Introduction to Mode. Calculation of modes by different methods. Merits and Demerits of Mode. Mode is the value which occurs the maximum number of times in a series of observations and has the highest frequency. Calculation of Mode 1. Calculation of mode in a series of individual observations (Ungrouped data) 2. Calculation of mode in a discrete series (Grouped data) 3. Calculation of mode in a continuous series (Grouped data) 4. Calculation of mode in a unequal class intervals (Grouped data)

1. BIOSTATISTICS AND RESEARCH METHODOLOGY
Unit-1: mode
PRESENTED BY
Gokara Madhuri
B. Pharmacy IV Year
UNDER THE GUIDANCE OF
Gangu Sreelatha M.Pharm., (Ph.D)
Assistant Professor
CMR College of Pharmacy, Hyderabad.
email: sreelatha1801@gmail.com

2. MODE
• It is a value which occurs the maximum number of times in a series of observations and has the highest
frequency. This value of the variable at which the curve reaches a maximum is called the mode.
• Mode is the easiest to calculate since it is the value corresponding to the highest frequency.
• It is derived from the French word “La mode’’ which means fashion.
• However according to croxton and cowden, “The mode of a distribution is the value at the point around
which the items tend to be most heavily concentrated’’. It may be regarded as the typical value of series
of values.
• A set of data may have a single mode , in which the case it is said to be unimodal.
• When concentration of data occurs at two or more points, such a series is called bimodal or multimodal,
depending on the number of such points.
• Example: RBCs number of 15 patients of a hospital were recorded as 30,32,33,31,35,37,40,36,39,36,34,
 36,35,41 and 38 Lac/mm3.
• Solution: Arrange the data in ascending order and prepare a frequency distribution table.
• Since the item 36 appears maximum number of times, i.e., 3times. Therefore , 36 is the value of mode
in the series.

3. Calculation of Mode
1) Calculation of mode in a series of individual observations (Ungrouped data)
2) Calculation of mode in a discrete series (Grouped data)
3) Calculation of mode in a continuous series (Grouped data)
4) Calculation of mode in a unequal class intervals (Grouped data)

4. 1) Calculation of mode in a series of individual observations
 Mode can be ascertained by mere inspection in case of individual observations. The values occurring the
maximum number of times are the modal class.
 Example: Find the mode of the following data relating to the weights of 10 patients.
 Solution:
Since the item 11 occurs the maximum number of times i.e., 4 times, the modal values is 11. If two values
have the maximum frequency, the series is bimodal.
Weight(k
gs)
1 2 3 4 5 6 7 8 9 10
Number of
patients
10 11 10 12 13 11 9 8 11 11
Weight(kg
s)
8 9 10 11 12 13
Number of
patients
1 1 2 4 1 1

5. 2) Calculation of mode in a discrete series
 Mode can be determined by looking to that value of the variable around which the items are most
heavily concentrated.
 Example: Find the mode of the following frequency distribution of the weights of the 10 tablets
 Solution: we find out the value 11 of the variable x occurs maximum numbers of times, i.e. 15.
But we notice that the difference between the frequencies of the values of the variable on both
sides of 15, which are very close to 11 is very small.
 This shows that the variable x are heavily concentrated on either side of 11. therefore , if we find
mode just by inspection, an error is possible.
 This problem is solved by the method of grouping as it is an irregular distribution in the sense that
the difference between maximum frequency 15 and frequency preceding it is very small.
 Let us prepare the grouping and analysis table.
Size(x) 4 5 6 7 8 9 10 11 12 13
Frequency
(f)
2 5 8 9 12 14 14 15 11 13

6. Size(x) Frequency(f
)
Col. Of two Col. Of two
leaving the
first(iii)
Col. Of
three
(iv)
Col. Of
three
leaving the
first (v)
Col. Of
three
leaving the
first two (vi)
4
5
6
7
8
9
10
11
12
13
2
5
8
9
12
14
14
15
11
13
7
17
26
29
34
13
21
28
26
15
35
40
22
40
39
29
43

