STATISTICS-AND-PROBABLITY-A-REVIEW-FOR-SHS.pdf

STATISTICS AND
PROBABILITY
REVIEW: PREPARATION FOR
SENIOR HIGH SCHOOL

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

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.

Terminologies
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
conclusion.

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
interested.
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.

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
variable.
Tabulation – the process of classifying or
grouping scores in the systematic
arrangement.

Con’t
Ungrouped data – data which have not been
organized or classified and usually exhibit no
pattern.
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

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
succeeding class.

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.

Con’t
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
height.

Population and Samples
 Population is a set of people or objects you are
interested in a particular study.
 - Finite population or infinite population
 Examples :
 finite – set of high school principals , senators ,
congressman
 Infinite population – set of all people in the
Philippines

Population and Sample
Population
Sample
Sample Statistics
Population
Parameters
Statistical Inference

SUBSCRIPT AND SUMMATION NOTATIONS
Subscript is a number or letter
representing several numbers
placed at the lower right of a
variable.
Summation symbol ∑ ( Greek capital
letter “ sigma “ ) is used to denote
that subscripted variables are to be
added.

Xi stands from x1 , x2 , x3 , … . Xn
= ( X1 ) + ( X2 ) + ( X3)+ … + ( Xn )
෍
𝑖=1
3
෍
𝑖=1
𝑛
𝑋
Read as “ the summation of the
x’s from I to 3 .

Examples:
1.
2.
∑
5
i=1
= x1 + x2 + x3 + x4
+x5
∑
35
i=22
=
xi
xi x22 + x23 + x24 + … +
x35

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
sources.
2. Secondary – are information already collected by someone
else. Are information take from published or unpublished data
previously gathered.

Methods in Collection of Data
 Direct or interview method
 Indirect or questionnaire method
 Registration method
 Observation Method
 Experiment Method

Sample
Population
(Parameter)
μ (mu)
Sampl
e
Statistic x
N
n =
1 +N(e)2
Where:
n- sample size
N- population size
e- margin of error

Given:
Population = 25,000
margin of error 5% (.05)
Solve for the sample size (n)
25,000
n=
1 + (25,000) (0.05)2
25,000
n=
1 + (25,000) (0.0025)
25,000
n=
1 + 62.5
25,000
n=
63.5
n= 393.70
say 394 or 400

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
returned
➢ SRS with Replacement- allows repeats in selection

Continuation of Sampling Techniques
2. Systematic Sampling – it is assumed that the
members of a
population are arranged in
a specific order.
Population Systematic
Sample

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
sample.
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.

Types of Systematic sampling
3. Stratified Random
Sampling
➢ The universe is divided into
L mutually exclusive
Sub-universe called strata
Population Stratified
Random Sample
➢ Independent Simple random samples are
Obtained from each stratum
a
b
c
d

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
42
Girls = 24 (14 ) = 8 girls
42

Stratified Random Sampling
Obtain a sample of 100 students
proportionally representing each level.
Level Number of Enrollees
Freshmen 500
Sophomores 420
Juniors 360
Seniors 300
Total

4. Cluster Sampling
P
Provinc
e
Town
Town
Town
Town
Barang
ay
Barang
ay
Barang
ay
Barang
ay
Barang
ay
Barang
ay

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
geographical basis

❖ Non- Random Sampling
▪ Purposive Sampling
▪ Quota Sampling
▪ Convenience Sampling

Chapter 3. Presentation of Data
 Textual presentation
 Tabular presentation
 Graphical presentation
▪ Statistical Table
Table Number and Heading
Stub Head Master Caption
Column
Caption
Column
Caption
Column
Caption
Column
Caption
Box
Hea
d
Body

Graphical
 Bar Graphs – Vertical Graph
0
1
2
3
4
5
6
Series 1
Series 2
Series 3

Horizontal Bar Graph
0 2 4 6
Category 1
Category 2
Category 3
Category 4
Series 3
Series 2
Series 1

Line graph
0
1
2
3
4
5
6
Category 1 Category 2 Category 3 Category 4
Series 1
Series 2
Series 3

Pie Chart
Sales
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr

Copyright © 2000 by Monica Yuskaitis
Vocabulary Review
• Sum – the answer to an
addition problem.
• Addend – the numbers you
added together to get the
sum.
6 + 9 = 15

