Research 3 Quarter 3 - MELC 1 Week 1-2 Inferential Statistics

Research 3
Quarter 3 - MELC 1
Week 1-2
Inferential Statistics
MICHELLE C. TENORIO
Subject Teacher
Learning Competency with Code
Utilize appropriate statistical tools in
inferential statistics in
interpreting data
(SSP-RS9-AID-III-q-t-7).
Background Information for Learners
Statistics deals with experimental designs and procedures which
include data collection, classification, organization and interpretation,
and decision making regarding these data. It can be broken down
into two essential areas: descriptive statistics and inferential
statistics.
Descriptive statistics refers to the methods of data collection,

organization, classification, summarization, and presentation. It
includes the procedures for constructing graphs, tables, and charts. it
also refers to the calculation of statistical descriptions such as the
measures of central tendency and the measures of variability.
Background Information for Learners
Inferential statistics refers to the process of arriving at a

conclusion about a population based on the information obtained
from a sample. A number that describes a characteristic of a
population is called a parameter. A number that describes a
characteristic of a sample is called a statistic. Research analysts
use statistical inference to estimate an unknown population
parameter by using a sample statistic.
DESCRIPTIVE STATISTICS
Data collection and organization
Tables and graphs can be most useful in describing data. They
often review more directly the important characteristics of the
data than what is possible in using more sophisticated statistical
analyses. There several ways of arranging and organizing data. Raw
data may be organized by constructing either an ungrouped or a
group distribution.
The following are the methods by which data can be arranged
in an orderly and understandable form: (1) listing the values in an
array; (2) constructing an ungrouped frequency distribution; and
(3) constructing a grouped frequency distribution.
1. Array
An array is an arrangement from highest to lowest or from lowest
to
highest.
2. Ungrouped frequency distribution
In an ungrouped frequency distribution, data scores are arranged
from
highest to lowest and the frequency of occurrence of each score is
indicated. This is also called a single-value grouping.
3. Grouped Frequency Distribution
In a grouped frequency distribution, the data are grouped into
categories or classes (class interval). Scores are assigned to mutually
exclusive classes which are defined in terms of grouping intervals
employed. A score in the sample belongs to only one class interval.
Grouped frequency distributions are constructed because it is not
economical to deal with a large number of cases. Some scores have
very
low frequency counts and it would not be logical to maintain these
scores
separate and distinct entities.
When grouping sample data, make the range of the class interval
neither too wide for the discrimination provided by the original
measurement to be lost nor too fine for grouping to be defeated. Most
researchers agree that the number of class intervals that can be
accommodated ranges from 5 to 20 (in behavioral sciences, it is from 10
to 20 classes).
When you have determined the number of class intervals appropriate
for a given set of data, use the following procedure.
a) Find the lowest and highest values in the sample data and get
their difference to add one to this difference to obtain the total number of
potential scores.
b) Divide this number by the number of class intervals that you
decided to have to obtain the number of scores or potential scores in each
class interval. If the result is not a whole number, round it to the nearest
whole number. This number is called the class size which is given the
symbol i. It is highly recommended that the calculated value be rounded
to the nearest whole odd number so that the middle score in each of the
class intervals is a whole number.
c) Take the lowest score in the set of data as the minimum value in
the lowest class interval and add i-1( i minus 1) to this value to obtain the
maximum value or score in the lowest class interval.
d) The next higher class interval begins with a number next to the
maximum score of the lowest class interval.
Example 1
Grouped Frequency Distribution of Ages of Person with
Diabetes (n=35)
Activity 1. Frequency Distribution
Given below is the frequency table on the result of the 100
item Special Curricular Program Admission Test to 40 applicants.
Activity 1. Frequency Distribution N=
Class Interval Frequency Cumulative Cumulative

Frequency Percentage
Distribuion
ASSIGNMENT
Given the following grades of randomly selected 38 students in
Research 9 . Construct the ungroup Frequency
45 62 64 48 65 74 75 76 77 78
71 46 73 69 68 91 93 94 95 92
50 79 56 79 58 88 86 95 99 54
61 82 84 85 89 88 87 55
ASSIGNMENT
Frequency Distribution
Class Interval Frequency Cumulative Cumulative

