Mode is modal value(Central Value)

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