重學Statistics, Cha2 Descriptive Statistics (Categorical and Quantitative Data)

2.1 Summary Categorical Data 

Frequency Distribution: 

A frequency distribution is a tabular summary of data showing the number (frequency) of items in each of several nonoverlapping classes.

Relative Frequency: 

Relative frequency of a class = Frequency of the class / n


2.2 Summarizing Quantitative Data

1. Determine the number of non overlapping classes. (5 -20)  問:怎麼科學地決定多少個?

2. Determine the width of each class.

Approximate class width = (largest data value - smallest data value) / Number of classes

3. Determine the class limits 決定最大值和最小值.


Plot the data:

1. Dot plot


2. Histograms: 



3. A variation of the frequency distribution that provides another tabular summary of quantitative data is the cumulative frequency distribution.

Ogive is a graph of a cumulative distribution.



2.3 Stem-and-leaf display

Stem-and-leaf display can be used to show both the rank order and shape of a data set simultaneously. 相對於histogram的好處,手寫容易,更多信息



1. Crosstabulation

A cross tabulation is a tabular summary of data for two variables.


2. Simpson's Paradox

The reversal of conclusions based on aggregate and unaggregated data is calledSimpson’s paradox.

我們可以看到在總體的數據中,Kendall的表現比 Luckett 好,但是當我們分別去看 unaggregated 數據的時候,在 Common Pleas 和 Municipal Court 的表現,Luckett 反而更好,這個原因在於兩個的數據基數差太大。




3. Scatter diagram & Trendline

A scatter diagram is a graphical presentation of the relationship between two quantitative variables,
and a trendline is a line that provides an approximation of the relationship.




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