TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPC
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i=1
N -1
SPC
分布的位置 Location Mean 均值 Median 中值 Mode 代表值 Quantiles 分位数
Q1 四分之一处 Q2 二分之一处 Q3 四分之三处 P＃％ 机率位置
数据的描述总览
Numercial Graphical
离散度 Spread Range 范围 Standard Deviation 标准偏差 Variance 变差 Stability Factor 稳定因子 Span 跨度 Interquartile Range 内分位宽度 Sum of Squares 平方和
Shape 形状 Histograms 直方图 Run Charts 运行图 Time Plots 时序图 Scatter Plots 散点图 Box Plots 盒状图 Block Chart 块图 Normality Plot 正态性图
Normal Distribution正态分布
fx(x)=
Mean均值
e 1
2ps2
-(x-)2/2s2
Bell-shape Symmetric Distribution
‘倒钟’状对称分布
s
2s s
s 2s
s
Measured by Standard Deviation 用标准偏差为尺度
mean
68.27 %
s
总体标准偏差
Sample Statistics
Estimate
Parameters
Population
统计活动的实质：用样本统计值来估计总体参数，从而了解总体
SPC
Population vs. sample 总体和样本计算公式
Population Mean 总体均值
Population Standard Deviation
100
0
60
70
80
90Leabharlann 100 110 120 130
Pos Skew
Frequency
Median
Mean
300
200
100
0
0
10
20
30
40
50
60
70
80
Neg Skew
SPC Sample mean of a distribution 样本均值 Mean = Average
N
= xi /N
X X-X (X- X)2
1 2 3 4 5 6 7 8 9 10
Mean ssquare
s
N
(Xi X )2
i=1
N -1
N
(Xi X )2
i=1
N -1
Using the form above, calculate the standard deviation for the numbers用上列的表计算以下5个数据的标准偏差：2， 1， 3， 5 ，4
i=1
= X1 + X2 +....XN N
Examples:例
Part weights零件重量: 8.47, 8.67, 9.34, 7.99
AVERAGE = 8.47 +8.67 + 9.34 + 7.99 = 8.62
平均值
4
SPC
Don’t Worry. That rope is one inch thick on the average.
* Population is the entire group or set of all possible events of interest in the particular study. 总体是被关注、研究的对象的 全部
* Sample is a subset of the population样本是从总体中抽出的 一部分
– Discrete (Count) Data
– 间断型数据（计数）
• Maintenance Equipment Failures, Number of Clogs
• Number of customer returns
> 如设备维修次数、阻塞次数等
> 客户退货次数
– Continuous Data
特性数据(定性)
– Categories
– 等级
– Yes, No
– 是非
– Go, No go
– 通止
– Machine 1, Machine 2, Machine 3 – 个体（如 1号机器, 2号机器, 3号机器)
– Pass/Fail
– 成败
• Variable Data
• 变量数据（定量)
计量型数据的描述-图形
数据分布图
在实际统计中， 统计结果是分段 表示的，因此作出的分布图为柱 形图。 在分析数据时，通常将它 拟合成连续的曲线。
# of ocurrence
Height(inch)
SPC Examples of distributions 不同的分布
Frequency
C o m p a ris o n o f D is trib u tio n s .
– 连续型数据 (计量)
• Decimal subdivisions are meaningful> 可有小数点 • Time, Pressure, Conveyor Speed > 如时间、压力、传送速度等
SPC
Histogram
Height of 90 ladies
Description of Continuous Data-Graphical
不要担心。 绳子是 平均一英寸粗
SPC Description of Quantitative Data-Dispersion or ‘Spread’ 计量型数据的描述-离散度
Range = maximum value - minimum value 范围=样本内最大值-最小值 Variance= mean squared distance from the mean 方差=数据与均值差距的平方之均值 Standard deviation = is the square root of the
SPC Exercise Solution计算结果:
X
1
2
2
1
3
3
4
5
5
4
6
7
8
9
10
15
M ean
3
s s q u a re
s
X -X
-1 -2 0 2 1
(X - X)2
1 4 0 4 1
10
2 .5 1 .5 8 1 1 3 9
N
(Xi X )2
i=1
N -1
N
(Xi X )2
l Deviation（偏差）
= observation - true mean观测值-均值
l Variance 方差 = mean or average of squared deviation scores
s2
is
the
偏差值的平方均值. symbol for variance方差的符号.
l Standard Deviation标准偏差 = square root of variance方差的开方.
