5. QUARTILE DEVIATION
Sometimes called semi-quartile range; is the spread of middle
50% of the scores around the median. Extreme scores will not
affect the quartile deviation.
Characteristics
1. Uses the 75th and 25th percentiles; difference between these
two percentiles is referred to as the interquartile range.
2. Indicates the amount that needs to be added to, and subtracted
from, the median to include the middle 50% of the scores.
3. Usually not used in additional statistical calculations.
6. QUARTILE DEVIATION
Symbols
Q = quartile deviation
Q1 = 25th percentile or first quartile
(P25) = score in which 25% of scores are below and 75% of scores
are above
Q3 = 75th percentile or third quartile
(P75) = score in which 75% of scores are below and 25% of scores
are above
7. STEPS FOR CALCULATION OF Q3
1. Arrange scores in ascending order.
2. Multiply N by .75 to find 75% of the
distribution.
3. Count up from the bottom score to the number
determined in step 2. Approximation and
interpolation may be required.
8. STEPS FOR CALCULATION OF Q1
1. Multiply N by .25 to find 25% of the distribution.
2. Count up from the bottom score to the number
determined in step 1.
To Calculate Q
Substitute values in formula: Q = Q3 - Q1
9. QUARTILE DEVIATION
Q1 = 25%
Q2 = 50%
Q3 = 75%
Q4 = 100%
Q2 - Q1 = range of scores below median
Q3 - Q2 = range of scores above median
10. PERCENTILES AND PERCENTILE RANKS
Percentile - a point in a distribution of scores below
which a given percentage of scores fall.
Examples: 60th percentile and 40th percentile
Percentile rank - percentage of the total scores that
fall below a given score in a distribution; determined
by beginning with the raw scores and calculating the
percentile ranks for the scores.
11. WEAKNESS OF PERCENTILES
1. The relative distance between percentile scores are the same, but
the relative distances between the observed scores are not.
2. Since percentile scores are based on the number of scores in a
distribution rather than the size of the score obtained, it is
sometimes more difficult to increase a percentile score at the ends
of the scale than in in the middle.
3. Average performers (in middle of distribution) need only a small
change in their raw scores to produce a large change in their
percentile scores.
4. Below average and above average performers (at ends of
distribution) need a large change in their raw scores to produce
even a small change in their percentile scores.
13. PROBLEM:
Mrs. Dela Cruz wants to get the analysis
on her pre-test in Statistics and
probability of grade 11 students in ABC
high school with 150 students in the
subject. Should she get the scores of one
class only?
14. RANDOM SAMPLING
Population
the whole group under study or investigation
Sample
subset taken from a population, either by random
sampling or by non-random sampling
a representation of the population where it is
hoped that valid conclusions will be drawn from
the population
15.
16. RANDOM SAMPLING
• a selection of n elements derived from the N
population, which is the subject of an
investigation or experiment, where each point of
the sample has an equal chance of being selected
using the appropriate sampling technique
18. TYPES OF RANDOM SAMPLING TECHNIQUES
1. LOTTERY SAMPLING - a sampling technique in
which each member of the population has an equal
chance of being selected
Example:
Members of the population have their names represented
by small pieces of paper that are then randomly mixed
together and picked out. In the sample, the members
selected will be included.
19. TYPES OF RANDOM SAMPLING TECHNIQUES
2. SYSTEMATIC SAMPLING - a sampling technique in
which members of the population are listed and samples are
selected at intervals called sample intervals
- every nth item in the list will be selected from a
randomly selected starting point.
Example: If we want to draw a 200 sample from a population
of 6,000, we can select every 3rd person in the list. In
practice, the numbers between 1 and 30 will be chosen
randomly to act as the starting point.
20. TYPES OF RANDOM SAMPLING TECHNIQUES
3. STRATIFIED RANDOM SAMPLING - a sampling
procedure in which members of the population are grouped on the
basis of their homogeneity
- used when there are a number of distinct subgroups in the
population within which full representation is required
- the sample is constructed by classifying the population
into subpopulations or strata on the basis of certain characteristics
of the population, such as age, gender or socio-economic status.
- the selection of elements is then done separately from
within each stratum, usually by random or systematic sampling
methods.
