3. MODE
▪ Mode is the most frequent value or category
in a distribution.
▪ Mode is not calculated but is simply spotted by
inspecting the values in a distribution.
▪ If all scores in a distribution are different, the
mode does not exist.
▪ If several values occur with equal frequency,
then there are several modes.
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4. CALCULATION FOR MODE OF
UNGROUPED DATA
▪ Example 1:
▪ The heights (in inches) of six female scientist are
shown below.
62, 64, 63, 61, 62, 66
▪ Solution:
▪ Mode = 62 inches
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5. CALCULATION FOR MODE OF
UNGROUPED DATA
▪ Example 2:
▪ Six strains of bacteria were tested to see how
long they could remain alive outside their normal
environment. The time, in minutes, is recorded
below. Find the mode.
2, 3, 5, 7, 8, 10
▪ Solution:
▪ Answer: No mode.
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6. MODE OF UNGROUPED DATA
(CONTINUED)
▪ Example 3:
▪ Eleven different automobiles were tested at a
speed of 15 miles per hour for stopping
distances. The data, in feet, are shown below.
Find the mode.
15, 18, 18, 18, 20, 22, 24, 24, 24, 26, 26
▪ Solution:
▪ Modes = 18 feet and 24 feet
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7. ▪ Example 4: The following data were collected on the number of blood
tests a local hospital conducted for a random sample of 50 days. Find
the mode.
Number of tests per day Frequency (days)
26 5
27 9
28 12
29 18
30 5
31 0
32 1
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8. ▪ Solution:
▪ Since 29 test were given on 18 days (the number of test that occurred
most often)
▪ Mode = 29 days
Number of tests per day Frequency (days)
26 5
27 9
28 12
29 18
30 5
31 0
32 1
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Highest
frequency
9. MODE OF GROUPED DATA
▪ The mode can be estimate by one of the following
methods:
▪ Calculation
▪ Histogram
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10. MODE OF GROUPED DATA
(CONTINUE)
▪ When data has been grouped in classes, the mode is the value at the
maximum point (frequency) on the graph.
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11. ▪ From a frequency distribution, the mode can be obtained
from the formula:
L = lower boundary of the modal class.
∆1 = difference between the frequency of the modal
class and the class immediately preceding it.
∆2 = difference between the frequency of the modal
class and the class immediately after it.
c = size of the modal class.
c
L
M
+
+
=
2
1
1
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Formula for the Mode of Grouped Data
12. ▪ Example 5: Find the modal class for the
frequency distribution of miles 20 runners ran in
one week.
Class Frequency
5.5 – 10.5 1
10.5 – 15.5 2
15.5 – 20.5 3
20.5 – 25.5 5
25.5 – 30.5 4
30.5 – 35.5 3
35.5 – 40.5 2
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13. ▪ Procedure:
▪ Step 1: Find the modal class.
- Modal class is the class with the highest
frequency.
▪ Step 2: Substitute in the formula.
▪ Step 3: Solve the mode.
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Calculation for Mode of Grouped Data
15. ADVANTAGE OF MODE
▪ The mode is the only measure of central
tendency available for nominal data.
▪ For example, suppose the patients seen in mental health clinic during a
given year received one of the following diagnoses: mental retardation,
organic brain syndrome, psychosis, neurosis and personality disorder.
The diagnosis occurring most frequently in the group of patients would
be called the modal diagnosis.
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16. DISADVANTAGE OF MODE
▪ The mode is not always unique.
▪ A data set can have more than one mode or the
mode may not exist for a data set.
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17. MODE OF CATEGORICAL DATA
▪ There is one situation in which the mode is the
only measure of central tendency that can be
used – when we have categorical, or non-numeric
data.
▪ In this situation, we cannot calculate a mean or a
median.
▪ The mode is the most typical value of the
categorical data.
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18. MODE OF CATEGORICAL DATA
(CONTINUE)
▪ Example 6: Twenty five college’s students were given a blood test to
determine their blood type. The data set are as follows:
A B B AB O O O B AB
B B B O A O A O O
O AB AB A O B A
Find the mode.
▪ Solution: Mode = O
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19. REFERENCES
1. Munro, B.H. (2005). Statistical Methods for Health Care
Research. 5th edition. Lippincott Williams & Wilkins.
2. Dunn, O.J., and Clark, V.A. (2001). Basic Statistics, A Primer
for the Biomedical Sciences . 3rd edition. Wiley-Inter Science.
3. Wayne, W. Daniel. (2005). Biostatistics, A Foundation
for Analysis in the Health Sciences. John Willey & Sons, Inc.
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20. “IF PEOPLE DO NOT BELIEVE THAT
MATHEMATICS IS SIMPLE, IT IS ONLY
BECAUSE THEY DO NOT REALIZE HOW
COMPLICATED LIFE IS”
~JOHN LOUIS VON NEUMANN
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