Definition
Mean
Means
Average

Definition
• Mean – the average of a
group of numbers.
2, 5, 2, 1, 5
Mean = 3

Mean is found by evening out
the numbers
2, 5, 2, 1, 5

Mean is found by evening out
the numbers
2, 5, 2, 1, 5
mean = 3

How to Find the Mean of a Group of
Numbers
• Step 1 – Add all the numbers.
8, 10, 12, 18, 22, 26
8+10+12+18+22+26 = 96

Numbers
• Step 2 – Divide the sum by
the number of addends.
8, 10, 12, 18, 22, 26
8+10+12+18+22+26 = 96
How many addends are there?

Numbers
• Step 2 – Divide the sum by
the number of addends.
6)96 sum
# of addends
1
6
36
6
6
3

Numbers
The mean or average of these
numbers is 16.
8, 10, 12, 18, 22, 26

What is the mean of these numbers?
7, 10, 16
11

2, 9, 14, 27
13

1, 2, 7, 11, 19
8

26, 33, 41, 52
38

Definition
Median
is in the
Middle

Definition
• Median – the middle number
in a set of ordered numbers.
1, 3, 7, 10, 13
Median = 7

How to Find the Median in a Group of
Numbers
• Step 1 – Arrange the numbers
in order from least to greatest.
21, 18, 24, 19, 27
18, 19, 21, 24, 27

Numbers
• Step 2 – Find the middle
number.
21, 18, 24, 19, 27
18, 19, 21, 24, 27

Numbers
• Step 2 – Find the middle
number.
18, 19, 21, 24, 27
This is your median number.

Numbers
• Step 3 – If there are two middle
numbers, find the mean of these
two numbers.
18, 19, 21, 25, 27, 28

Numbers
• Step 3 – If there are two middle
numbers, find the mean of these
two numbers.
21+ 25 = 46
2)46
23 median

What is the median of these numbers?
16, 10, 7
10
7, 10, 16

29, 8, 4, 11, 19
11
4, 8, 11, 19, 29

31, 7, 2, 12, 14, 19
13
2, 7, 12, 14, 19, 31
12 + 14 = 26 2) 26

53, 5, 81, 67, 25, 78
60
53 + 67 = 120 2) 120
5, 25, 53, 67, 78, 81

Definition
Mode
is the most
Popular

Definition
• A la mode – the most
popular or that which is in
fashion.
Baseball caps are a la mode today.

Definition
• Mode – the number that
appears most frequently in a
set of numbers.
1, 1, 3, 7, 10, 13
Mode = 1

How to Find the Mode in a Group of
Numbers
21, 18, 24, 19, 18
18, 18, 19, 21, 24

How to Find the Mode in a Group of
Numbers
• Step 2 – Find the number that
is repeated the most.
21, 18, 24, 19, 18
18, 18, 19, 21, 24

Which number is the mode?
29, 8, 4, 8, 19
8
4, 8, 8, 19, 29

1, 2, 2, 9, 9, 4, 9, 10
9
1, 2, 2, 4, 9, 9, 9, 10

22, 21, 27, 31, 21, 32
21
21, 21, 22, 27, 31, 32

Definition
Range
is the distance
Between

Definition
• Range – the difference between
the greatest and the least value
in a set of numbers.
1, 1, 3, 7, 10, 13
Range = 12

How to Find the Range in a Group of
Numbers
21, 18, 24, 19, 27
18, 19, 21, 24, 27

Numbers
• Step 2 – Find the lowest and
highest numbers.
21, 18, 24, 19, 27
18, 19, 21, 24, 27

Numbers
• Step 3 – Find the difference
between these 2 numbers.
18, 19, 21, 24, 27
27 – 18 = 9
The range is 9

What is the range?
29, 8, 4, 8, 19
29 – 4 = 25
4, 8, 8, 19, 29

What is the range?
22, 21, 27, 31, 21, 32
32 – 21 = 11
21, 21, 22, 27, 31, 32

What is the range?
31, 8, 3, 11, 19
31 – 3 = 28
3, 8, 11, 19, 31

What is the range?
23, 7, 9, 41, 19
41 – 7 = 34
7, 9, 23, 19, 41

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