研究 Data Science

• 18:10-21:00 
• 發現 Udacity 的課程中的大多是應用，基礎理論太少。
• Applied Statistics for The Behavioral Sciences 在基礎理論上著墨較為仔細。
• 研讀進度：Chapter 5 Correlation: A Measure of Relationship
• The Meaning of Correlation and the Correlation Coefficient
• Scatterplots and Correaltion
• Correlation Coefficients
• Computing the Pearson 
• Deviation Score Formula

繼續研讀 Applied Statistics for The Behavioral Sciences

•  10:30-15:00 
• 複習第4章 1) Determining Proportions 已知兩個分數，或兩個百分位，求中間分數所佔百分比, 2) Determining Percentiles 已知百分位，求對應的分數, 3) Determining Percentile Ranks 已知分數，求對應的百分位。
• 繼續第4章作業，完成第2-3題。
• 2. Assume that a set of 200 scores is normally distributed with a mean of 60 and a standard deviation of 12.
• a. What are the z scores corresponding to the raw scores of 76, 38, and 50?
• b. How many scores lie between the value of 48 and 80? 65 and 75? 34 and 52?
• c. How many scores exceed the values of 80, 60, and 40?
• d. How many scores are less than the values of 35, 50, and 75?
• e. Find P35, P80, PR55, and PR70.
• 3. The norms for a standardized mathematics test, assumed to be normally distributed, are as follows:
• National norms: mean=75, standard deviation=12
• Large-city: mean=68, standard deviation=15
• John has a score of 80, and Mary has a score of 65. What are their percentile ranks in terms of the national norms? in terms of the large-city norms?
• Table C.1 Areas under Standard Normal Curve for Values of z. 
• z Standard score
• Area between mean and z, 
• Area beyond z, 
• Ordinate
• Table C.2 Standard Scores (or Deviates) Corresponding to Divisions of the Area under the Normal Curve into a Larger Proportion (B)
• B, The larger area
• z, Standard score
• 解 2a
• 
• 
• 

繼續研讀 Applied Statistics for The Behavioral Sciences

• 17:00-19:00
• 開始第4章作業，完成第1題。

繼續研讀 Applied Statistics for The Behavioral Sciences

• 20:30-9:10
• Normalize Standard Scores

繼續研讀 Applied Statistics for The Behavioral Sciences

• 20:00-21:30 抽空進行
• 進度：復習 Using the Standard Normal Distribution
• Determining Proportions
• Determining Percentiles
• Determining Percentile Ranks

繼續研讀 Applied Statistics for The Behavioral Sciences

• 21:00-22:00

繼續研讀 Applied Statistics for The Behavioral Sciences

• 17:00-19:40

繼續研讀 Applied Statistics for The Behavioral Sciences

• 複習 Standard Scores
• 
• The z score indicates the number of standard deviations a corresponding raw score is above or below the mean.
• A distribution of z score (1) retains the shape of the distribution of the original scores, (2) has a mean of 0, and (3) has a variance and standard deviation of 1.
• 
• When developing a composite score from two or more individual scores, first transform the individual scores into standard scores. Then apply the weights to generate the weighted score.
• 
• =new or transformed score for a particular individual
• =desired standard deviation of the distribution
• =standard score for a particular individual
• =desired mean of the distribution
• To transform a distribution of scores into a distribution with a desired mean and standard deviation, multiply the z scores by the desired standard deviation and add the desired mean.

與翰洋繼續編訂SAT讀書計畫

• 13:30-16:00 抽空進行
• 教材
• 2016年9月1日至2017年2月28日
• 橘子數學
• 觀念物理
• 觀念化學
• 觀念生物
• 觀念地球科學
• 2017年3月1日至2019年1月31日
• Khan Academy：Math, Physics, Chemistry, Biology, World History, US History
• Applied Statistics for The Behavioral Sciences (Hinkle Wiersma Jurs)
• Concepts & Contexts Calculus (James Stewart)
• Fundamentals of Physics (Halliday.Resnick)

繼續研讀 Applied Statistics for The Behavioral Sciences

• Chapter 4 The Normal Distribution
• 3:50-8:50

常態分布的通用公式與圖形

給定一平均值與一標準差時，可得一特定的常態分布圖形

• The Nature of the Normal Distribution
• The Family of  Normal Distributions
• The normal distribution is not a single distribution but a family of distributions, each of which is determined by its mean and standard deviation.
• Properties of the Normal Distribution 
• A normal distribution is unimodal (having one mode), symmetrical (that is, the left and right halves are mirror images), and bell shaped, with its maximum height at the mean.
• A normal distribution is continuous. There is a value of Y (the height) for every value of X where X is assumed to be a continuous rather than a discrete variable. 
• A normal distribution is asymptotic to the X axis. This means that the farther the curve goes from the mean, the closer it gets to the X axis; but the curve never touches the X axis, no matter how far a particular score is from the mean of the distribution.
• The Standard Normal Distribution
• The standard normal distribution or unit normal distribution is the distribution of normally distributed standard scores with a mean equal to 0 and a standard deviation equal to 1.

