Calculation of mode

Calculation of
Mode
SUBMITTED BY
DR. SUNITA OJHA
ASSISTANT PROFESSOR
SURESH GYAN VIHAR UNIVERSITY
Mode
• It is repeated the highest number of times in the series by definition
• The mode of a distribution is the value at the point around which the items tend to
be most heavily concentrated.
• The main feature of mode is that it is the size of that item which has the maximum
number frequency.
1. Calculation of mode in a series of individual observations:
• The value occurring maximum number of times are the modal values.
Example1. Find the mode of the following data relating to the weights of a sample of
experimental animals
S.No. 1 2 3 4 5 6 7 8 9 10
Weight 10 11 10 12 12 11 9 8 11 11
Weight No. of
animals
8 1
9 1
10 2
11 4
12 1
13 1
• Since the item 11 occurs the maximum number of
times i.e. 4 times, the modal value is 11.
• If two values have the maximum frequency, the
series is bimodal.
2. Calculation of mode in a discrete series.
• Mode can be determined by looking to that
variable around which the items are most heavily
concentrated.
Value 6 8 10 12 14 16 18 20 22 24
Frequency 20 30 40 40 55 60 55 20 15 25
• In the above data modal value is 16, because it occurs the maximum no.
of times i.e. 60 times
• However, the values on the either side of 16 have also large frequencies.
• In such cases, it is desirable to prepare a grouping table and an analysis table.
• Grouping Table has six columns. Frequencies are added in two’s or three’s
• In column 1, maximum frequency is marked.
• In column 2, frequencies are added in two’s (1+2, 3+4, 5+6……).
• In column 3, frequencies are added in two’s leaving the first frequency
(2+3, 4+5, 6+7…).
• In column 4, frequencies are added in three’s (1+2+3, 4+5+6, 7+8+9…).
• In column 5, frequencies are added in three’s leaving the first frequency
(2+3+4, 5+6+7, 8+9+10,….).
• In column 6, frequencies are added in three’s leaving the first two
frequencies (3+4+5, 6+7+8, 9+10+11,….).
• Mark the maximum frequency in each column.
• Prepare the analysis table to find out the exact value of the modal class.
Variable (x) 2 4 6 8 10 12 14 16 18 20
Frequency
(f)
15 20 25 27 30 20 15 21 10 11
Grouping Table
Variable
(x)
Col.1 Col.2 Col.3 Col.4 Col.5 Col.6
2 15 35 60
4 20 45 72
6 25 52 82
8 27 57 77
10 30 50 65
12 20 35 56
14 15 27 46
16 21 22 42
18 10 21
20 11
Analysis Table
Col.
No.
2 4 6 8 10 12 14 16 18 20
1 1
2 1 1
3 1 1
4 1 1 1
5 1 1 1
6 1 1 1
Total 1 3 5 4 1
Variable (x)
• In this example the modal value is 10. because it shows maximum frequency.
• However, the concentration of the items is more on the either side of this value.
• After grouping analysis the modal value is found to be 8 and not 10.
• Mode is affected by the frequencies of the neighboring items.
2. Calculation of mode in a discrete series.
Mode can be calculated by the formula:
𝑀𝑜𝑑𝑒 = 𝐿 +
𝑓1 − 𝑓0
2𝑓1 − 𝑓𝑜 − 𝑓2
× 𝑖
L= Lower limit of the modal class
f0= frequency of the class preceding modal class
f1= frequency of modal class
f2= frequency of the class succeeding modal class.
i= Class interval
Here modal class is 30-60.
L= 30
f0=21
f1= 51
f2= 35
i= 10
Mode= 30+(51-21/2*51-21-35)10
=30+6.52
=36.52
Classes Frequency
0-10 5
10-20 21
20-30 51
30-40 35
40-50 18
50-60 30
References
Khan, I. A., & Khanum, A. (1994). Fundamentals of biostatistics. Ukaaz.
Sharma, A. K. (2005). Text book of biostatistics I. Discovery Publishing House.
Daniel, W. W., & Cross, C. L. (2018). Biostatistics: a foundation for analysis in
the health sciences. Wiley.
