Everywhere you go, everything you see, statistics is all around. I for one, did not realize how important and relevant statistics was in our everyday lives until taking this course. Everything is run by statistics; the kind of coffee available in Dunkin’ Donuts, the flavors of ice cream at Dairy Queen, and even the clothes we buy in stores. Statistics evaluates what works in our growing and complex society nowadays. All of these selections would not be available to us without the statistical backing that they will sell and that people enjoy them. I actually play video games competitively and travel to competitions to win money. I pick and choose my teammates almost solely based on the statistics that are on the leaderboards. If they have a combination of a high-win loss ratio, high accuracy, and a high points per-match; then they must be a good addition to the team. Of course there are other factors such as communication and team chemistry, but these can be improved and worked on over time. Statistics is also evident in school. When reflecting upon my passed academic endeavors, I’ve realized that everything is also based on statistics. Grade point average almost always determines what other colleges you can gain admittance to, as well as earning scholarships and awards. Also statisticaly evaluated at times is SAT scores. Through statistics students are placed in different group levels by their individual grades. Even in sports statistics can be found. Baseball batters are evaluated based on their batting averages. There is even a slugging average which is different than batting average and determines how often they achieve extra-base hits. In my major, statistics is also very important. I am a Psychology Major and in this area of studies, I will be dealing with a ton of studies which are all about statistical calculations and experiments. In this field they used Simple Random Sampling, probability sampling and convenience sampling. An...

...techniques.
Firstly we look at data analysis. This approach starts with data that are manipulated or processed
into information that is valuable to decision making. The processing and manipulation of raw
data into meaningful information are the heart of data analysis. Data analysis includes data
description, data inference, the search for relationships in data and dealing with uncertainty
which in turn includes measuring uncertainty and modelling uncertainty explicitly.
In addition to data analysis, other decision making techniques are discussed. These techniques
include decision analysis, project scheduling and network models.
Chapter 1 illustrates a number of ways to summarise the information in data sets, also known as
descriptive statistics. It includes graphical and tabular summaries, as well as summary measures
such as means, medians and standard deviations.
Uncertainty is a key aspect of most business problems. To deal with uncertainty, we need a basic
understanding of probability. Chapter 2 covers basic rules of probability and in Chapter 3 we
discuss the important concept of probability distributions in some generality.
In Chapter 4 we discuss statistical inference (estimation), where the basic problem is to estimate
one or more characteristics of a population. Since it is too expensive to obtain the population
information, we instead select a sample from the population and then use the information in the
sample to infer the...

...Trajico, Maria Liticia D.
BSEd III-A2
REFLECTION
The first thing that puffs in my mind when I heard the word STATISTIC is that it was a very hard subject because it is another branch of mathematics that will make my head or brain bleed of thinking of how I will handle it. I have learned that statistic is a branch of mathematics concerned with the study of information that is expressed in numbers, for example information about the number of times something happens. As I examined on what the statement says, the phrase “number of times something happens” really caught my attention because my subconscious says “here we go again the non-stop solving, analyzing of problems” and I was right. This course of basic statistic has provided me with the analytical skills to crunch numerical data and to make inference from it. At first I thought that I will be alright all along with this subject but it seems that just some part of it maybe it is because I don’t pay much of my attention to it but I have learned many things. I have learned my lesson.
During our every session in this subject before having our midterm examination I really had hard and bad times in coping up with this subject. When we have our very first quiz I thought that I would fail it but it did not happen but after that, my next quizzes I have taken I failed. I was always feeling down when in every quiz I failed because even though I don’t like this...

...Worksheet 1 - Basic Concepts
1. What is Inferential statistics?
Inferential statistics uses observations of past occurrences or available data i.e. descriptive statistics to make decisions about future possibilities and/or the nature of the entire body of data. Inferential statistics draws conclusions or makes interpretations, predictions and inferences about a population based upon an analysis of a sample.
2. Give 2 different techniques which are used in descriptive statistics to represent the data.
Tables or graphs (histograms, boxplots, etc) or numerical summaries
3. Define each of the following terms:
a) Variable
The topics/issues under investigation in statistical analysis. The variable is a characteristic or property of the members of the population which may vary e.g. height, weight, perception etc.
b) Population
The total group about which information is being sought. If information is sought about voting intentions, the population is all those people eligible to vote in an electorate, or a state or the nation.
c) Sample
A sample is a group taken from the population. Most statistical situations do not allow an entire population to be used for analysis (usually because it is too large, the geographical dispersion of subjects, logistical issues, funding, time restraints etc) so a sample must be used. The sample chosen should be representative of and reflect all of the...

