Unformatted text preview: series of individual observations,
mode is often found by mere inspection.
Example 29:
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.
128 Example 30:
1. 12, 10, 15, 24, 30 (no mode)
2. 7, 10, 15, 12, 7, 14, 24, 10, 7, 20, 10
∴ the modes are 7 and 10
Grouped Data:
For Discrete distribution, see the highest frequency and
corresponding value of X is mode.
Continuous distribution :
See the highest frequency then the corresponding value of class
interval is called the modal class. Then apply the formula.
1 ×C Mode = M 0 = l +
1 + 2 l = Lower limit of the model class
1 = f1f0
2 =f1f2
f1 = frequency of the modal class
f0 = frequency of the class preceding the modal class
f2 = frequency of the class succeeding the modal class
The above formula can also be written as
f1 f 0
Mode = l +
×c
2f1  f 0  f 2
Remarks :
1. If (2f1f0f2) comes out to be zero, then mode is obtained
by the following formula taking absolute differences
within vertical lines.
( f1 − f 0 )
2. M0= l +
×c
 f1 − f 0  +  f1 − f 2 
3. If mode lies in the first class interval, then f0 is taken as
zero. 129 4. The computation of mode poses no problem in
distributions with openend classes, unless the modal
value lies in the openend class.
Example 31:
Calculate mode for the following :
C I
050
50100
100150
150200
200250
250300
300350
350400
400 and above f
5
14
40
91
150
87
60
38
15 Solution:
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
Mode = M0 = l + = 200 + f1 f 0
×c
2f1  f 0  f 2 15091
× 50
2 × 150 − 91 − 87 2950
122
= 200 + 24.18 = 224.18
= 200 + Determination of Modal class :
For a frequency distribution modal class corresponds to the
maximum frequency. But in any one (or more) of the following
cases
130 i.If the maximum frequency is repeated
ii.If the maximum frequency occurs in the beginning or at the
end of the distribution
iii.If there are irregularities in t...
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 Winter '08
 Moshiri
 Business, Statistics

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