# Module Overview

### Statistics & Probability

The purpose of this module is to provide the learner with the statistical concepts and tools necessary for any engineering or science graduate, as well as underpinning specific engineering topics such as statistical process control, quality control and reliability analysis. To do this, the learner will cover the fundamental ideas of probability and descriptive statistics, moving on to Hypothesis testing and the design of experiments.

MECH H2017

##### ECTS Credits

5

*Curricular information is subject to change

Descriptive Statistics

Calculation of mean, mode, median and standard deviation. Grouped data, calculation of class intervals, calculation of mean, mode, median and standard deviation for grouped data. Data representation and types of charts. Linear regression and correlation as data analysis techniques.

Probability

The definition of the fundamental ideas of events, experiments and probability. Independent events, conditional probabilities and the addition and multiplication laws. Permutations and combinations. The concepts of a random variable and its distribution, the definition of population parameters in terms of the probability distribution function and the cumulative probability distribution. Discrete and continuous probability distributions, including the exponential, normal, binomial and Poisson distributions. Examples of the role of these distributions in reliability prediction, component failures and designing for reliability.

Hypothesis testing

The concept of a statistic. The Central Limit Theorem and the concept of standard error. The common population parameters as statistics. The concept and limitations of a Hypothesis test, including type I and II errors and their probabilities. The representation of the results of a test; critical values and confidence intervals. Distributions including the ‘Student t’, the chi-square and the F distributions. Standard tests, including tests on means and variances, paired sample and unpaired tests on comparisons of means. Categorical tests using the chi-square distribution, such as goodness-of-fit tests to a distribution and tests for independence. Linear regression and correlation as statistical tests. The design of experiments and the comparison of group means by one- and two-way analysis of variance.

Module Content & Assessment
Assessment Breakdown %
Formal Examination70