...typically have? You take a random sample of 51 reduced-fat cookies and test them in a lab, finding a mean fat content of 4.2 grams. You calculate a 95% confidence interval and find that the margin of error is ±0.8 grams. A) You are 95% confident that the mean fat in reduced fat cookies is between 3.4 and 5 grams of fat. B) We are 95% confident that the mean fat in all cookies is between 3.4 and 5 grams. C) We are 95% sure that the average amount of fat in the cookies in this study was between 3.4 and 5 grams. D) 95% of reduced fat cookies have between 3.4 and 5 grams of fat. E) 95% of the cookies in the sample had between 3.4 and 5 grams of fat. Determine the margin of error in estimating the population parameter. 12) How tall is your average statistics classmate? To determine this, you measure the height of a random sample of 15 of your 100 fellow students, finding a 95% confidence interval for the mean height of 67.25 to 69.75 inches. A) 1.5 inches B) 0.25 inches C) 1.06 inches D) 1.25 inches E) Not enough information is given. 12) 11) 10)
3
Construct the indicated confidence interval for the difference between the two population means. Assume that the assumptions and conditions for inference have been met. 13) The table below gives information concerning the gasoline mileage for random samples of trucks of two different types. Find a 95% confidence interval for the difference in the means m X - m Y. Brand X Brand Y 50 50 20.1 24.3 2.3 1.8 13)...

...Lecture Notes on Introductory Statistics, I
(P.P. Leung)
Lecture notes are based on the following textbook:
N.A. Weiss (2012), Introductory Statistics, 9th edition, Pearson.
Chapter 1 The Nature of Statistics 統計本質
§1.1 Two kinds of Statistics
§1.4 Other Sampling Designs (其他抽樣方法)
Chapter 1 The Nature of Statistics 統計本質
What is Statistics? 何謂統計?
From Wikipedia, the free encyclopaedia:
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the natural and social sciences to the humanities. Statistics is also used for making informed decisions in government and business.
Statistical methods can be used to summarize or describe a collection of data; this is called descriptive statistics. In addition, patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and then used to draw inferences about the process or population being studied; this is called inferential statistics. Both descriptive and inferential statistics comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject....

...of 1000 flights and proportions of three routes in the sample. He divides them into different sub-groups such as satisfaction, refreshments and departure time and then selects proportionally to highlight specific subgroup within the population. The reasons why Mr Kwok used this sampling method are that the cost per observation in the survey may be reduced and it also enables to increase the accuracy at a given cost.
TABLE 1: Data Summaries of Three Routes
Route 1
Route 2
Route 3
Normal(88.532,5.07943)
Normal(97.1033,5.04488)
Normal(107.15,5.15367)
Summary Statistics
Mean
88.532
Std Dev
5.0794269
Std Err Mean
0.2271589
Upper 95% Mean
88.978306
Lower 95% Mean
88.085694
N
500
Sum
44266
Summary Statistics
Mean
97.103333
Std Dev
5.0448811
Std Err Mean
0.2912663
Upper 95% Mean
97.676525
Lower 95% Mean
96.530142
N
300
Sum
29131
Summary Statistics
Mean
107.15
Std Dev
5.1536687
Std Err Mean
0.3644194
Upper 95% Mean
107.86862
Lower 95% Mean
106.43138
N
200
Sum
21430
From the table above, the total number of passengers for route 1 is 44,266, route 2 is 29,131 and route 3 is 21,430 and the total numbers of passengers for 3 routes are 94,827.
Although route 1 has the highest number of passengers and flights but it has the lowest means of passengers among the 3 routes. From...

...compliments the regular mathematics and therefore both are tested in primary schools. Mathematics is the written application of operation. It teaches students to think clearly, reason well and strategize effectively. Mental Mathematics is the ability to utilise mathematical skills to solve problems mentally. The marks scored by pupils generate statistics which are used by teachers to analyse a student’s performance and development of theories to explain the differences in performance.
The Standard 3 class is where the transition from junior to senior level occurs where teachers expect the transference of concrete to abstract thinking would have occurred.
A common theory by many primary school teachers is ‘Students perform better in Mathematics than Mental math. Mental math is something that has to be developed and involves critical thinking. Mental math requires quick thinking and the student must solve the problem in their minds whereas in regular mathematics, the problem can be solved visually. Therefore, teachers should take these factors into consideration while testing and marking students in these areas.’
In this study, the statistics of 30 students of a standard 3 class of San Fernando Boys’ Government School will be analysed to determine the truth of this theory.
DATA COLLECTION METHODS
Mathematics and mental mathematics marks of term 1 of the class of 2013 were obtained from a Standard 3 teacher of San Fernando Boys’...

...central tendency of the sample.
6. Measures of dispersion: range, the interquartile range, the variance, and the standard deviation. What do these measures tell you about the “spread” of the data? Why is it important to spend time performing basic descriptive statistics prior to conducting inferential statistical tests?
Variance of a sample = S2 = =
Standard Deviation of sample S=
Range is the difference between the highest and the lowest values (250-100) = 150
Interquartile Range takes into consideration the fact that there are data extremes that affect the range. In the case of the data above, most of the values are around the median but two values (250 and 275) are extremes. In this scenario, Interquartile range is a better indication of the dispersion of the distribution
100 100 103 104 105 Q1 107 110 110 114 115 M 115 115 115 115 117 Q2 117 118 120 250 275
• Q1 = (105+107)/2 = 106
• Q2 = (117+117)/2 = 117
• IR = 117-106 =9
It is important to evaluate data and look at the entire picture to determine whether something fits or does not. The fact that we get two measurements that were extreme might be an indication that something may have gone wrong. Descriptive statistics in such a case becomes instrumental in our analysis
Type I and Type II Error: The concept of Type I and Type II Error is critical and will come into play with each statistical test you perform. Discuss the implications of...

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