Statistical methods and Data analysis study notes 1

Statistical tools, techniques and methodologies for quality improvement and recycling projects:

Histogram

Numerical description Amount (mean, standard deviation, scale, etc.)

Scatter chart

Line graph (connecting points with lines in scatter plots)

Control chart: (sample mean),R(sample very poor), and s(sample standard deviation)

Sampling scheme

Test design

Collect data to be aware of the following steps:

Detailing the objectives of a study, investigation, or test

Determine the variables of interest

Choosing the right design for investigation or scientific research

Collect Data

Method of sampling:

Simple random sampling

Stratified Random sampling

than estimated

Overall sampling

System sampling

The statistical field can be divided into two main branches: descriptive statistics and inferred statistics

An appropriate generalization measure can provide a good, broad-brush depiction of the original set of measured values. By reducing a large number of measurements to a few of these descriptive statistics, we can understand the information contained in the data

Data numeric descriptive measure of a single variable

The two most common types of numeric descriptive measures are the central trend metric and the variability metric . That is, we want to describe the center of the measured value distribution and how the measured value changes relative to the distribution center. In order to distinguish the overall numerical descriptive measure and the numerical descriptive measure of the sample, the former is the parameter and the latter is the statistic quantity. In the related problems of statistical inference, the numerical values of various parameters can not be calculated, but the corresponding statistics from the samples may be calculated, and the corresponding overall parameters are estimated with the obtained values.

Center Trend Measurement

The majority of

Number of Median

Arithmetic average

A mean is a common measure of a set of measured values, but it can be distorted by the presence of one or more extreme values in the collection. In such cases, extreme values (also known as outliers) tend to bias the mean to find the equilibrium point of the data, thus distorting the meaning of the most central measure of the mean value. A workaround for the mean is the truncated mean, which removes the maximum and minimum number of values and averages the remaining numbers.

Memory number Mo median Md mean μ intercept mean TM

What are the links between these center trend metrics

The answer depends on the degree of bias (skewness) of the data

The important thing to remember is that we cannot confine ourselves to only one central trend metric. For some data sets, it is necessary to use a variety of measures to make an accurate and descriptive summary of the data's central trends.

Variability metrics:

Difference between the maximum and the minimum of the extreme difference

Percentile n the p% percentile of a set of measured values by size refers to a value that has a maximum of p% in the set that is smaller than it, and has at most ( 100-p)% is larger than its measured value.

Four-digit spacing (IQR)

Refers to the difference between three-fourths and One-fourth decimal points, i.e.

IQR = 75% - The number of bits of 25%

Dispersion (difference between the measured value and the mean)

Variance

Standard deviation

Coefficient of variation = standard deviation /| mean value |

Reference documents:

statistical methods and data analysis R.L. Otter, M. Longenecker

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Statistical methods and Data analysis study notes 1