Republic of
the Philippines
UNIVERSITY OF EASTERN PHILIPPINES
University Town, Northern Samar, Philippines
Web: http://uep.edu.ph; Email: uepnsofficial@gmail.com
GRADUATES SCHOOL
Master of Science in Biological Science
BioEd803 "BIOSTATISTICS"
nd
2 Semester, SY 2023-2024
Student Name:
JELY L. DE PEDRO
Program/ Year Level:
MS Biological Science – 1
GS Professor:
RIZA BASIERTO
Score:
Date:
APRIL 12, 2024
1. Explain the concept and significance of variability.
CONCEPT:
The concept of variability refers to the extent to which data or observations vary or differ from
each other. It is a measure of the dispersion or spread of values within a dataset. Variability is an
important concept in statistics and data analysis as it provides insights into the diversity or
consistency of the data.
SIGNIFICANCE:

Describing Data Distribution: Variability helps us understand the range of values
and the diversity within a dataset. It provides information about how data points are
spread out or distributed. By examining the variability, we can gain insights into the
patterns, trends, and characteristics of the data.

Assessing Data Quality: Variability can be used as an indicator of data quality. If
there is a high degree of variability in a dataset, it suggests that the data points are
diverse and may have different characteristics. On the other hand, low variability
may indicate that the data points are similar or clustered around a central value.
Assessing variability can help identify potential errors, outliers, or inconsistencies in
the data.

Making Inferences and Generalizations: Variability is crucial for making accurate
inferences and generalizations from a sample to a population. In statistics,
variability is often used to calculate the margin of error and confidence intervals. A
larger variability implies a wider range of possible values, which affects the
precision and reliability of statistical estimates and predictions.
DOCUMENT NO.:
UEP-GS-FM-012
REVISION NO.:
00
EFFECTIVITY DATE:
September 16, 2023
Page 1 of 1

Comparing and Contrasting: Variability allows for meaningful comparisons and
contrasts between different groups or datasets. By comparing the variability of two
or more datasets, we can determine if there are significant differences in their
distributions. For example, in scientific research, comparing the variability of
experimental and control groups can help determine the effectiveness of a
treatment or intervention.

Decision Making: Variability plays a crucial role in decision making under
uncertainty. When there is variability in the outcomes or potential risks, decisionmakers need to consider the range of possible outcomes and their associated
probabilities. Understanding the variability helps in assessing the potential risks
and rewards, and making informed decisions.
2. Discuss the merit and limitation of range and quartile deviation.
The range is a measure of variability that calculates the difference between the maximum
and minimum values in a dataset. While the range has some merits, it also has certain
limitations that should be considered.
Merits of Range:

Simplicity: The range is a simple and straightforward measure of variability. It is
easy to understand and calculate, making it accessible to individuals with limited
statistical knowledge.

Quick Assessment of Data Spread: The range provides a quick assessment of
how spread out the data points are. By comparing the range of different datasets,
you can get a general idea of the differences in variability between them.

Useful for Identifying Outliers: The range can help identify potential outliers in a
dataset. Outliers are data points that are significantly different from the majority of
the data. By examining the range, extreme values that fall outside the expected
range can be easily identified.
Limitations of Range:

Sensitivity to Extreme Values: The range is highly sensitive to extreme values or
outliers in the dataset. A single extreme value can greatly affect the range, making
it less representative of the overall variability of the data.

Lack of Information about Data Distribution: The range only considers the
maximum and minimum values and does not provide information about the
distribution of the data points within that range. It does not take into account the
shape, spread, or any patterns in the dataset.

Limited Statistical Information: The range provides a very basic measure of
variability and does not capture the full picture of the data. It does not provide
information about the average distance between data points or the degree of
variation around the mean.
DOCUMENT NO.:
UEP-GS-FM-012
REVISION NO.:
00
EFFECTIVITY DATE:
September 16, 2023
Page 2 of 2

Insensitive to Changes in Central Tendency: The range is insensitive to changes in
the central tendency of the data, such as the mean or median. Two datasets with
different means but the same range would be considered equally variable, even
though their distributions may be different.

Sample Size Dependency: The range can be influenced by the sample size.
Smaller sample sizes may result in a smaller range, while larger sample sizes may
lead to a larger range, even if the underlying variability of the population remains
the same.
The quartile deviation, also known as the interquartile range (IQR), is a measure of
variability that calculates the difference between the upper quartile (75th percentile)
and the lower quartile (25th percentile) in a dataset. The quartile deviation has both
merits and limitations that should be considered.
Merits of Quartile Deviation:

Robust to Outliers: The quartile deviation is a robust measure of variability that is
less sensitive to outliers compared to the range or standard deviation. It focuses on
the middle 50% of the data, making it less influenced by extreme values. This
makes it a useful measure when dealing with datasets that contain outliers.

