4. Descriptive Statistics
- This includes the techniques which
are concerned with summarizing
and describing numerical data.
This method can either be
graphical or computational.
- For easy understanding , tables ,
graphs and charts that display
data are used
5. Inferential statistics
The technique by which decisions about statistical population
, made based only on a sample having been observed or a
judgment having been obtained. This kind of statistics is
concerned more with the generalizing information or making
inference about population.
Consist of generalizing from samples to population, performing
hypothesis testing, determining relationships among variables
and making predictions.
Data- a set of observations, values, elements or
objects under consideration
Population (N)- complete set of all possible
observations or elements. It consist of the total
collection of observations or measurements that
are of interest to the statistician or decision
maker and about which they are trying to draw
8. Sample (n)- Representative of a
population. It is a collection of some , but
not all , of the elements of the population
under study in which the statistician is
Variable- attribute of interest observable
on each entity in the universe. It is a
characteristic which may take on different
value like sex, weight, income, size, ages,
IQ, sales and temperature.
9. Dependent Variable – it is the value
affected by change in other factors and
is called the criterion variable.
Independent Variable – its changes
caused other variables to change in
value and is called the predictor
Tabulation – the process of classifying or
grouping scores in the systematic
Ungrouped data – data which have not been
organized or classified and usually exhibit no
Parameter – is the characteristics of
population which is measurable.
Frequency distribution – the tabulation of
scores or measures group with class intervals.
Class Frequency – it is the number of
measures of observations in an interval
11. Class Intervals or Stated Class Limits – these
are classes or ranges of values that the
observations can assume. Each class
interval has a lower limit and an upper limit.
Class Boundaries or Real or Exact Class
Limits – these are the exact values of class
limits by at least 0.5. It is the upper limit of
one class and the lower limit of the
12. Class Mark – it is the midpoint of a class interval in a
frequency distribution and taken as the average of
the lower and upper limits.
Class Size – it is the width of class intervals and
measures the interval between the first value of one
class and the first value of the next class.
Continuous Data – data that may progress from one
class to the next without a break and may be
expressed by either whole number or fractions.
Discrete Data – data that does not progress from
one class to the next without a break.
Frequency Polygon – a graph which is
constructed by connecting points above
the midpoint of a step and the height
equal to the frequency of the steps.
Histogram – a frequency curve which
aims to composed of a series of
rectangles constructed with the steps as
the base and the frequency as the
14. Population and Samples
Population is a set of people or objects you are
interested in a particular study.
- Finite population or infinite population
finite – set of high school principals , senators ,
Infinite population – set of all people in the
16. SUBSCRIPT AND SUMMATION NOTATIONS
Subscript is a number or letter
representing several numbers
placed at the lower right of a
Summation symbol ∑ ( Greek capital
letter “ sigma “ ) is used to denote
that subscripted variables are to be
17. Xi stands from x1 , x2 , x3 , … . Xn
= ( X1 ) + ( X2 ) + ( X3)+ … + ( Xn )
Read as “ the summation of the
x’s from I to 3 .
20. Chapter 2 . Collection of Data
Two types of data
1. Primary – are information collected by a person or organization
that will be using the information. This are first – hand or original
2. Secondary – are information already collected by someone
else. Are information take from published or unpublished data
21. Methods in Collection of Data
Direct or interview method
Indirect or questionnaire method
Population = 25,000
margin of error 5% (.05)
Solve for the sample size (n)
1 + (25,000) (0.05)2
1 + (25,000) (0.0025)
1 + 62.5
say 394 or 400
24. Sampling Techniques
1. Simple Random Sampling (SRS)- most basic method of
probability sample, assigns equal probabilities of selection to
each possible sample. Equal chance of being selected.
▪ Lottery or fishbowl sampling
▪ Table of Random Numbers
➢ SRS without Replacement- drawn papers are no longer
➢ SRS with Replacement- allows repeats in selection
25. Continuation of Sampling Techniques
2. Systematic Sampling – it is assumed that the
members of a
population are arranged in
a specific order.
26. Systematic Sampling
For a population of N element where n units will be taken. Let
K = N / n.
For example: 50- students in a class whose names are
arranged alphabetically , 10 students are to be taken as
K = 50 / 10 = 5. Suppose from the first 5 , the 3rd student is
chosen at random. 3rd , 8th , 13th , 18th … 48
or if every 5th member is selected, samples consists of 5th , 10th ,
15th and so on.
27. Types of Systematic sampling
3. Stratified Random
➢ The universe is divided into
L mutually exclusive
Sub-universe called strata
➢ Independent Simple random samples are
Obtained from each stratum
28. Stratified Random Sampling
The sample size should be proportional to the size of the
stratum in the population.
Suppose in the class of 42 students , 18 boys and 24 girls. If a
sample of 14 students be chosen such the number of boys
and girls are proportionally represented.
Boys = 18 ( 14 ) = 6 boys
Girls = 24 (14 ) = 8 girls
29. Stratified Random Sampling
Obtain a sample of 100 students
proportionally representing each level.
Level Number of Enrollees
30. Continuation of Sampling Techniques
4. Cluster Sampling
31. 4. Cluster Sampling - can be
done by subdividing the
population into smaller units
selecting only at random some
primary units where the study
would then be concentrated.
Sometimes it is referred to as “
area sampling “ because it is
frequently applied on a
33. Chapter 3. Presentation of Data
▪ Statistical Table
Table Number and Heading
Stub Head Master Caption