Finals Flashcards
The practice or science of collecting and
analyzing numerical data in large quantities,
especially for the purpose of inferring
proportions in a whole from those in a
representative sample
Statistics
The study and manipulation of data,
including ways to gather, review, analyze,
and draw conclusions from data.
Statistics
a branch of mathematics dealing with the
collection, analysis, interpretation, and
presentation of masses of numerical data
Statistics
simply defined as the study and manipulation of data
Statistics
Statistics in Education
❖ Measurement and evaluation are essential
part of teaching learning process
❖ In this process we obtained scores and then
interpret these score in order to take
decisions
❖ Statistics enables us study these scores
objectively
❖ It makes the teaching learning process more
efficient
Roles of Statistics in Education
- It helps the teacher to provide the most
exact type of description
✓ When we want to know the student, we
administer a test or observe the child
✓ Then from the result we describe about the
students performance or trait
✓ Statistics helps the teacher to give an
accurate description of the data.
Roles of Statistics in Education
- It makes the teacher definite and exact in
procedure and thinking.
✓ Sometimes due to lack of technical
knowledge, the teachers become vague in
describing students’ performance
✓ But Statistics enable him/her to describe the
performance by using some language and
symbols which makes interpretation definite
and exact.
Roles of Statistics in Education
- It enables the teacher to summarize the
results in a meaningful and convenient form.
✓ Statistics give order to data
✓ It helps the teacher to make the data precise
and meaningful and to express it in
understandable and interpretable manner
Roles of Statistics in Education
- It enables the teacher to draw general
conclusions.
✓ Statistics help to draw conclusions as well as
extracting conclusions.
✓ Statistical steps help to say about how much
faith should be placed in any conclusion and
about how far we may extend our
generalization
Roles of Statistics in Education
- It helps the teacher to predict the future
performance of the students.
✓ Statistics enables the teacher to predict how
much of a thing will happen under
conditions we know and have measured.
✓ For example the teacher can predict the
probable score of the student in the finale
examination from his entrance test score
Roles of Statistics in Education
- Statistics enables the teacher to analyze some
of the casual factors underlying complex and
otherwise be-wildering(confusing) events;
✓ It is common factor that the behavioral
outcome is a resultant of numerous casual
factors.
✓ The reason why a particular student
performs poor in a particular subject are
varied and many
Roles of Statistics in Education
- Statistics enables the teacher to analyze some
of the casual factors underlying complex and
otherwise be-wildering(confusing) events;
✓ So with the appropriate statistical methods,
we can keep the extraneous variables
constant and can observe the cause of failure
of the pupil in a particular subject.
Values that the variables can assume
Data
Characteristics that is observable or
measurable in every unit of universe
Variable
The set of all possible values of a
variable
Population
A subgroup of a population
Sample
❖ Words or codes that represent a class
or category
❖ Express as a categorical attribute
(gender, religion, marital status,
highest educational attainment)
Qualitative variables
Number that represent an amount or
a count.
Quantitative variables
❖ Numerical data, sizes are meaningful
and answer questions as “how many”
or “how much”
❖ Example are height, weight,
household size, number of registered
cars
Quantitative variables
Data that can be counted (number of
days, number of siblings, usual
number of text messages sent in day)
Discrete variables
It can assume all values between any
two specific values like 0.5, 1.2 etc
and data can be measured (weight,
height, body temperature
Continuous variables
Data created by assigning observations into
various independent categories and then
counting the frequency of occurrence within
each of the categories.
Nominal
This is the most primitive level of measurement.
Nominal
It is used when we want to distinguish one
object from another for identification
purposes.
Nominal
In this level, we can say that one object is
different from another, but the amount of
difference between them cannot be
determined
We cannot tell that one is better or worse
than the other.
❖ Gender, Nationality, and civil status are
nominal scale.
Nominal
A scale in which scores indicate only relative amounts or rank order
In this level, data are arranged in some specified order or rank
Ordinal
When objects are measured in this level, we can say that one is better or greater than the other. But we cannot tell how much more or how much less of the characteristics one object has than the other.
The ranking of contestants in a beauty contest, of
siblings in the family, or of honor students in the
class are of ordinal scale.
Ordinal
A scale in which equal differences in scores represent
equal differences in amount of the property
measured, but with an arbitrary zero point.
Interval
If the data are measured in this level, we can
say not only one object is greater or less than another,
but we can also specify the amount of difference.
Interval
Interval
The scores in an examination are of the interval scale
of measurement.
❖ To illustrate, suppose Maria got 50 in Math
examination while Martha got 40. We can say that
Maria got higher than Martha by 10 points.
All the properties of an interval scale with the
additional property of zero indicating a total
absence being measured
Ratio Scale
It is like the
interval level. The only difference is that this
level always starts from an absolute or true zero
point.
Ratio Scale
If the data are measured in this level, we can say
that one object is so many times as large or small
as the other.
Ratio Scale
Example of Ratio Scale
For example, suppose Mrs. Reyes weighs 50 kg, while
her daughter weighs 25 kg. We can say that Mrs.
Reyes is twice as heavy as her daughter . Thus, weight
is an example of data measured in the ratio scale.
A single value that attempts to describe a set of data by identifying the central position within that set of data
Measures of central tendency
measures of central tendency are sometimes called
measures of central location
Measures of central tendency
They are also classed as summary statistics.
The mean (often called the average) is most
likely the measure of central tendency that you
are most familiar with, but there are others,
such as the median and the mode
most commonly used measure
of central position
Mean
It is the sum of measures divided by the
number of measures in a variable.
Mean
It is also used to describe a set of data
where measures cluster or concentrate at a
point
Mean
Occasionally, we want to find the mean of a set
of values wherein each value or measurement
has a different weight or degree of importance.
Weighted mean
the middle entry or term in a
set of data arranged in either increasing or
decreasing order.
Median
It is a positional measure. Thus,
the values of the individual measures in as
set of data do not affect. It is affected by the
number of measures and not by the size of
the extreme values.
Median
❖ It is the measure or value which occurs most
frequently in a set of data.
❖ It is the value with the greatest frequency.
Mode
a continuous probability distribution that is
symmetrical on both sides of the mean, so the
right side of the center is a mirror image of
the left side.
Norman Distribution Curve
The normal distribution is often called the
______ because the graph of its probability
density looks like a ___.
bell curve
Also called spread or dispersion refers to
how spread out a set of data is.
Variability
It gives you a way to describe how
much data sets vary and allows you to use
statistics to compare your data to other
sets of data.
Variability
The four main ways to
describe variability in a data set
range
interquartile range
variance
standard deviation
The difference between the highest and
lowest value in a set.
Range
Quartiles segment any distribution that’s
ordered from low to high into four equal
parts.
Interquartile range
A measure of dispersion, meaning it is a
measure of how far a set of numbers is
spread out from their average value.
Variance
A measure of the amount of variation or
dispersion of a set of values.
Standard deviation
It is the square root of the variance
determined by
the number of peaks it contains. Most
distributions have only one peak but it is
possible that you encounter distributions
with two or more peaks.
Modality
It is a measure of the symmetry of
a distribution. The highest point of a
distribution is its mode. The mode marks
the response value on the x-axis that occurs
with the highest probability.
Skewness
A distribution
is skewed if the tail on one side of the mode
is fatter or longer than on the other: it is
______
asymmetrical
Statistical measure that defines how heavily
the tails of a distribution differ from the tails
of a normal distribution.
Kurtosis
This identifies whether the tails of a
given distribution contain extreme values
Kurtosis