Describes Data Spread: The quartile deviation provides information about the
spread or dispersion of the central portion of the data. By calculating the difference
between the upper and lower quartiles, it gives an indication of the range of values
where the majority of the data lies. This can help in understanding the distribution
of the data.

Resistant to Skewed Data: The quartile deviation is less affected by skewed data
distributions compared to other measures of variability. It is based on percentiles
rather than the mean, which makes it suitable for datasets that do not follow a
normal distribution or have significant skewness.

Useful for Comparing Groups: The quartile deviation can be used to compare the
variability between different groups or datasets. By calculating the quartile
deviation for each group, you can assess if there are significant differences in the
spread of values. This is particularly useful in research or statistical analysis where
group comparisons are important.
Limitations of Quartile Deviation:

Limited Information about Data Distribution: The quartile deviation provides
information about the spread of the central portion of the data, but it does not
provide details about the entire distribution. It does not capture information about
the shape, tails, or specific patterns within the dataset.

Ignores Variability in the Outer Tails: The quartile deviation focuses only on the
middle 50% of the data and ignores the variability in the outer tails. If there is
substantial variability in the extreme values, it will not be reflected in the quartile
deviation measure.
DOCUMENT NO.:
UEP-GS-FM-012
REVISION NO.:
00
EFFECTIVITY DATE:
September 16, 2023
Page 3 of 3

Less Precise than Other Measures: The quartile deviation provides a rough
estimate of variability compared to other measures such as the standard deviation.
It does not take into account the individual differences between data points, but
rather provides a summary measure of the spread.

Loss of Information: By calculating the quartile deviation, some information about
the data is lost. It condenses the variability into a single value, which may not
capture the nuances or finer details of the data distribution.
3. List the merits and limitations of standard deviation
Merits of Standard Deviation:

Describes Variability: The standard deviation provides a quantitative measure of
the spread or dispersion of data points around the mean. It gives an indication of
how closely or widely the data is distributed around the average value.

Sensitive to Individual Data Points: The standard deviation takes into account the
differences between each data point and the mean. It considers the individual
deviations from the mean, giving more weight to data points that are further away
from the average. This sensitivity makes it a useful measure for detecting outliers
or extreme values.

Widely Used and Understood: The standard deviation is one of the most
commonly used measures of variability in statistics. It is widely understood and
accepted, making it easy to communicate and compare across different datasets
or studies.

Basis for Statistical Inference: The standard deviation is a fundamental
component in many statistical calculations and inference procedures. It is used to
calculate confidence intervals, conduct hypothesis tests, and estimate the
precision of statistical estimates. It provides a measure of uncertainty and
variability that is essential for making statistical inferences.

Reflects Data Distribution: The standard deviation is influenced by the shape and
characteristics of the data distribution. It captures the spread of the data, whether
it follows a normal distribution, skewed distribution, or has other patterns. This
makes it a versatile measure that can be applied to various types of data.
Limitations of Standard Deviation:

Sensitive to Outliers: The standard deviation is highly sensitive to outliers or
extreme values in the dataset. Outliers can have a significant impact on the
standard deviation, especially if they are far away from the mean. This sensitivity
can distort the measure of variability and make it less representative of the
majority of the data.

Affected by Sample Size: The standard deviation is influenced by the sample size.
Smaller sample sizes may result in larger standard deviations, while larger sample
sizes tend to yield smaller standard deviations. This dependence on sample size
should be considered when comparing standard deviations between different
DOCUMENT NO.:
UEP-GS-FM-012
REVISION NO.:
00
EFFECTIVITY DATE:
September 16, 2023
Page 4 of 4
datasets.

Assumes Normal Distribution: The standard deviation assumes that the data
follows a normal distribution. While it can still be calculated for non-normal data,
its interpretation may be limited in such cases. Other measures, such as the
interquartile range, may be more appropriate for non-normal distributions.

Lack of Intuitive Interpretation: The standard deviation is a measure of dispersion,
but its value does not have an intuitive interpretation on its own. It is not
immediately clear what a certain value of standard deviation signifies unless it is
compared to other values or benchmarks. This can make it challenging for nonstatisticians to interpret and understand.