SPC
统计学基础 Basic
Statistics
SPC What is statistics?什么是统计
Definition of statistics: 统计的定义
Populations and Samples 总体和样本
* Statistics are facts and figures.统计是事实和数据
variance and provides a measure of the standard distance from the mean. 标准偏差=方差的开方
SPC
Standard Deviation 标准偏差
l Deviation score（偏差值） is the distance from the mean.是离开均值的距离
* Statistics consist of a set of methods and rules for organizing and interpreting observations from populations and samples统计通过一系列方法和规则来组织、解释来自总体和 样本的观测值
A Statistic: 统计值
ENTIRE POPULATION总体
SAMPLE WITHIN (subset)样本
•A numerical value that describes a sample •用来描述样本的数值
SPC
Two Types of Data 统计获得的两种数据
• Attribute Data
The mean and median will be affected by the nature of the distribution of numbers. 均值和中值都受数据分布的影响
Mode: Most frequently occurring value in a data set. In a Pareto this is the largest bar on the chart. 众数：数据中重复次数最多的值，
15.865%
2s s
15.865%
s 2s
s
Measured by Standard Deviation 用标准偏差为尺度
Median: Reflects the 50% rank - the center number after a set of numbers has been sorted from low to high.中位数：反映 系列的一半—将一组数据按大小顺序排列，取中间的一个数据 Does not include all values in calculation 计算中未包含全部数据 Is “robust” to extreme outlier scores. 对特殊值的干扰有抵抗
300
200
Right-tailed
100
0
60
70
80
90
100
110
120
130
C2
Frequency
50
0
20
30
40
50
60
70
80
90
100 110
C1
Symmetric
Distribution 对称分布
SPC Description of Quantitative Data-Central Tendency 计量型数据的描述-中心位置 Mean: Arithmetic average of a set of values 均值：算数平均值 Reflects the influence of all values反映全部数据的影响 Strongly Influenced by extreme values受特殊值干扰大
SPC
Statistics or parameters? 样本统计值与总体参数？
SAMPLE样本
X = Sample Mean样本均
值
POPULATION总体
= Population Mean总体均值
s = s^
= Sample Standard
Deviation样本标 准偏差
s = Population Standard Deviation
在柏拉图上表现为最高的那条柱
SPC Relationship: mean and median 均值和中位数的比较 Mean, Median
Frequency
100
50
0 20 30 40 50 60 70 80 90 100 110
No rm a l
Median
Mean
Frequency
300
200
s is the symbol for the standard deviation.标准偏差的符号
= Population
Mean 总体的均值
i Deviation (distance from mean)偏差
The Standard Deviation is a Measure of Variability 标准偏差是对变异的描述
总体标准偏差
Sample Mean 样本均值
Sample Standard Deviation
样本标准偏差
N
Xi
= i1 N
s =S=
N
(X i ) 2
i= 1
N
n
x i
^ =
x=
i=1
n
s^ = s =
n
(X i X ) 2
i=1
n -1
SPC Example: Calculating “sigma”计算练习
300
200
100
0
0
10
20
30
40
50
60
70
80
C3
C o m p a ris o n o f D is trib u tio n s .
Two-tailed
100
Frequency
Left-tailed
Negative Skew负斜
Positive Skew正斜
C o m p a ris o n o f D is trib u tio n s .
