Ed 216 E-Portfolio of Delos Reyes: 2011

Martes, Mayo 17, 2011

We are MSU-Graduate Students. This blog site is designed as a partial requirement in EDUC 216( Applied Statistics in Education).With this blog, the author is aspiring for strategies and methods which are useful to develop her potentials for the 21st century skills which are blended with higher order thinking skills, multiple intelligences, ICT and multimedia.

Introduction

Every single one of us has the process of greatness because greatness is determined by service to yourself and to others . By- Oprah Winfry.

Everyday of my life I am trying to do good as many as I could. I always ask God's blessing and love to do this. How frequently I did those things were unrecorded, as long as I doing. Tallying is not required to do something good, but the important is I am learning. For one a half decade,forgot the role of being student, but I never cease learning. I am updating myself through seminars, which sponsored by the DepEd and other private institutions.

As teacher to student to students in school and also teacher two my four children , I see to it that before the end of the day. I did something which is best for my students and that is learning.

Charles M Schab one of the philosophers said: " The man who has done his best has done something. The man who who has done less than his best has done nothing."

I. TABLE OF CONTENTS OF MY PORTFOLIO IN EDUC 216

Chapter 1 Introduction to Statistics

Chapter 2 Variables : The Subject Matter for Statistics & Research

Chapter 3 Measures of Central Location

Chapter 4 Measures of Variation

Chapter 5 Simple Correlation

Chapter 6 Simple Regression

Chapter 7 The Normal Probability Distribution

Chapter 8 Statistical Estimation & Sampling Theory

Chapter 9 Statistical Inference

Chapter10 Z-Test of One Sample Means

Chapter11 T-Test of Significance

Chapter12 ANOVA

Chapter13 Factorial ANOVA

Chapter14 The Chi-Square Test

Chapter15 Computer Statitical Applications using MS Excel

II. SAMPLES OF E-PORTFOLIO

1. Powerpoint Presentations

2. Video for Demo Teaching

3. Resources / Links

4. Multimedia

5. Games

Measures of Central Tendency

Measure of central tendency or location is single v value about which the set of

observations tend to cluster. It is also called the average.

The Arithmetic Mean or simply the mean, denoted by X, is the sum of all the

observations divided by the total number of all observations divided by the total number

of observations. In the symbols, if we let X_i = the value of the i^th observation and n =

number of observation, then the mean is given by

X = ƩX

For grouped data,

X = ƩfX_i_where:X_i is the Midpoint

N f is the frequency

Another formula in computing the grouped mean of a frequency distribution is by coding.

X = Midpt + C ( Ʃfd)

Here, Midpoint is an assumed mean, which is chosen from the class marks, C is the class size or the class interval and d is the deviation of the i^th from X computed as

d = X_i -X_O_where; X_o is the Mdpt

Properties of Mean

The mean of the deviations of the observations from the mean is always equal to zero. Ʃ(X_i – X)
the sum of the squared deviations of the observations from the mean is smallest,

Ʃ(Xi – X)² = minimum

The mean reflects the magnitude of every observation, since every observation contributes to the value of the mean.

It is easily affected by the presence of extreme values, and hence not a good measure of central tendency when extremes observations do occur.

Means of subgroups maybe combined when properly weighted. Combined mean is called the weighted arithmetic mean.

The Median

The median, denoted by M_d, is a single value that divides an array of observations into two equal parts, such that, fifty percent of the observations fall below it and fifty percent fall above it. The formula given below:

For ungrouped data:

M_d = X_{( N+1)} if N is odd.

₂

M_d = X_nif N is even

₂

For grouped data:

M_d = L_md + c ( N/2 – F_b)

f_md

where:

L_md = lower True class boundary (TCB) of the median class, where the median class is a class whose less than Cumulative Frequency ( <CF) is greater than or equal to ½ of N.

C = class size

F_b = “less than” cumulative frequency of the class immediately preceding the median calss

F_md = frequency of the median class

Properties of the Median

It is positional value and hence is not affected by the presence of the extreme values unlike the mean.
The sum of the absolute deviations from a point, say a, is smallest when a is equal to the median,

Ʃ/ X_i – M_d/ is minimum

For group data, the equivalent expression is

Ʃ f_i/X_i – M_dg/ is minimum

The median is not suitable further computations and hence median of subgroups cannot be combined in the same manner as the mean.
The median data can, the mode is calculated even with open-ended intervals provide the median class in no open- ended.