Loss of Information: Like any summary statistic, the standard deviation
condenses the variability of the data into a single value. This loss of information
can mask important details about the data distribution, such as asymmetry,
multimodality, or specific patterns.
4. Elucidate average deviation or mean deviation.
The average deviation, also known as the mean deviation, is a measure of variability that
quantifies the average difference between each data point in a dataset and the mean of that
dataset. It provides an indication of how much, on average, each data point deviates from the
mean.
To calculate the average deviation, follow these steps:
1. Calculate the mean of the dataset by summing all the values and dividing by the total
number of data points.
2. For each data point, subtract the mean from the value to find the deviation.
3. Take the absolute value of each deviation to ensure that negative and positive
deviations do not cancel each other out.
4. Calculate the average of these absolute deviations by summing them up and dividing by
the total number of data points.
The average deviation is expressed in the same units as the data and provides a measure of
dispersion around the mean. Here are some key points about the average deviation:

Reflects Individual Differences: The average deviation considers the individual
differences between each data point and the mean. It takes into account both
positive and negative deviations, providing a balanced measure of variability.

Sensitive to Outliers: The average deviation is sensitive to outliers or extreme
values in the dataset. Outliers can have a significant impact on the average
deviation, especially if they are far away from the mean. This sensitivity can make
the measure less robust in the presence of outliers.

Less Commonly Used: While the average deviation is a valid measure of variability,
it is less commonly used compared to other measures such as the standard
DOCUMENT NO.:
UEP-GS-FM-012
REVISION NO.:
00
EFFECTIVITY DATE:
September 16, 2023
Page 5 of 5
deviation or the interquartile range. This is because the average deviation does not
have some desirable statistical properties and can be more difficult to interpret.

Interpretation: The average deviation provides a measure of the average amount
by which each data point deviates from the mean. However, its value does not
have a direct intuitive interpretation. It is often used in conjunction with other
measures of variability to provide a more comprehensive understanding of the
data spread.

Calculation and Comparison: The calculation of the average deviation is relatively
straightforward, but it is important to note that it is not directly comparable to
other measures of variability like the standard deviation. The average deviation
tends to yield larger values than the standard deviation for the same dataset.
5. Explain coefficient of variance with example.
The coefficient of variation (CV) is a statistical measure that expresses the relative variability or
dispersion of a dataset in relation to its mean. It is calculated by dividing the standard deviation
of the dataset by the mean and multiplying the result by 100 to express it as a percentage.
The formula for calculating the coefficient of variation is as follows:
CV = (Standard Deviation / Mean) * 100
Here's an example to illustrate the concept of coefficient of variation:
Let's consider two datasets, Dataset A and Dataset B, representing the monthly incomes of two
individuals over a year:
Dataset A: [2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500, 6000, 6500, 7000, 7500]
Dataset B: [3000, 3500, 4000, 4500, 5000, 5500, 6000, 6500, 7000, 7500, 8000, 8500]
To calculate the coefficient of variation for each dataset, we need to calculate the mean and
standard deviation first:
Dataset A:
Mean = (2000 + 2500 + 3000 + 3500 + 4000 + 4500 + 5000 + 5500 + 6000 + 6500 + 7000 + 7500)
/ 12 = 4750
Standard Deviation = 1920.285
Dataset B:
Mean = (3000 + 3500 + 4000 + 4500 + 5000 + 5500 + 6000 + 6500 + 7000 + 7500 + 8000 + 8500)
/ 12 = 5750
Standard Deviation = 1920.285
Now, we can calculate the coefficient of variation for each dataset:
Coefficient of Variation (Dataset A) = (1920.285 / 4750) * 100 = 40.43%
DOCUMENT NO.:
UEP-GS-FM-012
REVISION NO.:
00
EFFECTIVITY DATE:
September 16, 2023
Page 6 of 6
Coefficient of Variation (Dataset B) = (1920.285 / 5750) * 100 = 33.39%
In this example, both datasets have the same standard deviation, indicating the same
absolute variability. However, Dataset A has a lower mean than Dataset B, resulting in a higher
coefficient of variation. This suggests that Dataset A has a higher relative variability compared to
its mean, while Dataset B has a lower relative variability.
The coefficient of variation allows for the comparison of variability between datasets with
different means. It is particularly useful when comparing datasets with different scales or units,
as it normalizes the variability relative to the mean. A higher coefficient of variation indicates
higher relative variability, while a lower coefficient of variation suggests lower relative variability.
DOCUMENT NO.:
UEP-GS-FM-012
REVISION NO.:
00
EFFECTIVITY DATE:
September 16, 2023
Page 7 of 7