Illustration :
If the scores for a given sample distribution are:
|
32 |
32 |
35 |
36 |
37 |
38 |
38 |
39 |
39 |
39 |
40 |
40 |
42 |
45 |
then the mode would be 39 because a score of 39 occurs 3 times, more than any other score. The mode may be seen on a frequency distribution as the score value which corresponds to the highest point. For example, the following is a frequency polygon of the data presented above:
A distribution may have more than one mode if the two most frequently occurring scores occur the same number of times. For example, if the earlier score distribution were modified as follows:
|
32 |
32 |
32 |
36 |
37 |
38 |
38 |
39 |
39 |
39 |
40 |
40 |
42 |
45 |
then there would be two modes, 32 and 39. Such distributions are called bimodal. The frequency polygon of a bimodal distribution is presented below.
In an extreme case there may be no unique mode, as in the case of a rectangular distribution.
Application:
Applet :
Examples for practice :
The number of points scored in 7 football games are listed below. Which score occurred most often?
7, 13, 18, 24, 9, 3 18.
(Solution)The following is the number of problems that Ms. Matty assigned for homework on 10 different days. What is the mode?
8, 11, 9, 14, 9, 15, 18, 6, 9, 10
(Solution)In a crash test, 11 cars were tested to determine what impact speed was required to obtain minimal bumper damage. Find the mode of the speeds given in miles per hour below.
24, 15, 18, 20, 18, 22, 24, 26, 18, 26, 24
(Solution)A marathon race was completed by 5 participants. What is the mode of these times given in hours?
2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr, 4.9 hr
(Solution)On a cold winter day in January, the temperature for 9 North American cities is recorded in Fahrenheit. What is the mode of these temperatures?
-8, 0, -3, 4, 12, 0, 5, -1, 0
(Solution)
Find the mode for the following data using Excel:
Comments :
The mode is not sensitive to extreme scores. Suppose the original distribution was modified by changing the last number, 45, to 55 as follows:
32
32
35
36
37
38
38
39
39
39
40
40
42
55
The mode would still be 39.
In any case, the mode is a quick and dirty measure of central tendency. Quick, because it is easily and quickly computed. Dirty because it is not very useful; that is, it does not give much information about the distribution.
