MODE
The mode or the modal score is a score or scores that occurred most in the distribution.
It is classified as unimodal, bimodal, trimodal or mulitimodal.
Unimodal is a distribution of scores that consists of only one mode.
Bimodal is a distribution of scores that consists of two modes.
Trimodal is a distribution of scores that consists of three
modes or multimodal is a distribution of scores that
consists of more than two modes.
MODE
Examples:
Find the Mode.
1. The ages of five students are: 17, 18, 23, 20, and 19 2. The following are the descriptive evaluations of 5
teachers: VS, S, VS, VS, O
3. The grades of five students are : 4.0, 3.5, 4.0, 3.5, and 1.0
4. The weights of five boys in pounds are: 117, 218, 233, 120, and 117
Your turn!
Find the mode and interpret it.
1. The following table shows the frequency of errors committed by 10 typists per minute.
2. A random sample of 8 mango trees reveals the following number of fruits they yield
3. The following are the scores of 9 students in a Mathematics quiz.: 12, 15, 12, 8, 7, 15, 19, 24, 13
Mango Tree A B C D E F G H
No. of fruits 80 70 80 90 82 82 90 82
Typists A B C D E F G H I J
No. of errors per min. 5 3 3 7 2 8 8 4 7 10
MODE
Example: Scores of 10 students in Section A, Section B and Section C.
Scores of Section A Scores of Section B Scores of Section C
25 25 25
24 24 25
24 24 25
20 20 22
20 18 21
20 18 21
16 18 21
12 10 18
10 9 18
7 7 18
MODE
The score that appeared most in Section A is 20, hence, the mode of Section A is 20. There is only one mode, therefore, score distribution is called unimodal.
The modes of Section B are 18 and 24, since both 18 and 24 appeared twice. There are two modes in Section B, hence, the distribution is a bimodal distribution.
The modes for Section C are 18, 21, and 25. There are
three modes for Section C, therefore, it is called a
trimodal or multimodal distribution.
Uni-modalBi-modal
Formula:
Mode = Lo +
--- *CI
2f1-f0-f2
OR, Mode = = L0 + d1/d1+d2*CI
Where, L0 is the lower limit of Modal class
f1 is the frequency of modal class
f0 is the frequency preceding modal class
f2 is the frequency succeeding modal class
CI is the Class Width of Modal class.
d1= f1-f0 and d2 = f1-f2
MODE
Mode for Grouped Data
In solving the mode value in grouped data, use the formula:
d1
X = L̂ B + d1 + d2 x c.i
LB = lower boundary of the modal class
Modal Class (MC) = is a category containing the highest frequency d1 = difference between the frequency of the modal class and the
frequency above it, when the scores are arranged from lowest to highest.
d2 = difference between the frequency of the modal class and the
frequency below it, when the scores are arranged from lowest to highest.
c.i = size of the class interval
MODE
Example: Scores of 40 students in a science class consist of 40 items and they are tabulated below.
C-I-Inclusive C-I-Exclusive f
10 – 14 9.5-14.5 5
15 – 19 14.5-19.5 2
20 – 24 19.5-24.5 3
25 – 29 24.5-29.5 5
30 – 34 29.5-34.5 2-f0
35 – 39 34.5-39.5 9-f1-modal class
As having Max freq
40 – 44 39.5-44.5 6-f2
45 – 49 44.5-49.5 3
50 – 54 49.5-54.5 5
n = 40
MODE
Modal Class = 35 – 39 LL of MC = 35
c.i =
LB = 34.5
d1 = f1-f0 = 9 – 2 = 7 d2 = f1-f2 = 9 – 6 = 3
5
d1
X = L̂ B + d1 + d2 x c.i
7 x 5
= 34.5 + 7 + 3
= 34. 5 + 35/10 = 34.5 + 3.5 X̂ = 38
The mode of the score distribution that consists of 40 students
is 38, because 38 occurred several times.
Mode = 14 + 2/0 = Indeterminate
Mode = 14 + 20/(20+22) = 14 + 20/42 = 14.47
MODE
Properties of the Mode
• It can be used when the data are qualitative as well as quantitative.
• It may not be unique.
• It is affected by extreme values.
• It may not exist.
When to Use the Mode
• When the “typical” value is desired.
• When the data set is measured on a nominal scale.
