Book Report #45: Introductory Statistics Part 1.
Begin: 8/15/2024
Finish: 11/14/2024
Title: Introductory Statistics Part 1,
Author: Barbara Illowsky, Susan Dean
De Anza College
Why I choose to Read this book:
This was the book used for the Merced College Statistics class. I had to learn about statistics to tutor the students with their class assignments, homework and tests. Reading this book has helped me learn new things and challenged my mind. It helped in my analytical and critical thinking skills.
What I learned from this book:
Collecting Data and Sampling:
Statistics deals with the collection, analysis, interpretation and presentation of data. Organizing and summarizing data is called Descriptive Statistics. Two ways to summarize data are by graphing and using numbers. After studying probability an probability distribution, we use formal methods for drawing conclusions. The formal method is called Inferential Statistics. We use statistics probability to determine how confident we are that our conclusion is correct. A statistics is a number that represent a property of a sample. A parameter is a numerical characters of the whole population that can be estimated by a statistics. A variable is a characteristics or measurement that can be determined for each member of a population. Data are the actual values of a variable. Randomness of sample is the key too getting samples. Probability is the likelihood that a specific event will occur.
Descriptive Statistics:
Is the numerical and graphical ways to describe and display your data: Stemlots, histograms, frequency polygons, time series graph, box plots, scatter plots are graphical ways to present the data. It shows the distribution of data.
Probability:
Is a number that gives likelihood that a specific event will occur. Tool to calculate probabilities: Contingency table, Tree Diagram and Venn Diagram. Probability is the workhorse of statistical analysis.
Discrete Random Variables (DRV):
Is outcome of experiment that can be counted. We use several probability distributions for Discrete Random Variables: Binomial, Geometric, Hypergeometric and Poisson Probability Distributions. Probability Distribution Function (PDF) is a mathematical description of a DRV in an equation or a table listing all the possible outcomes of an experiment an the probability associated with each outcome.
Continuous Random Variable (CRV):
CRV changes like weight, batting averages and length of time. The Probability Density Function (PDF) is used to describe probabilities for CRV. The big picture of how to describe a distribution was to describe three things: The shape, the center and the spread. The simplest shape that a distribution can have is a flat line. This distribution is called a Uniform Distribution F(x)=C a constant, other forms of distribution are exponential, Binomial and Poisson distributions. The shape of the Poisson Histogram is skewed right. Specific families of distributions were modeled by formula including: Uniform, Poisson, exponential and Binomial distributions.
The Normal Distribution:
Th most famous shape of Distribution, is the Bell shaped curve which is called the Gaussian or Normal Distribution. No matter what shape of the population data with which we started, the distribution of the sample means will converge to a Normal Curve. Setting the mean=0 and Standard Deviation (SD) =1, gives the standard Normal Curve. The proportion of the population whose values differ the mean value less than 1 times SD is 68%, 2 times SD is 95%. The 3 SD proportion is 99.7%. The number of SD away from the mean is called the Z-score.
The Central limit Theorem (CLT):
The distribution of sample means and sums of each sample will tend to have a normal bell-shaped distribution. CLT is used to find the probability for the mean and of a sum or total. This also applies to percentiles for means and sums.
How will this book contribute to my success upon release:
This Statistics book will allow me to understand Statistics and help tutor students attending Merced College. This book has lots of Mathematical principles that I have learned to improve my analytical and critical thinking skills. This information can be shared with communities which I hope to volunteer my teaching, tutoring and mentoring services.