7. ANALYSIS TABLE
X
Col. no
4 5 6 7 8 9 10 11 12 13
i 1
ii 1 1
iii 1 1
iv 1 1 1
v 1 1 1
vi 1 1 1
Total
frequency
1 3 5 4 1
But by inspection one is likely to say that the modal value is 11, since it occurs the maximum
numbers of times, i.e., 15, which is incorrect as revealed by analysis and grouping table which
gives the correct modal value as 10 (though it occurs 14 times).

8. 3) Calculation of mode in a continuous series
 Modal class : it is the class in a groped frequency distribution in which the mode lies. This modal class
can be determined either by inspection or with the help of grouping table. After finding the modal class ,
we calculate the mode by the following formula.
 Mode = 𝑙 +
𝑓𝑚−𝑓1
2𝑓𝑚−𝑓1−𝑓2
× 𝑖
 Where 𝑙 = the lower limit of the modal class
i = the width of the modal class
𝑓1 = the frequency of class preceding the modal class
𝑓𝑚 = the frequency of the modal class
𝑓2 = the frequency of the class succeeding the modal class
Sometimes, it so happened that above formula fails to give the mode. In this case, the modal value lies in a
class other than the one containing maximum frequency. In such cases, we take the help of the following
formula
Mode = 𝑙 +
∆2
∆1− ∆2
× 𝑖
Where, 𝑙 = 𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙, ∆1 = 𝑓𝑚 − 𝑓1 ∆2 = (𝑓𝑚 − 𝑓2)

9.  Example: Find the mode of the following data
 Solution: From the above table, it is clear that the maximum frequency is 32 and it lies in the class 16 – 20.
Thus modal class is 16 – 20
Here 𝑙 = 16 , 𝑓𝑚 = 32, 𝑓1 = 16, 𝑓2 = 24, i = 5
Mode = 𝑙 +
𝑓𝑚−𝑓1
2𝑓𝑚−𝑓1−𝑓2
× 𝑖
= 16 +
32−16
64−24−16
× 5
= 16 + 3.33 = 19.33
Clinical
trial
frequency
1 - 5 6 - 10 11 - 15 16 - 20 21 - 25
No of
patients
7 10 16 32 24

10. 4) Calculation of mode in unequal class intervals
 Before we compute the mode in unequal class –intervals, the class-intervals should be made equal and
frequencies should be adjusted accordingly.
 Example: calculate the mode of the following distribution:
 Solution: In this problem the class-intervals are unequal,
therefore, we must adjust the frequencies and make the
class-intervals equal.
mode lies in the class = 130 – 140
mode = 𝑙 +
∆2
∆1+ ∆2
× 𝑖
L = 130, ∆1 =(27 -20) = 7 , ∆2 = (27 – 17) = 10, i = 10
mode = 130 +
7
7+ 10
× 10
= 130 +
70
17
= 130 + 4.12
Mode = 134.12
No of
tablets
100 - 110 110 - 130 130 - 140 140 - 160 160 - 170 170 - 180
No of
capsules
11 40 27 34 12 6
No of tablets No of capsules
100 - 110 11
110 - 120 20
120 - 130 20
130 - 140 27
140 - 150 17
150- 160 17
160 - 170 12
170 - 180 6

11. Merits of Mode
 Mode is easy to calculate and can be determined by a mere observation of the data.
 The mode is not unduly affected by extreme items
 It is simple and precise
 Mode is the point where there is no more concentration of frequencies. Hence , it is the
best representative of the data.
Demerits of Mode
 The mode is not based on all the observations.
 The value of the mode cannot be determined in bimodal distribution.
 It is not a rigidly defined measure. Sometimes the exact value of the modal class cannot
be known by inspection of the data. Therefore it is necessary to prepare grouping table
and then an analysis table to find out the modal class