Basic Statistics for Engineering

Statistics is the science of collecting, analyzing, and interpreting data. In engineering, statistics are used to handle uncertainty, control quality, and make reliable decisions based on measured data.

1. Mean / Average

The mean is the sum of all data points divided by the number of data points.

  • Formula: μ=∑xiN\mu = \frac{\sum x_i}{N}
  • Engineering Meaning: Used to find the expected value of a property, such as the average tensile strength of a batch of rebar.

2. Median

The median is the middle value of an ordered dataset.

  • Concept: Half of the data is greater than the median, and half is less.
  • Engineering Meaning: It is more robust against outliers than the mean. For example, if a sensor occasionally returns a wildly erroneous value, the median provides a much closer estimate of reality.

3. Variance and Standard Deviation

Variance measures how far a set of numbers is spread out from their mean. Standard deviation is the square root of the variance.

  • Formulas:
    • Variance: σ2=∑(xi−μ)2N\sigma^2 = \frac{\sum (x_i - \mu)^2}{N}
    • Standard Deviation: σ=∑(xi−μ)2N\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}}
  • Engineering Meaning: Extremely important in quality control (Six Sigma) and manufacturing tolerances. A small standard deviation means manufactured parts are consistently close to the target dimension.

4. Basic Probability

Probability is the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).

  • Formula: P(A)=Number of favorable outcomesTotal number of possible outcomesP(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
  • Engineering Meaning: Used in reliability engineering to calculate the chances of system failure (e.g., Mean Time Between Failures, MTBF) and in risk assessments.