常態分配的公式怎麼推導出來?

• 首先用中心極限定理推導出這種分佈的機率密度函數正比於，然後透過平移、縮放，最後調整外圍的那個常數使其包圍著的面積是1而得來。 
• 平移與平均值有關。縮放與標準差有關，使面積為1的係數也與標準差有關。
• 機率論，大數定律

繼續研讀 Applied Statistics for The Behavioral Sciences

• 研究 如何用 Excel 自動化解題，進度：第3章第1題。
• 10:00-16:00

繼續研讀 Applied Statistics for The Behavioral Sciences

• 10:20-13:00
• Computer Example: The Survey of High School Seniors Data Set
• Standard Scores
• The z score indicates the number of standard deviations a corresponding raw score is above or below the mean.
• Properties of z Scores
1. The distribution of standard scores preserves a shape similar to that of the original distribution of raw scores.
2. The mean of the distribution of z scores will always equal 0 regardless of the value of the mean in the raw score distribution.
3. The variance of the distribution of z scores always equals 1. Since the standard deviation is the square root of the variance, the standard deviation will also equal 1.
• Weighted averages
• When developing a composite score from two or more individual scores, first transform the individual scores into standard scores. Then apply the weights to generate the weighted score. 
• Transformed Standard Scores
• To transform a distribution of scores into a distribution with a desired mean and standard deviation, multiply the z scores by the desired standard deviation and add the desired mean.
• 下一次進行 Exercises 

繼續研讀 Applied Statistics for The Behavioral Sciences

• 12:40-14:10
• Measures of Variation
• Measures of variation are lengths of intevrals on the scale of measurement that indicate the variation, or spread, of scores in a distribution.
• Range
• The range is defined as the number of units on the scale of measurement that indicate the highest and lowest values.
• Box Plots
• Box plots can be used to provide a graphical summary of both the central tendency and variation of a distribution of scores.
• Outliers
• An outlier is defined as a unusual score in a distribution that may warrant special consideration.
• Other Measures of Variation
• Mean Deviation (離均值)
• The mean deviation is the average of the absolute values of the deviation scores.
• Variance (變異數)
• The variance is defined as the average of the sum of squared deviations around the mean.
• Standard Deviation (標準差)
• The standard deviation is the square root of the variance. It is expressed in the same units as the original measurement of the variable.

繼續研讀 Applied Statistics for The Behavioral Sciences

• Measures of Central Tendency
• The mode is the most frequent score in a distribution.
• The median is the point below which 50 percent of scores fall.
• The mean is the arithmetic average of the scores in a distribution.
• Two important properties of the mean are
1. The sum of deviations from the mean is zero.
2. The sum of squared deviations from the mean is minimum.
• 7:00-13:20 抽空進行

繼續研讀 Applied Statistics for The Behavioral Sciences

• Use of Percentiles and Percentile Ranks
• The ordinal nature of percentiles limits the statistical operations appropriate for them.
• Raw scores and percentile ranks are for the most part inappropriate for making comparisons across distributions.
• 21:00-21:40

繼續研讀 Applied Statistics for The Behavioral Sciences

• A percentile is the point on the scale of measurement for the distribution at of below which a given percentage of score is located.
• The percentile rank of a score is a point on the percentile scale that gives the percentage of scores falling at or below the specified score.

繼續研讀 Applied Statistics for The Behavioral Sciences

• Graphing Frequency Distributions
• Histogram
• Frequency Polygon
• The Cumulative Frequency Distribution and Its Graph
• Shapes of Frequency Distributions
• Computer Example: The Survey of High School Seniors

Chapter 3

Describing Distributions: Individual Scores, Central Tendency, and Variation

• Percentiles
• Computing percentiles

• 10:50-12:00

研讀 Applied Statistics for The Behavioral Sciences

• 6:50-8:30

研讀 Applied Statistics for The Behavioral Sciences

• Organizing and Graphing Data 
• Organizing Data
• Stem-and-Leaf Displays
• Frequency Distribution
• Class Intervals
• Exact Limits of the Class Interval
• Assumption for Class Intervals Greater then One Unit
• Graphing Data
• Constructing a Graph
• Bar Graphs
• Scatterplots
• 7:30-15:30 抽空進行

研讀 Applied Statistics for The Behavioral Sciences

• Organizing and Graphing Data
• 21:30-22:00