The Mode

The mode, denoted by M_o, is the value that occurs most frequently in the given data set. For grouped data, the mode is calculated using the formula:

f_mo– f_b

M_o = L_MO + c 2f_mo – f_b - f_a

Where:

L_mo = Lower TCB of the model class, where the modal class is the class with the highest frequency

c = class size

f_mo = frequency of modal class

f_b = frequency of the class immediately preceding the modal class

f_a = frequency of the class immediately following the modal class

Properties of the Mode

The mode is determined by the frequency and not by the values of the observations.
It cannot be manipulated algebraically and hence modes of subgroups cannot be combined.
The mode can be defined with qualitative and quantitative variables.
The mode is very much affected by the method of grouping data.
It cannot be computed with open-ended intervals provided the modal class is not open-ended.

Example: Solve the mean of the ungrouped Data.

Scores of 10 students of a 50-item test in English 1

X= 19, 15, 20, 31, 42, 31, 36, 18, 28,46

Solve mean ( X )

X = ƩX/N

= 286/10

= 28.6

Solve the Median (Md) Md = 10 +1 Md =5.5^th

If N is even 2 5.5^th of X

Md = N+1

Arrange the score from the lowest to highest or from the highest to the lowest.

X = 15, 18. 19, 20, 28, 31, 31, 36, 42, 46

Here N is even.

Md is the half way between 28 and 31. Add these two scores, the divide by two.

Md = 28 + 31

= 59/2

= 29.5

If N is odd.

Example:

X = 23, 28, 35, 38, 41, 46, 50

Determine the halfway.

Md = N + 1

2 So, 4^th score from left to the right or from the right to the left is 38.

= 7+1 Therefore the is Md = 38.

= 8/2

= 4^th score

Solve the mode.

Determine the mode of 10 students’ score in a 50-item test in English 1.

Arrange the scores from the lowest to the highest.

X = 15, 18, 19, 20, 28, 31, 31, 36, 42, 46

Look for a score that appeared most.

Answer: Mo = 31 Since 31 occurred twice

Solve Mean, Median, Mode for grouped data

Example:

A frequency distribution of 65 students’ score in 100-item test in Mathematics 1.

Class interval	Mdpt(X)	f	fx	c	cf
82-86	84	2	168	6	12
77-81	79	4	316	5	20
72-76	74	1	74	4	4
67-71	69	0	0	3	0
62-66	64	11	704	2	22
56-61	59	8	472	1	8
52-56	54	15	810	0	0
47-51	49	10	490	-1	-10
42-46	44	4	176	-2	-8
37-41	39	6	234	-3	-18
32-36	34	4	136	-4	-16
Total		65	3580	11	14

X = Mdpt + c (Ʃfd/N) Md = LL + c(N/2 –Ʃcf<) Mo = LL+c/2 (f_1-f₂)

= 54 + 5 (11/65) fc 2f_o-f₂-f₁

= 54.85 = 52 + 5(65/2 – 24) = 52+5/2(8-10)

15 2(15-10-8)

= 52 + 5(32.5 – 24) = 52+2.5(-2)

15 -6

= 52 + 5 (8.5) = 52.5+ 0.83

15 = 53.33

= 52 + 2.83

= 54.83

Measures of Variability

MEASURES OF VARIABILITY:
The presentation on this topic using the power point is very good.
Variability, the reporter emphasized that it is a spread out of the data. How tied up the distribution.
The reporter started with his report by reviewing the Mean.
Absolute Variability
a.Absolute Range= highest score-lowest scoere
b. Total Range= highest score-lowest score. Then the result will be added by one.
c. Kelly Range= P90-P10
It is good here if the data given is arranged from the highest to the lowest.
Quartile Deviation is applied when N is less than 30. QD= Q3-Q1/2.
Quartile Deviation is getting the middlemost score. Quart means 4.
Q3=3n/4
Q1=N/4
Quartile Deviation from the group data. This is applicable if N is 30 or more. Here solve first the Q3.
Formula:
Q= L+C(3N/4-summation of cF<)
__________________________
(CF)
I was not able to cope with the explaination of the following:
1. Average deviation
2. Variance
3.Correction
4.Variance from group data
5.Class deviation
6. others
I was confused in the above mentioned topic, maybe because of the different formula. So tomorrow I will bring this to the attention of the reporter to review first before proceeding to the next topics.
"Wise man talk because they have something to say. Fools man talk because they have to say something." By Plato.

Simple Regression

Simple Linear Regression

Welcome May 2, 2011. It’s Monday.

Today, I am taking notes from our reporter. Last week, my classmates requested me to compute the data manually. OK, you are my boss as said by PNOY. Their request was granted.

