 16.9 17.1 17.3 17.4 17.5 17.5 17.9 18.3 18.4 18.5 18.5 18.6 18.7 18.8 18.8 19.3 19.4 19.5 20.5 20.5 20.7 21.3 22.5 23.4

16.9, 17.5, 18.5, 18.8 and 20.5 appear twice in the list, while the other numbers appear only once. The modes are therefore 16.9, 17.5, 18.5, 18.8 and 20.5.

Since the numbers of number in the list is even (30 numbers), the median is the sum of the 15th and 16th numbers divided by two. The median is therefore

Given a list, by frequency distribution with a class interval of we mean a table where the numbers are sorted by class intervals of .

The frequency of a class interval is the number of numbers in the list that belong to the class interval.

The Midpoint of a group: for example the midpoint of the class interval is

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