The mode is the value that appears most frequently in a data set. It represents the peak of a distribution. There are several ways to calculate the mode depending on if the data is in an individual observation, discrete series, or continuous series. For a continuous series, the modal class is identified which has the highest frequency, and a formula is applied using the lower limit of that class, and the frequencies of the modal, preceding, and succeeding classes. Examples are provided to demonstrate calculating the mode for different data presentations.

1. Mode
Dr. RMKV
Assistant Professor

2. MODE
 The mode is the number that appears most frequently in a data set
 It is an actual value, which has the highest concentration of items
in and around it.
 For example, in placing an order for shoes or ready-made
garments the modal size helps because this sizes and other sizes
around in common demand.

3. Mode is 6

4. Formula
 Individual observation: For ungrouped data or a series of
individual observations, mode is often found by mere
 Discrete Series: For Discrete distribution, see the highest
frequency and corresponding value of X is mode.

5. Formula
 Continuous Series: See the highest frequency then the
corresponding value of class interval is called the modal class.
apply the formula.
 Mode = Mo =𝒍 +
𝚫𝟏
𝚫𝟏+𝚫𝟐
∗ 𝒄
 l = Lower limit of the model class Δ1= f1-f0 Δ2 = f1-f2 f1 =
= frequency of the modal class f0 = frequency of the class
the modal class f2 = frequency of the class succeeding the
class

6. Illustration _Individual Observation
 2 , 7, 10, 15, 10, 17, 8, 10, 2
 Mode = M0=10
 In some cases the mode may be absent while in some cases there
may be more than one mode.
 12, 10, 15, 24, 30 (no mode)
 7, 10, 15, 12, 7, 14, 24, 10, 7, 20, 10
 The modes are 7 and 10

7. Illustration _Discrete Series
 From the following data, find the value of Mode
 The Mode is 5380 because Rs. 5380 have high frequency
Income 4000 4500 5060 5380 5800 6600
No. of
Person
24 26 20 30 16 6

8. Illustration _Discrete Series
1. The following data pertaining to the number of members in a
family. Find mode size of the family.
 The Mode size of family is 6 because 6 have high frequency
No. of
family
numb
er
1 2 3 4 5 6 7 8 9 10 11 12
No. of
family
1 3 5 6 10 13 9 5 3 2 2 1

9. Illustration_ Continuous Series
 Calculate mode for the following :
Highest Frequency – f1
f0
f2

10.  The highest frequency is 150 and corresponding class interval is
200 – 250, which is the modal class.
 Here L =200,f1=150,f0=91, f2=87, C=50
 𝛥1= f1 - f0 = 150 – 91 = 59
 𝛥2 = f1 - f2 = 150 – 87 = 63
 Mode = M0 = 𝑙 +
𝛥1
𝛥1+𝛥2
∗ 𝑐
 = 200+
59
59+63
x 50
 = 200+
59
122
x 50
 = 200+0.484 x 50
 = 200 + 24.2 =224.2
 Mode is 224.2

11. Illustration_ Continuous Series
 Find the mode from the following table gives the distribution of
the number of workers according to the weekly wage in a
company.
Weekly
wage
(in
Rs.100’ s)
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Numbers
of
workers
5 10 15 18 7 8 5 3
f1
f0 f2

12.  The highest frequency is 18 and corresponding class interval is 30 –
40, which is the modal class.
 Here L =30, f1=18,f0=15, f2=7, C=10
 𝛥1= f1 - f0 = 18 -15 = 3
 𝛥2 = f1 - f2 = 18 – 7 = 11
 Mode = M0 = 𝑙 +
𝛥1
𝛥1+𝛥2
∗ 𝑐
 = 30 +
3
3+11
x 10
 = 30+
3
14
x 10
 = 30+0.214 x 10
 = 30 + 2.14 = 32.14
 Mode is 32.14