21. STRATIFIED RANDOM SAMPLING
Example:
Using stratified random sampling, select a sample of 400
students from the population which are grouped according to
the cities they come from. The table shows the number of
students per city.
City Population
A 12,000
B 10,000
C 4,000
D 2,000
22. STRATIFIED RANDOM SAMPLING
Solution:
To determine the number of students to be taken as sample from each
city, we divide the number of students per city by total population (N=
28,000) multiply the result by the total sample size (n= 400).
City Population Sample (n)
A 12,000
12,000
28,000
400 = 171
B 10,000
10,000
28,000
400 = 143
C 4,000
4,000
28,000
400 = 57
D 2,000
2,000
28,000
400 = 29
23. TYPES OF RANDOM SAMPLING TECHNIQUES
4. CLUSTER SAMPLING - sometimes referred to as
area sampling and applied on a geographical basis
- first sampling is performed at higher levels before going
down to lower levels
Example: Samples are taken randomly from the provinces
first, followed by cities, municipalities or barangays, and
then from households.
24. TYPES OF RANDOM SAMPLING TECHNIQUES
5. MULTI-STAGE SAMPLING uses a combination of
different sampling techniques
Example: When selecting respondents for a national
election survey, we can use the lottery method first for
regions and cities. We can then use stratified sampling to
determine the number of respondents from selected areas
and clusters.
25. Directions: Identify the terms being described and write your answer on a
separate sheet of paper.
1. It refers to the entire group that is under study or investigation.
2. It is a subset taken from a population, either by random or non-random
sampling technique. A sample is a representation of the population where
one hopes to draw valid conclusions from about population.
3. This is a selection of n elements derived from a population N, which is
the subject of the investigation or experiment, where each sample point
has an equal chance of being selected using the appropriate sampling
technique.
4. A sampling technique where every member of the population has an
equal chance of being selected.
5. It refers to a sampling technique in which members of the population are
listed and samples are selected in intervals called sample intervals.
26. Directions: Identify the type of sampling method.
1. The teacher writes all the names of students in a piece of
paper and puts it in a box for the graded recitation.
2. The teacher gets the class record and calls every 4th
name in the list.
3. Every five files out of 500 files will be chosen.
4. There are 20 toddlers, 40 teenagers, 45 middle aged and
55 senior citizens in a certain area. Samples are taken
according to the total number of people in the area.
5. All the names of the employees of the company are put
in a raffle box.
27. EXERCISE
Directions: Get the samples needed for each
category using stratified random sampling.
There are 20 members of taekwondo club, 40 math
club members, 60 drama theatre members, and 30
members of science club. The researchers want to
get 20 respondents out of these organizations.
Identify the samples to be taken in each
organization.
29. Directions: Study the cases below. Identify which
of the cases involves measures from a population
and a sample.
1.A researcher randomly selected a sample of 1000
people in Barangay, 143 and asked if they used a
certain coffee product and 40% of them said yes.
2.A researcher interviewed all the students in a
certain school to identify their insights about their
favorite shoe brand.
30. PARAMETER
- a descriptive population measure
- a measure of the characteristics of the
entire population (a mass of all the units
under consideration that share common
characteristics) based on all the elements
within that population.
31. Example:
1. All people living in one city, all-male
teenagers worldwide, all elements in a
shopping cart, and all students in a
classroom.
2. The researcher interviewed all the students of
a school for their favorite apparel brand.
32. STATISTIC
- the number that describes the sample
- can be calculated and observed directly
- a characteristic of a population or sample group
NOTE: You will get the sample statistic when you
collect the sample and calculate the standard
deviation and the mean. You can use sample statistic
to draw certain conclusions about the entire
population.
33. Example:
1.Fifty percent of people living in the U.S. agree
with the latest health care proposal.
Researchers can’t ask hundreds of millions of
people if they agree, so they take samples or
part of the population and calculate the rest.
2.Researcher interviewed the 70% of covid-19
survivors.
34. Directions: Decide whether the statement describes a
parameter or statistic. Write your answer on a separate
sheet of paper.
1. The average income of 40 out of 100 households in a
certain Barangay is P 12, 213.00 a month.
2. Percentage of red cars in the Philippines.
3. Number of senior high schools in Region 3.
4. A recent survey of a sample of 250 high school students
reported the average weight of 54.3 kg.
5. Average age of students in East High School.