N -1
SPC
分布的位置 Location Mean 均值 Median 中值 Mode 代表值 Quantiles 分位数
Q1 四分之一处 Q2 二分之一处 Q3 四分之三处 P＃％ 机率位置
数据的描述总览
Numercial Graphical
离散度 Spread Range 范围 Standard Deviation 标准偏差 Variance 变差 Stability Factor 稳定因子 Span 跨度 Interquartile Range 内分位宽度 Sum of Squares 平方和
Shape 形状 Histograms 直方图 Run Charts 运行图 Time Plots 时序图 Scatter Plots 散点图 Box Plots 盒状图 Block Chart 块图 Normality Plot 正态性图
Normal Distribution正态分布
fx(x)=
Mean均值
e 1
2ps2
-(x-)2/2s2
Bell-shape Symmetric Distribution
‘倒钟’状对称分布
s
2s s
s 2s
s
Measured by Standard Deviation 用标准偏差为尺度
mean
68.27 %
s
总体标准偏差
Sample Statistics
Estimate
Parameters
Population
统计活动的实质：用样本统计值来估计总体参数，从而了解总体
SPC
Population vs. sample 总体和样本计算公式
Population Mean 总体均值
Population Standard Deviation
100
0
60
70
80
90Leabharlann 100 110 120 130
Pos Skew
Frequency
Median
Mean
300
200
100
0
0
10
20
30
40
50
60
70
80
Neg Skew
SPC Sample mean of a distribution 样本均值 Mean = Average
N
= xi /N
X X-X (X- X)2
1 2 3 4 5 6 7 8 9 10
Mean ssquare
s
N
(Xi X )2
i=1
N -1
N
(Xi X )2
i=1
N -1
Using the form above, calculate the standard deviation for the numbers用上列的表计算以下5个数据的标准偏差：2， 1， 3， 5 ，4
i=1
= X1 + X2 +....XN N
Examples:例
Part weights零件重量: 8.47, 8.67, 9.34, 7.99
AVERAGE = 8.47 +8.67 + 9.34 + 7.99 = 8.62
平均值
4
SPC
Don’t Worry. That rope is one inch thick on the average.
* Population is the entire group or set of all possible events of interest in the particular study. 总体是被关注、研究的对象的 全部
* Sample is a subset of the population样本是从总体中抽出的 一部分
– Discrete (Count) Data
– 间断型数据（计数）
• Maintenance Equipment Failures, Number of Clogs
• Number of customer returns
> 如设备维修次数、阻塞次数等
> 客户退货次数
– Continuous Data
特性数据(定性)
– Categories
– 等级
– Yes, No
– 是非
– Go, No go
– 通止
– Machine 1, Machine 2, Machine 3 – 个体（如 1号机器, 2号机器, 3号机器)
– Pass/Fail
– 成败
• Variable Data
• 变量数据（定量)
计量型数据的描述-图形
数据分布图
在实际统计中， 统计结果是分段 表示的，因此作出的分布图为柱 形图。 在分析数据时，通常将它 拟合成连续的曲线。
# of ocurrence
Height(inch)
SPC Examples of distributions 不同的分布
Frequency
C o m p a ris o n o f D is trib u tio n s .
– 连续型数据 (计量)
• Decimal subdivisions are meaningful> 可有小数点 • Time, Pressure, Conveyor Speed > 如时间、压力、传送速度等
SPC
Histogram
Height of 90 ladies
Description of Continuous Data-Graphical
不要担心。 绳子是 平均一英寸粗
SPC Description of Quantitative Data-Dispersion or ‘Spread’ 计量型数据的描述-离散度
Range = maximum value - minimum value 范围=样本内最大值-最小值 Variance= mean squared distance from the mean 方差=数据与均值差距的平方之均值 Standard deviation = is the square root of the
SPC Exercise Solution计算结果:
X
1
2
2
1
3
3
4
5
5
4
6
7
8
9
10
15
M ean
3
s s q u a re
s
X -X
-1 -2 0 2 1
(X - X)2
1 4 0 4 1
10
2 .5 1 .5 8 1 1 3 9
N
(Xi X )2
i=1
N -1
N
(Xi X )2
l Deviation（偏差）
= observation - true mean观测值-均值
l Variance 方差 = mean or average of squared deviation scores
s2
is
the
偏差值的平方均值. symbol for variance方差的符号.
l Standard Deviation标准偏差 = square root of variance方差的开方.