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Calculation of mode

  • 1. Calculation of Mode SUBMITTED BY DR. SUNITA OJHA ASSISTANT PROFESSOR SURESH GYAN VIHAR UNIVERSITY
  • 2. Mode • It is repeated the highest number of times in the series by definition • The mode of a distribution is the value at the point around which the items tend to be most heavily concentrated. • The main feature of mode is that it is the size of that item which has the maximum number frequency. 1. Calculation of mode in a series of individual observations: • The value occurring maximum number of times are the modal values. Example1. Find the mode of the following data relating to the weights of a sample of experimental animals S.No. 1 2 3 4 5 6 7 8 9 10 Weight 10 11 10 12 12 11 9 8 11 11
  • 3. Weight No. of animals 8 1 9 1 10 2 11 4 12 1 13 1 • Since the item 11 occurs the maximum number of times i.e. 4 times, the modal value is 11. • If two values have the maximum frequency, the series is bimodal. 2. Calculation of mode in a discrete series. • Mode can be determined by looking to that variable around which the items are most heavily concentrated. Value 6 8 10 12 14 16 18 20 22 24 Frequency 20 30 40 40 55 60 55 20 15 25 • In the above data modal value is 16, because it occurs the maximum no. of times i.e. 60 times
  • 4. • However, the values on the either side of 16 have also large frequencies. • In such cases, it is desirable to prepare a grouping table and an analysis table. • Grouping Table has six columns. Frequencies are added in two’s or three’s • In column 1, maximum frequency is marked. • In column 2, frequencies are added in two’s (1+2, 3+4, 5+6……). • In column 3, frequencies are added in two’s leaving the first frequency (2+3, 4+5, 6+7…). • In column 4, frequencies are added in three’s (1+2+3, 4+5+6, 7+8+9…). • In column 5, frequencies are added in three’s leaving the first frequency (2+3+4, 5+6+7, 8+9+10,….). • In column 6, frequencies are added in three’s leaving the first two frequencies (3+4+5, 6+7+8, 9+10+11,….). • Mark the maximum frequency in each column. • Prepare the analysis table to find out the exact value of the modal class.
  • 5. Variable (x) 2 4 6 8 10 12 14 16 18 20 Frequency (f) 15 20 25 27 30 20 15 21 10 11 Grouping Table Variable (x) Col.1 Col.2 Col.3 Col.4 Col.5 Col.6 2 15 35 60 4 20 45 72 6 25 52 82 8 27 57 77 10 30 50 65 12 20 35 56 14 15 27 46 16 21 22 42 18 10 21 20 11
  • 6. Analysis Table Col. No. 2 4 6 8 10 12 14 16 18 20 1 1 2 1 1 3 1 1 4 1 1 1 5 1 1 1 6 1 1 1 Total 1 3 5 4 1 Variable (x) • In this example the modal value is 10. because it shows maximum frequency. • However, the concentration of the items is more on the either side of this value. • After grouping analysis the modal value is found to be 8 and not 10. • Mode is affected by the frequencies of the neighboring items.
  • 7. 2. Calculation of mode in a discrete series. Mode can be calculated by the formula: 𝑀𝑜𝑑𝑒 = 𝐿 + 𝑓1 − 𝑓0 2𝑓1 − 𝑓𝑜 − 𝑓2 × 𝑖 L= Lower limit of the modal class f0= frequency of the class preceding modal class f1= frequency of modal class f2= frequency of the class succeeding modal class. i= Class interval
  • 8. Here modal class is 30-60. L= 30 f0=21 f1= 51 f2= 35 i= 10 Mode= 30+(51-21/2*51-21-35)10 =30+6.52 =36.52 Classes Frequency 0-10 5 10-20 21 20-30 51 30-40 35 40-50 18 50-60 30
  • 9. References Khan, I. A., & Khanum, A. (1994). Fundamentals of biostatistics. Ukaaz. Sharma, A. K. (2005). Text book of biostatistics I. Discovery Publishing House. Daniel, W. W., & Cross, C. L. (2018). Biostatistics: a foundation for analysis in the health sciences. Wiley.