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

2. 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

3. Some very basic formulae
Ch48 Statistics by Chtan FYHSKulai

4. 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

5. 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

6. 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

7. 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

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

9. 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

10. 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

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

12. 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

13. 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

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

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

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

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

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

19. 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

20. 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

21. 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

22. Ch48 Statistics by Chtan FYHSKulai
The end
Ch48 Statistics by Chtan FYHSKulai