Thursday, April 7, 2011

Mode

In statistics, the mode is the value that occurs most frequently in a data set or a probability distribution. In some fields, notably education, sample data are often called scores, and the sample mode is known as the modal score.

Like the statistical mean and the median, the mode is a way of capturing important information about a random variable or a population in a single quantity. The mode is in general different from the mean and median, and may be very different for strongly skewed distributions.

The mode is not necessarily unique, since the same maximum frequency may be attained at different values. The most ambiguous case occurs in uniform distribution, wherein all values are equally likely.
The mode in a list of numbers refers to the list of numbers that occur most frequently. A trick to remember this one is to remember that mode starts with the same first two letters that most does. Most frequently - Mode. You'll never forget that one!

Example 1:

Find the mode of:
9, 3, 3, 44, 17 , 17, 44, 15, 15, 15, 27, 40, 8,

Put the numbers is order for ease:
3, 3, 8, 9, 15, 15, 15, 17, 17, 27, 40, 44, 44,

The Mode is 15 (15 occurs the most at 3 times)

*It is important to note that there can be more than one mode and if no number occurs more than once in the set, then there is no mode for that set of numbers.

Occasionally in statistics you'll be asked for the 'range' in a set of numbers. The range is simply the the smallest number subtracted from the largest number in your set. Thus, if your set is 9, 3, 44, 15, 6 - The range would be 44-3=41. Your range is 41.

A natural progression once the 3 terms in statistics are understood is the concept of probability. Probability is the chance of an event happening and is usually expressed as a fraction. But that's another topic!

Example 2 :
 Stem Leaf 10 1 1 1 1 2 20 2 3 3 4 30 1 3 2 3 1 40 1 3 3 50 1 5 4 2 3

Mode => 101

101 appeared most frequently. ( at 4 times )