Basic Statistics in Six Sigma

Statistical thinking

using data to grasp how processes work, identify root causes, measure improvements, and make decisions based on evidence

Data driven decision-making

Based on factual results

Inferential statistics

Make predictions about population from sample data; use confidence intervals and apply hypothesis testing; use during analyze phases

Descriptive statistics

Summarize data using mean, median, mode, and range; used during measure phase

mean

the average and balance point of data

when to use the mean

 when data is balanced around center; avoid with skewed data outliers

Right skewed distribution

 mean is greater than the median

Left skewed distribution

mean is less than the median

median

The middle value in the dataset

when to use the median

when there's extreme values, to represent typical cases in skewed datasets, and to capture central tendency reliably

Population

the entire group you want to study or analyze

Sample

a smaller subset selected for analysis

Importance of sampling

Reduce costs by testing fewer items, save time and be more efficient, and handle destructive testing through sample selection

Random sampling

equal selection opportunity that prevents biased

Mode

the most frequent value in a dataset; helps pinpoint most dominant characteristics or issues

Multimodal distribution

2 modes

trimodal distribution

3 modes

range

The difference between highest and lowest data values

Wide range

high variability

narrow range

low variability; process consistency

Limitations of range

sensitive to outliers, doesn’t show data clustering, and ignores data distribution details

Variance equation

Σ(x-ẍ)² / n; Find mean, determine difference between each value and the mean, square each difference to remove negative (-) signs, sum squared difference and divide by the number of points

Reasons for squaring differences

Prevent cancellation of + and - deviations and turn all value positive