Ch48 Statistics by Chtan FYHSKulai Chapter 48 Statistics 统计学 Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai 参考书 ：普通数学高三第29章 高级数学高二上册 Ch48 Statistics by Chtan FYHSKulai

Some very basic formulae Ch48 Statistics by Chtan FYHSKulai

Ungrouped Data Grouped Data Mean 𝒙 = 𝒙 𝟏 + 𝒙 𝟐 +… 𝒙 𝒏 𝒏 Median Middle element of an arranged series. 𝑴 𝒆 =𝑳+ 𝒏 𝟐 − 𝒇 𝒔 𝒇 𝑼−𝑳 Mode The element with the highest frequency The group with the highest frequency 平均数 中位数 众数 (Modal class) Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai Ungrouped Data Grouped Data Mean deviation 𝑴.𝑫.= 𝒙 𝒊 − 𝒙 𝒏 𝑴.𝑫.= 𝒙 𝒊 − 𝒙 ∙ 𝒇 𝒊 𝒇 𝒊 Standard deviation 𝒔= 𝒙 𝒊 − 𝒙 𝟐 𝒏 𝒔= 𝒙 𝒊 − 𝒙 𝟐 ∙ 𝒇 𝒊 𝒇 𝒊 variance 𝝈= 𝒙 𝒊 − 𝒙 𝟐 𝒏 𝝈= 𝒙 𝒊 − 𝒙 𝟐 ∙ 𝒇 𝒊 𝒇 𝒊 平均差 标准差 方差 Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai Lower quartile Q1 : 25% 下四分位 median Second quartile Q2 : 50% 上四分位 Upper quartile Q3 : 75% Quartile deviation, Q.D.= 𝑸𝟑−𝑸𝟏 𝟐 四分位差 Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai 𝑴 𝒆 =𝑳+ 𝒏 𝟐 − 𝒇 𝒔 𝒇 𝑼−𝑳 Acc. frequency 𝒏 𝟐 𝑼−𝑳 𝑴 𝒆 −𝑳 = 𝒇 𝒏 𝟐 − 𝒇 𝒔 f fs 𝒙 𝒊 L Me U Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai Coefficient of variation = 𝒔 𝒙 ×𝟏𝟎𝟎% Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai Advantages The coefficient of variation is useful because the standard deviation of data must always be understood in the context of the mean of the data. The coefficient of variation is a dimensionless number. So when comparing between data sets with different units or widely different means, one should use the coefficient of variation for comparison instead of the standard deviation. Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai Disadvantages 1. When the mean value is near zero, the coefficient of variation is sensitive to small changes in the mean, limiting its usefulness. 2. Unlike the standard deviation, it cannot be used to construct confidence intervals for the mean. Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai Index Number 指数 Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai A very simple index number is called price relative. 价比 Price relative= 𝑷 𝟏 𝑷 𝟎 ×𝟏𝟎𝟎 Base period price Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai Composite index number 𝒙 𝒊 : 𝒊 𝒕𝒉 𝒆𝒍𝒆𝒎𝒆𝒏𝒕, 𝝎 𝒊 :𝒘𝒆𝒊𝒈𝒉𝒕𝒆𝒅 𝒄𝒐𝒎𝒑𝒐𝒔𝒊𝒕𝒆 𝒊𝒏𝒅𝒆𝒙 𝒏𝒖𝒎𝒃𝒆𝒓 = 𝝎 𝒊 𝒙 𝒊 𝝎 𝒊 Similarly, Weighted average Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai Price index 物价指数 Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai 𝑷𝒓𝒊𝒄𝒆 𝒊𝒏𝒅𝒆𝒙= 𝝎 𝒊 𝒙 𝒊 𝝎 𝒊 Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai Cost of living index 生活消费指数 Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai Cost of living 𝐢𝐧𝐝𝐞𝐱 = 𝝎 𝒊 𝒙 𝒊 𝝎 𝒊 Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai Moving Average 平均移动数 Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai 𝒍𝒆𝒕 𝒙 𝟏 , 𝒙 𝟐 ,…, 𝒙 𝒏 be a series and let k <𝒏 be a fixed periodic number. Then, Its moving average : Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai 𝒚 𝟏 = 𝒙 𝟏 + 𝒙 𝟐 +…+ 𝒙 𝒌 𝒌 𝒚 𝟐 = 𝒙 𝟐 + 𝒙 𝟑 +…+ 𝒙 𝒌+𝟏 𝒌 𝒚 𝟑 = 𝒙 𝟑 + 𝒙 𝟒 +…+ 𝒙 𝒌+𝟐 𝒌 ⋯⋯ y1, y2, y3, … is called the k-period moving average series. Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai 高级数学高二上册 Pg. 208 总复习8 Q1-Q11 Ch48 Statistics by Chtan FYHSKulai

Ch48 Statistics by Chtan FYHSKulai The end Ch48 Statistics by Chtan FYHSKulai