AP Statistics U1 Note

零风PLFJY Lv2
  2025-09-20 17:32:37 2025-09-20 17:32:37 Created   2025-10-17 15:21:11 2025-10-17 15:21:11 Updated    709 Words  3 Mins  

Exam Structure

40 MCQ + 6 FRQ

1.1 Data Analysis (数据的分类)

  • Individual: 参与统计的个体

  • variable: 一个特质（eg: gender、frequency）

  • value: eg: gender里的细分比如Male、Female，frequency的细分：one time、often、 hardly

  • count: 数量

Categories of var

  • Categorical Variable: enum bool

  • Quantitative Variable: int double

  • Distribution: Describe the condition of the data

  • Population: Whole dataset

  • Sample: Part of the dataset

Analyze Variable

How to spot a misleading graph ?

  1. missing axis labels or scale (刻度)
  2. cut off x or y axis or start at a weird place
  3. picture instead of a bar

Categorical:

Pie chart / Bar chart / Two-way table

Quantitative:

histogram / boxplot / bar chart

Marginal distribution and Conditional distribution (Categorical Variable、Two-way table)

MaleFemaleTotal
one timenumnum cnum a
oftennumnumnum
hardlynumnumnum
Totalnumnum dnum b

Marginal distribution:

The proportion of count of all individuals in a variable among the total individuals (a/b) (d / b)

Conditional distribution:

指定了条件(与另一个value的intersect)的values的count在指定总数中的占比，若没有指定总数，则默认为全部的总数(b)

Relative frequency:

有可能是上面两个任意一个，看要求什么，不管怎么说分母都是 total

Other graphs to describe data

Segmented bar graph

Side by side bar graph

1.2 Displaying quantitative data with graphs

分布 (shape)

描述分布 (4个维度 SCSO)

Shape

正态分布 Normal Distribution（对称）

拱起来的在中间

左偏 skew倾斜 to the left

左边much longer than the right

拱起来的在右边

右偏 skew to the right

右边much longer than the left

拱起来在左边

skew
来源:medium.com

Center

把整个数据分成两半

一般取 mean 或者 median

还可以叫做 typical

Spread 波动性

表示数据的离散程度，分散就大，聚合就小

一般用 Range 或者 [standard deviation](#Standard Deviation 标准方差)

Outliers

异常值 （极大或极小）

[How to determine](#Identify outliers)

An example

The data shows that the distribution is roughly symmetric.(Reason) Therefore it is approximately as a normal distribution.(Shape) The center of the data is between 227 and 252.(Center) The data varies from 56 to 422.(Spread) We do not see any observations outside the pattern of the distribution.(Outliers)

Plots

Q: 选哪个图：
A: 选什么图，因为它是什么数据，什么图能更好的展示它的 distribution

Dot plot

Stem plot

记得一定要写 Key !!!!!

Key: 一个tips用来描述你展示的值represent什么东西

eg:
Key: 7|7 = 77 apples each day

Histogram

frequency histogram / relative frequency histogram (more useful)

  • shows frequency
  • no spaces each bar
Drawbacks
  • no individual data just interval
  • cannot find median

1.3 Describing Quantitative data with numbers

Measuring Center

Means

Median

(value at 50%)

Mode

Measuring Spread

Range

maximum - minimum

IQR (描述波动性的)

(value at 75%) -(value at 25%)

Identify outliers:

or

Box Plot

  1. number line + label
  2. determine minimum,,(median),, and maximum
  3. a line connect minimum and maximum
  4. Box betweenand
  5. a line at
  6. usually using median and IQR to measure the center and spread

We only know: five values above

We can’t know: sample size, sample mean

Standard Deviation 标准方差



s: sample variance 样本方差 VS population variance 总体方差

Def: 数据围绕平均值的离散程度

使用条件：用mean去描述center的时候才可以用这个去描述数据的波动性

不具有抗性，可能由于outlier的影响变得更小或者更大

Variance 方差

  • Title: AP Statistics U1 Note
  • Author: 零风PLFJY
  • Created at : 2025-09-20 17:32:37
  • Updated at : 2025-10-17 15:21:11
  • Link: https://blog.plfjy.top/ap-statistics/ap-statistics-u1-note/
  • License: This work is licensed under CC BY-NC-SA 4.0.
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On this page
AP Statistics U1 Note
  1. Exam Structure
  2. 1.1 Data Analysis (数据的分类)
    1. Categories of var
    2. Analyze Variable
    3. Marginal distribution and Conditional distribution (Categorical Variable、Two-way table)
    4. Other graphs to describe data
  3. 1.2 Displaying quantitative data with graphs
    1. 描述分布 (4个维度 SCSO)
    2. Plots
  4. 1.3 Describing Quantitative data with numbers
  5. Measuring Center
    1. Means
    2. Median
    3. Mode
  6. Measuring Spread
    1. Range
    2. IQR (描述波动性的)
    3. Standard Deviation 标准方差
    4. Variance 方差