I am hesitant to do this because the approach I am going to do this in a traditional way. But I have my computer to show it’s correct. We enjoyed the moment for everybody was busy solving on their sits and to the board. This is what we call “hands on process”. We just follow the formula given. We completed first each column only to those are needed in the formula.

At about 9:30 in the morning, my report was finished. Then after that, we enjoyed sharing our experience and eat together our snacks, which I prepared. Most of them said, “thank you” because according to them, they clearly understand my topic.

Before I end my reaction for today, please allow me to write the formula below. For the least squares Linear Regression Equation.

y= a + bx

Where:

b= Ʃ (x – x) (y – y)

Ʃ ( x – x)²

a= y – b x

The standard Error of Estimate

S_e = Ʃ (y – y )²

N - 2

S_e= ƩY₁² – a Y_{1 –}b (Y_{1 –}Y₁)

N - 2

The Normal Probability Distribution

May 4, 2011

By: Ma’am Clarence

May 4, 2011, 8:00-10:00 in the morning, it’s Statistics time. If our teacher is beautiful, our reporter is also beautiful.

The reporter introduces first the five (5) standard scores. The formula is

Z= x – x

Where:

Z= Standard Score

X= Any row score or unit of measurement

X= Mean of the Distribution of scores

S= Standard Deviation

Second, she now discussed the Normal Curve and Characteristics of the Normal Distribution, the formula can be seen on page 80 of the reference book.

She emphasizes the percentage of distribution in the curve from midpoint to

-1

= .3435 the same value to + 1

Calexton and I asked the reporter on how about if the curve is between two + 1

and +2. What is the percentage of distribution? The reporter was not able to show the table.

Wow! It’s very advantage because Richard Agapay is with us. He can easily search through internet. The contribution I made is that I found the table at the last part of my book.

Through the session, it ended with a little knowledge regarding to the topic. I promised to myself that I will study more at home.

Thank you ma’am Clarence for a delicious snacks.

Statistical Estimation of Sampling Theory

Statistical Estimation of sampling Theory

Today is Wednesday, May 4, 2011.

Please welcome our reporter Ma’am M. Pilapil. She will be discussing with us the Sample Distribution.

For sampling distribution we can compute a mean, variance, standard deviation is called the standard error.

Any quantity obtained for a sample for the purpose of estimating a population parameter is called a SAMPLE STATISTICS OR STATISTICS.

Kinds of sampling

Sample Random Sample- N elements is selected from a population of N elements using a sampling plan which each of the possible samples has the same chance of selection.
Stratified Random Sampling- when the population of interest consists that each subpopulations, or strata, a sampling plan that ensures that each population sample is represented by each sample.
A Cluster Sample is a simple random sample of clusters from the available cluster in the population
The kth systematic random sample involves the random selection of one of the first k elements in an ordered population and then systematic selection of every kth element.

Examples:

Assume that the weights of 3000 female students of UST are normally distributed with mean 45 kg and standard deviation of 2kg. If 80 samples consisting of 25 students each are obtained, what would be the expected mean and standard deviation of the resulting sampling distribution of means if sampling were done a) with replacement, b) without replacement?

Solution:

a) with replacement

and

b) without replacement

and

In how many example of example1 would you expect to find the mean between:

a) 44.7 and 46.1?

b) Less than 46 kg?

44.7 - 45

a. 44.7 kg in standard units =-----------------

0.4

= -0.75

46.1 - 45

46.1 in standard units =----------------------

0.4

= 2.75

Proportion of samples with mean between44.7 and46.1

=( area under the normal curve between z = - 0.75 and the z= 2.75)

=0.2734 + 0.4970 = 0.7704

Then the expected number of samples= (80)(0.7704) or 62

46-45

b) 46 kg in standard units ---------------- =2.5

0.4

Proportion of samples with means less than 46 kg

=(area under the normal curve less than z=2.5)

= 0.5 + 0.4938 = 0.9938

Then the expected number of samples = (980)(0.9938) 0r 80.

Statistical Inference

9. STATISTICAL INFERENCE

Today is May 6, 2011 (Friday). Without much a do please welcome our reporter Ma’am Agustin.

Our session started with prayer.

Ready begin…

An estimate of a population parameter given by a single number is called a point of estimate of the parameter. An estimate of populations parameter may be considered to lie is called interval estimate of the parameter.

CONFIDENCE INTERVALS FOR MEANS

The percentage confidence is often called the confidence level. The numbers in the confidence limits is called confidence or coefficients critical values and are denoted by z.