SPC
统计学基础 Basic
Statistics
SPC What is statistics?什么是统计
Definition of statistics: 统计的定义
Populations and Samples 总体和样本
* Statistics are facts and figures.统计是事实和数据
variance and provides a measure of the standard distance from the mean. 标准偏差=方差的开方
SPC
Standard Deviation 标准偏差
l Deviation score（偏差值） is the distance from the mean.是离开均值的距离
* Statistics consist of a set of methods and rules for organizing and interpreting observations from populations and samples统计通过一系列方法和规则来组织、解释来自总体和 样本的观测值
A Statistic: 统计值
ENTIRE POPULATION总体
SAMPLE WITHIN (subset)样本
•A numerical value that describes a sample •用来描述样本的数值
SPC
Two Types of Data 统计获得的两种数据
• Attribute Data
The mean and median will be affected by the nature of the distribution of numbers. 均值和中值都受数据分布的影响
Mode: Most frequently occurring value in a data set. In a Pareto this is the largest bar on the chart. 众数：数据中重复次数最多的值，
15.865%
2s s
15.865%
s 2s
s
Measured by Standard Deviation 用标准偏差为尺度
Median: Reflects the 50% rank - the center number after a set of numbers has been sorted from low to high.中位数：反映 系列的一半—将一组数据按大小顺序排列，取中间的一个数据 Does not include all values in calculation 计算中未包含全部数据 Is “robust” to extreme outlier scores. 对特殊值的干扰有抵抗
300
200
Right-tailed
100
0
60
70
80
90
100
110
120
130
C2
Frequency
50
0
20
30
40
50
60
70
80
90
100 110
C1
Symmetric
Distribution 对称分布
SPC Description of Quantitative Data-Central Tendency 计量型数据的描述-中心位置 Mean: Arithmetic average of a set of values 均值：算数平均值 Reflects the influence of all values反映全部数据的影响 Strongly Influenced by extreme values受特殊值干扰大
SPC
Statistics or parameters? 样本统计值与总体参数？
SAMPLE样本
X = Sample Mean样本均
值
POPULATION总体
= Population Mean总体均值
s = s^
= Sample Standard
Deviation样本标 准偏差
s = Population Standard Deviation
在柏拉图上表现为最高的那条柱
SPC Relationship: mean and median 均值和中位数的比较 Mean, Median
Frequency
100
50
0 20 30 40 50 60 70 80 90 100 110
No rm a l
Median
Mean
Frequency
300
200
s is the symbol for the standard deviation.标准偏差的符号
= Population
Mean 总体的均值
i Deviation (distance from mean)偏差
The Standard Deviation is a Measure of Variability 标准偏差是对变异的描述
总体标准偏差
Sample Mean 样本均值
Sample Standard Deviation
样本标准偏差
N
Xi
= i1 N
s =S=
N
(X i ) 2
i= 1
N
n
x i
^ =
x=
i=1
n
s^ = s =
n
(X i X ) 2
i=1
n -1
SPC Example: Calculating “sigma”计算练习
300
200
100
0
0
10
20
30
40
50
60
70
80
C3
C o m p a ris o n o f D is trib u tio n s .
Two-tailed
100
Frequency
Left-tailed
Negative Skew负斜
Positive Skew正斜
C o m p a ris o n o f D is trib u tio n s .