概率统计
基础知识
对话窗改建案例
某医院针对客户投诉挂号处窗口太高的问题，决定进行改建以适合绝大多数客户（99%)的身高。
为此，医院抽检了50人的身高，作为设定窗口高度的基准。
（m）
均值:
所有数据的算数平均值
反映所有数据的信息
受奇异值影响
中位数:
将数据从大到小排序，位置在中间的数
不大 受奇异值影响
众数:
出现频率最多的数
不大 受奇异值影响
对话窗改建案例续
1 2 2 2 2 3 3 4 4 30
对话窗改建案例续
计算下列数的均值、中位数和众数：
均值：
中位数：
众数：2
1 2 3 4……………………………………………..30
离异值
直方图(Histogram)
1
4
2
2
1
分析：
不存在离异值，所以采用均值。 X = 米
中等个人数多，特高特矮的人数少，服从正态分布
50人身高的直方图
对话窗改建案例续
均值决定正态分布曲线的位置。
标准差决定正态分布曲线的宽度。数据越分散，标准差越大。
正态分布的两个参数
对话窗改建案例续
X
s
R
工作和生活中很多数据都服从或近似服从正态分布。许多统计分析都以假定数据服从正态分布为前提，如均值－极差控制图，方差分析，T检验等。
标准差与概率
对话窗改建案例续
-1s
3s
-3s
-2s
2s
1s
%
%
%
描述数据离散的统计量 方差 (s2 ; s2 ):
每一个单值与均值差的平方和的平均(n-1)
标准差 (s ; s):
方差的平方根，是描述数据离散的最常用统计量
极差: 一组数中的最大数与最小数之差
对话窗改建案例续
对话窗的设定
身高的均值 米
身高的标准差。用Excel中的stdev()计算得 S = 米
对话窗改建案例续
（+3*)
（－3*)
SPC-Basic Statistics
Start off by introducing the Kick off speaker: Champion, VP,GM,ect.
Go through SPACER
Administrative:
- Bathrooms & telephones
- Messages
- Pagers on vibrate
- Food and menu
- Get up and stand during lecture
1st Assignment- Have the class introduce themselves, background, expectations, and name as many BB’s and the status of their projects.
SPC-Basic Statistics
SPC-Basic Statistics
Example: House prices
People looking at houses and find 4 houses in the area priced as follows: $115K, $80K, $100K, $175K. Avg and Median pretty close together ($).
Add 1 more house at $. Mean is greatly shifted upwards while median stays at $115K.
If you have even # of values, median is the average of the center 2 values.
Median is less affected by shift in values, mean is greatly affected by shift in values. Median is useful if significant outliers exist. For example, average home price my be highly influenced if Bill Gates moved in the area but the median would not be affected appreciably.
SPC-Basic Statistics
Example: House prices
People looking at houses and find 4 houses in the area priced as follows: $115K, $80K, $100K, $175K. Avg and Median pretty close together ($).
Add 1 more house at $. Mean is greatly shifted upwards while median stays at $115K.
If you have even # of values, median is the average of the center 2 values.
Median is less affected by shift in values, mean is greatly affected by shift in values. Median is useful if significant outliers exist. For example, average home price my be highly influenced if Bill Gates moved in the area but the median would not be affected appreciably.
SPC-Basic Statistics
SPC-Basic Statistics
SPC-Basic Statistics
SPC-Basic Statistics
11
Traditional range based sample standard deviation estimation table:
n d2 .
2
3
4
5
6
7
8
9
10
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SPC-Basic Statistics
11
Traditional range based sample standard deviation estimation table:
n d2 .
2
3
4
5
6
7
8
9
10
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