http://www.ck12.org Chapter 6. Measures of Central Tendency - Basic
6.3 The Mode
Learning Objectives
- Understand the concept of the mode.
- Identify the mode of a set of given data.
- Identify the mode of a set of data given in different representations.
Introduction
Do you remember the problem presented in the lesson on mean that dealt with the hand spans of students in a
classroom? If you were making gloves for the winter Olympics, what measurement would be of interest to you?
The mode of a set of data is simply the number that appears most frequently in the set. If two or more values appear
with the same greatest frequency, each is a mode. When no value is repeated, there is no mode. The word ’modal’
is often used when referring to the mode of a data set. An example would be the response to the question “What
is the mode of the numbers?” The response may be writes as “The modal number is 4.” Observation, rather than
calculation, is necessary when determining the mode of a data set.
Example 1:What is the mode of the numbers?
a) 1, 2, 2, 4, 5, 5, 5, 7, 8?
b) 1, 3, 5, 6, 7, 8, 9
Solution:
a) The modes of the above numbers are 2 and 5, since both numbers appear twice and no other number is repeated.
b) There is no mode for these values since none of the values is repeated.
Example 2:The life of a new type of battery was measured (in hours) for a sample of 24 batteries with the following
results:
34 , 28 , 36 , 30 , 33 , 32 , 35 , 31 , 28 , 29 , 30 , 27
31 , 25 , 32 , 30 , 32 , 30 , 29 , 34 , 31 , 33 , 35 , 29
What is the modal number of hours for the tested batteries?
Solution:
It is not necessary, but you may find it easier to determine the mode if the data was organized –arranged from smallest
to largest.
25 , 27 , 28 , 28 , 29 , 29 , 29 ,30, 30, 30, 30, 31
31 , 31 , 32 , 32 , 32 , 33 , 33 , 34 , 34 , 35 , 35 , 36
The mode of the number of hours for the tested batteries is 30 since it is repeated 4 times. If the data set contains
a large number of data, the mode can be readily seen if the values are represented in a tally chart. Creating a tally
chart is less time consuming than creating a frequency chart –you don’t have to constantly review the numbers. The
tally can be placed beside the number when you come to it in the data set.