Frequency Percentage
Distribuion
THANK YOU!!
MEASURES OF CENTRAL TENDENCY
A measure of central tendency is a value that can represent a set of
data or a group of values.
There are three most commonly used measures of central tendency: the
mean, the median, and the mode.
Mean
The mean is the average of the values in the sample. The sum of all the
values in a set of data is divided by the total number of values in the set. It
is the most stable measure of central tendency although it can easily be
affected by extreme values. Its value need not be among the values in the
set.
Mean
There are several methods of finding the mean. The mean of ungrouped
data is given by the formula:
Where,
X = sample mean
Xi = values in the set
n = sample size, the total number of values in the set
Example No. 1
The following numbers are the values in an ungrouped data set.
When your data are in the form of an ungrouped frequency
distribution where each different value of X has a frequency f,
then the sample has to be calculated using the following
equation.
.
where, X1, X2…and Xn are values of X in the set of values, n is

the number of values, and f1 f2…and fn is their representative
frequencies.
Example No. 1.1
Find the mean of the ungrouped frequency distribution below.
Solution:
The mean of the ungrouped frequency
distribution above is 26.31
How do you calculate the mean of the scores when the set of
scores is organized in a grouped frequency distribution?
To get the mean of a set of values arranged in a grouped
frequency distribution, use the following formulas
.
.
Example No.1.2
Below is an example of a grouped frequency distribution. Calculate the
mean of this group of scores.
.
Solution
Assume that class interval 25 - 29 in the frequency distribution contains
the mean. Your assumed mean is the midpoint of this class interval
which is 27.
The class deviations from the mean are the values shown in the third
.
column of the table above. The fourth column shows the calculated
values of fi di. The computed mean is .
The mean of the grouped frequency

distribution is 26.68.
Median
The median is the value that falls in the middle position when the
measurements are ranked from the lowest to the highest. It divides
the ranked scores into two equal parts. To obtain the value of the
median, rank the values from the smallest to the largest. If the total
.
number of scores is odd, locate the middle value. If the total number
of scores is even, locate the two middle scores and take their
average, that is
Example 1.3
Calculate the median of the following ranked scores 2, 5, 6, 8, 10, 11.
Solution:
The middle scores are 6 and 8. The median, therefore, is (6+8)/2=7.
.
First, locate the class interval containing the median. Once it is
located the information needed to plug into the formula will be easily
found. Then, the median can be calculated
.
.
The calculated median is 18.07.

Mode
The mode is the most frequently occurring score in a set of
measurements. It is the easiest to determine the measure of central
tendency. In an ungrouped frequency distribution, the score with the
highest frequency is the mode.
.
Example 1.5
Find the mode in the following
distribution
The most frequently occurring score in this set is 9.

Since there is only one score in the set given in the example above that
occurs most frequently then this set is called unimodal. In some cases, there
are more than one mode in a set of scores. If there are two modes, the set is
said to be bimodal. if there are more than two modes it is called multimodal.
In a grouped frequency distribution, the mode can be determined by
locating the class interval with the highest frequency. The midpoint of
this class interval is the mode of the distribution.
Example 1.6
Consider the following grouped frequency distribution
The class interval with the highest frequency is 40-49. The midpoint of this
class interval is 44.5. Therefore, the mode for this distribution is 44.5.
MEASURE OF VARIABILITY
A measure of variability is used to determine the spread of scores

in a distribution. It gives an idea of how much the scores deviate from
the center of the distribution. It is an important consideration when the
properties of the data set are being investigated because it tells how
much scores in a data set vary from one another.
There are several measures of variability: range, mean deviation,
variance, and standard deviation.
Standard Deviation
Since the variance uses squared deviations of scores from
the mean, the unit for it is also a square of the unit of the
scores. To revert to the original unit of the scores, you can get
the square root of the variance. The calculated value is called
the standard deviation of the set of scores.
The following are the formulas for calculating the
population standard deviation (𝜎)and the sample standard
deviation (s)
Continue using the set of scores in Example 2. For this
particular set of scores, the population standard deviation is,
If this is a sample, the standard deviation will be

Activity 2
Directions: Consider the following grouped frequency distribution
and provide the needed data below.
II.
Determine the sample variance and the
sample standard deviation of the
following data
10, 11, 9, 17, 13, 15, 13 and 20
A PICTURE IS
WORTH A
THOUSAND
WORDS

Research 3 Quarter 3 - MELC 1 Week 1-2 Inferential Statistics

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Research 3

Descriptive statistics refers to the methods of data collection,

Inferential statistics refers to the process of arriving at a

Class Interval Frequency Cumulative Cumulative

Class Interval Frequency Cumulative Cumulative

where, X1, X2…and Xn are values of X in the set of values, n is

The mean of the grouped frequency

The calculated median is 18.07.

The most frequently occurring score in this set is 9.

A measure of variability is used to determine the spread of scores

If this is a sample, the standard deviation will be

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