1. MODE
SUBMITTED TO:- DR. YASMIN BANU
SUBMITTED BY:- VAISHALI CHOUDHARY
BSC 2nd YEAR (BTZ)
(2018 – 19)
DEPARTMENT OF
BIOTECHNOLOGY
2. S
Y
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P
S
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• INTRODUCTION
• DEFINITION
• METHODS OF COMPUTING MODE IN INDIVIDUAL SERIES
• METHODS OF COMPUTING MODE IN DESCRETE SERIES
• METHODS OF COMPUTING MODE IN GROUP SERIES
• MERITS
• DEMERITS
• USES
• REFRENCES
3. I
N
T
R
O
D
U
C
T
I
O
N
• The word mode is made from the French language
LaMade , which means fashion or system .
• The value of the variable for which the frequency is
maximum is called mode or modal value and is
denoted by Z or Mo.
4. D
E
F
I
N
I
T
I
O
N
• Mode is defined as the value of maximum
frequency.If each value occurs only once then
there is no mode or all the values are mades.
• If there are two or more values with maximum
frequency,there may be two or more modes.Such
frequency distribution is called multi modal.
• Thus a frequency distribution with two modes is
called bimodal with three modes is called
trimodal.
5. INDIVIDUAL SERIES
• BY INSPECTION:- When the number of the observation is small
mode is obtained at a glance by looking which one of the observation
occurs most frequently.
• BY MAKING DISRETE SERIES OR GROUPED
SERIES:- When the number of observation is large convert
the individual series into discrete or grouped series and locate
mode accordingly.
• WITH HELP OF MEAN AND MEDIAN:-Using the
empirical formula.
Mode = 3 Median – 2 Mean
6. BY INSPECTION
• ILLUSTRATION
• The following data sbows the ages of 20 students
in a class find the mode:-
15,17,18,20,22,24,21,17,16,15,21,22,23,22,17,22,18,22,19,20
Solution:- place the number in ascending order :-
15,15,16,17,17,17,18,18,19,20,20,21,21,22,22,22,22,22,23,24
• 22 → 5 times presebt in series
Obviously 22 years age belong to maximum number of
students Hence
• Mode is 22 year
7. MAKING GROUPED & DISCRETE
• The discrete series for the given data is as follows:-
X Y
15 → 2
16 → 1
17 → 3
18 → 2
19 → 1
20 → 2
21 → 2
22 → 5
23 → 1
24 → 1
8. HELP OF MEAN & MEDIAN
• ILLUSTRATION(2)
• The following are the marks obtained by biotech student find the mode:-
2,0,9,15,11,17,19,21,22,23,25,26,27,28,31,32,33,34,35,45
Solution:- arrange the values in ascending order:-
0,2,9,11,15,17,19,21,22,23,25,26,27,28,31,32,33,34,35,45
Since each value occurs once there is no mode or all the values are mode.
However we can find the mode using the empirical formula :
Mode = 3 Median – 2 Mean
Arithmetic mean of these values:
X = ∑X / N
= 455 / 20
= 22.75
9. SYNOPSIS
• Median of these values:
M = 10th value + 11th value
2
= 23 + 25
2
= 24
Mode = 3 Median – 2 Mean
= 3 × 24 - 2 × 22.75
= 26.50
M = N/2th + (N/2 + 1)th
2
10. DISCRETE SERIES
1. BY INSPECTION
2. BY GROUPING
1. BY INSPECTION:- When there is a regularity and homogeneity in
the series then there is a single mode which can be located at a glance by
looking into the frequency column for having maximum frequency.
11. • ILLUSTRATION(1)
Find mode from the following series:-
Height (in cm) no.of person
150 2
160 4
170 8
180 10
190 6
200 5
210 3
Solution:-by inspection of the frequency it is noted that the maximum
frequency is 10 which corresponds to the value 180 hence mode is 180 cm.
12. 2. BY GROUPING METHOD:-
• When there are irregulation in the frequencies increase or decrease in hapharard
way or two or more frequencies are equal then it is not obvious that which one is
the maximum frequency.
• In such case we use the method of grouping to decide which one maybe
considered as maximum frequency.
• That is we try to find out single mode by using grouping method.
• This method involve the following steps.
a. PREPARE GROUPING TABLE
b. PREPARE ANALYSIS TABLE
c. FIND MORE
13. a. FOR PREPRING A GROUPING TABLE WE PROCEED AS FOLLOWS:-
• COLUMN 1 :- given frequencies
• COLUMN 2 :- given frequency are added in two’s
• COLUMN 3 :- the given frequencies are added in two’s living out the first
frequency
• COLUMN 4 :- the given frequencies are added in there’s
• COLUMN 5 :- the given frequencies are added in there’s living out the first
frequency
• COLUMN 6 :- the given frequency are added in there’s living out the first two
frequencies.
14. b. CONSTRUCTION OF ANALYSIS TABLE :- The value containing the maximum
frequency are noted down for each column and are written in a table called
analysis table.
c. LOCATION OF MODE :- The value of the variable which occurs maximum
number of time in the analysis table is called mode
ILLUSTRATION(2) :- calculate mode from following series :-
X = 12, 13, 14, 15, 16, 17, 18
F = 2, 10, 3, 8, 9, 8, 7
17. GROUPED SERIES
• The process of computing mode in case of a grouped series or grouped frequency
distribution with the help of formula involves the following steps.
1. Determine the modal class (in exclusive forms). The class having the maximum
frequency is called modal class.this is done either by inspection or by grouping
method.
2. Determine the value of mode by applying the formula:-
Z = L1 + f1 - f2 × ( L2 – L1 )
2f1 – f0 – f2
OR
Z = L1 + f1 - f0 × i
2f1 – f0 – f2
18. • ILLUSTRATION(1)
The distribution wages in a factory is as follows, calculate the mode :-
WAGES(IN RS NO. OF WORKERS
0 – 10 6
10 – 20 9
20 – 30 10
30 – 40 16
40 – 50 12
50 – 60 8
60 – 70 7
19. Solution :- by inspection the maximum frequency is 16 hence the modal class is
(13–14)
f0 = frequency of the pre modal class ( 20–30) = 10
f1 = frequency of the modal class (30–40) = 16
f2 = frequency of the subceeding modal class (40–50) = 12
L2 = 40 , L1 = 30
Formula :- Z = L1 + f1 - f0 × i
2f1 – f0 – f2
Z = 30 + 16–10 (40 -30)
2×16-10-12
Z = 36
Mode is 36
20. MERITS
• It can be determined without much mathematical
calculation.In discrete mode can be located even by
inspection.
• It is readily comprehensible and easily understood.
• It is a value, which always exists in the series.
• It is not affected by the values of extreme items .
• All the items of a series are not required for its determination.
• It can be very easily determine from graph.
• It can be calculate with open and class – intervals.
21. DEMERITS
• It is ill defined,indeterminate and indefinite.
• It is not based on all the observation of a series and hence it is
rarely used in any higher biological or scientific purposes.
• It is not capable of further mathematical operation.
• It may be unrepresentative in many cases.
• It may be impossible to get a definite value in many cases , as
there may be 2, 3 or more modal values.
• As compared to mean, it is affected to a greater extent by
fluctuations of sampling .
22. U
S
E
S
• When a quick and approximate measuremente of central
tendency is desired.
• When the measure of central tendency should be the
most typical value.
• When there are many numbers and tha frequency of the
numbers progress smoothly.
• When you have non-numerical data (categorical data).
• Data are categorical in nature and values can only fit
into one class.
• Eg. Hair color, political affiliation, religion.
