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Measure of Central Tendency or also called the average is a single value
that attempts to describe a data set by identifying the central position at which
the observations tend to cluster.
The Arithmetic Mean
The arithmetic mean or simple the mean, denoted by Greek letter
(population) and ̅ (sample), is defined as the sum of all observations divided by
the total number of observations. It is best used when there are no extremes
values on the data set.
In symbols,
= population mean
∑ = sum of all the observations
N= population size
̅ = sample mean
∑ = sum of all the observations
N= sample size
Population
∑
Sample
∑
̅
Computation of the Arithmetic Mean:
1. Given the set of observations: 12, 13, 7, 11, 5 . The mean is computed as:
∑
̅
2. The following are the weight (in kilograms) of 10 selected cancer patients.
46
43
37
52
48
60
34
40
55
41
̅
∑
3. A scientist made six measurements of the ionization energy of helium (in
electron volts), obtaining 24.55, 24.65 ,24.56. 24.56, 24.62, 24. 57. Calculate
the mean of these measurements.
̅
∑
4. Four separate blood tests revealed that a patient had total blood
cholesterol levels of 240, 235, 225, and 215. Find the mean of the blood
cholesterol levels.
∑
̅
The Median
The median, denoted by Md , is a single value which divides an array of
observations into two equal parts such that fifty percent of the observations fall
below it and fifty percent fall above it. It is a positional value and hence is not
affected by the presence of extreme values unlike the mean.
The formula is given below:
Computation of the Median:
1. Given the set of observations: 5 , 10, 17, 15, 6, 8, 11. Compute for the
median.
Step 1. Determine whether the number of observation is odd or even.
n = 7 , therefore n is odd
Step 2. Arrange the observations in numerical order from smallest to
largest or largest to smallest.
5, 6, 8, 10, 11, 15, 17
5
6
8
Step 3. Compute for the median.
10
11
15
17
2. The following are the preliminary grades of 8 nursing students.
85
97
81
77
86
84
94
93
Step 1. Determine whether the number of observation is odd or even.
n = 8 , therefore n is even
Step 2. Arrange the observations in numerical order (ascending order
or descending order).
77, 81, 84, 85, 86, 93, 94, 97
77
81
84
85
86
93
94
97
Step 3. Compute for the median.
3. Find the median of the list: 6 , 7, 18, 13, 14.
Solution : Arrange the list in numerical order(ascending or descending
order) , then locate the middle value if n is odd.
6
7
13
14
18
4. Find the median of the list: 6 , 7, 18, 13, 14, 9.
Solution : Arrange the list in numerical order(ascending or descending
order) , then solve for the mean of the two middle values if n is even.
6
7
9
13
14
18
The Mode
The mode, denoted by Mo, is the value which occurs most frequently or has
the highest frequency in the given data set. It is used when a rough or quick
estimate of the central value is wanted.
Types:
1. Unimodal
2. Bimodal
3. Trimodal
4. Multimodal
Computation of the mode:
1. Given the data set: 5, 8, 9, 7 , 6 .
Solution: Each observation in the data set occurs only once. Because no
observation occurs more often than the others, there is no mode.
Mo= no mode
2. The following are the ages of 6 nurses in a small private hospital.
45
25
25
45
31
31
Solution: Each observation in the data set occurs twice. Because no
observation occurs more often than the others, there is no mode.
Mo= no mode
3. Blood type of the 10 patients who tested positive for COVID-19.
O
O
A+
BAB+
O
BA+
B+
ABMo= O
4. Height (in centimeters) of 7 malnourished students.
143
132
150
143
148
Mo= 143 and 148
148
References
Aufmann, R. et al. (2018). Mathematics in the Modern World. Manila: Rex
Bookstore, Inc.
An Introduction to Statistical Methods and Data Analysis (Ott & Longnecker,
2010)
Mathematical Excursions (Aufmann et al., 2018)
Statistics for the Social Sciences (Beligan, 2011)