Statistics I

The details
Mathematical Sciences
Colchester Campus
Undergraduate: Level 4
Monday 13 January 2020
Friday 20 March 2020
01 October 2019


Requisites for this module


BE310, EC114, EC252, MA200, MA216, MA225, MA314, MA318, MA319, MA322

Key module for

BSC N233 Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N324 Actuarial Science (Including Year Abroad),
BSC N325 Actuarial Science (Including Foundation Year),
BSC C831 Cognitive Science,
BSC C832 Cognitive Science (Including Year Abroad),
BSC C833 Cognitive Science (Including Placement Year),
BSC L1G2 Economics and Mathematics (Including Placement Year),
BSC LG11 Economics and Mathematics,
BSC LG18 Economics and Mathematics (Including Foundation Year),
BSC LG1C Economics and Mathematics (Including Year Abroad),
BSC L1G1 Economics with Mathematics,
BSC L1G3 Economics with Mathematics (Including Placement Year),
BSC L1G8 Economics with Mathematics (Including Foundation Year),
BSC L1GC Economics with Mathematics (Including Year Abroad),
BSC GN13 Finance and Mathematics,
BSC GN15 Finance and Mathematics (Including Placement Year),
BSC GN18 Finance and Mathematics (Including Foundation Year),
BSC GN1H Finance and Mathematics (Including Year Abroad),
BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Statistics (Including Foundation Year),
BSC G1G4 Mathematics with Computing (Including Year Abroad),
BSC G1G8 Mathematics with Computing (Including Foundation Year),
BSC G1GK Mathematics with Computing,
BSC G1IK Mathematics with Computing (Including Placement Year),
BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad),
BSC I1G3 Data Science and Analytics,
BSC I1G3CE Data Science and Analytics,
BSC I1GB Data Science and Analytics (Including Placement Year),
BSC I1GBCE Data Science and Analytics (Including Placement Year),
BSC I1GC Data Science and Analytics (Including Year Abroad),
BSC I1GF Data Science and Analytics (Including Foundation Year)

Module description

For students outside of the Department, an appropriate A level in Mathematics (or equivalent) is required for this module. If you are unsure whether you meet theis criteria please contact before attempting to enrol. This module introduces students to the basic ideas of probability (combinatorial analysis and axioms of probability), conditional probability and independence, probability distributions, and provides introductions to handling data using descriptive statistics. This module uses R software package to clarify and illustrate theoretical concepts of probability, to show how random variables are generated and how they vary, to know how to construct appropriate diagrams for data summary.

Module aims

Descriptive statistics:
Data collection and summary. Stem/leaf plots and histograms. Measures of location (Mode, median, mean).

Measures of spread. Quartiles. Box plots. Variance and standard deviation. Transformations.

Relative frequency. Probability as a limit. Events. Union and intersection. Addition rule. Exclusive events. Independent events. Multiplication rule.

Permutations and combinations.

Conditional probability. Total probability theorem, Bayes' theorem.

Discrete probability distributions:

Discrete random variables. Probability distributions. Expectation. Algebra of expectations.

Variance. Bernoulli distribution. Binomial distribution (sampling with replacement).

Mean and variance of Bernoulli and binomial.

Poisson distribution (and applications).

Derivation of the Poisson. Approximation to the binomial.

Continuous probability distributions:

Density function as limit of histograms. Properties of probability density function (pdf). Cumulative distribution function (cdf). Uniform and exponential distribution. Expectations. Variance. Median, mode. Distributions of functions of random variables; change of variables formula

Normal distribution. Use of tables. Central limit theorem. Additivity.
Moment generating function;

Use of the R computer package to carry out statistical analysis.

Module learning outcomes

On completion of this module students should be able to: understand how to calculate and interpret simple summary statistics; how to choose and construct appropriate diagrams to illustrate data sets; use R for the data analysis examples of the course; understand and apply the addition rule and multiplication rule of probability; understand the basic ideas of conditional probability including the application of the total probability theorem and Bayes' theorem; understand and recognise situations appropriate for Binomial and Poisson models; calculate expectations and variances for discrete and continuous random variables, understand the ideas of probability density function and the distribution function; understand the change of variables formula and know how to calculate the distributions of functions of random variables; understand moment generating functions; recognise the central role of the normal distribution, be able to reduce normal random variables to standard form and be able to use tables of normal probabilities; understand the basic ideas of central limit theorem.

Module information


Descriptive statistics:

- Data collection and summary
- Stem/leaf plots and histograms
- Measures of location (mode, median, mean)
- Measures of spread
- Quartiles
- Box plots
- Variance and standard deviation
- Transformations


- Relative frequency
- Probability as a limit
- Events
- Union and intersection
- Addition rule
- Exclusive events
- Independent events
- Multiplication rule
- Permutations and combinations
- Conditional probability
- Total probability theorem
- Bayes' theorem

Discrete probability distributions:

- Discrete random variables
- Probability distributions
- Expectation
- Algebra of expectations
- Variance
- Bernoulli distribution
- Binomial distribution (sampling with replacement)
- Mean and variance of Bernoulli and binomial
- Poisson distribution (and applications)
- Derivation of the Poisson
- Approximation to the binomial

Continuous probability distributions:

- Density function as limit of histograms
- Properties of probability density function (pdf)
- Cumulative distribution function (cdf)
- Uniform and exponential distribution
- Expectations
- Variance
- Median, mode
- Distributions of functions of random variables
- Change of variables formula
- Normal distribution
- Use of tables
- Central limit theorem
- Additivity
- Moment generating function

Learning and teaching methods

This module consists of 30 contact hours consisting of 20 lectures and 10 classes. There are three revision lectures in the summer term.


  • Upton, Graham J. G.; Cook, Ian. (1996) Understanding statistics, Oxford: Oxford University Press.

The above list is indicative of the essential reading for the course. The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students. Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework   Homework 1     50% 
Coursework   Test     50% 
Exam  195 minutes during Summer (Main Period) (Main) 

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
0% 100%
Module supervisor and teaching staff
Prof Berthold Lausen, email:
Dr Dan Brawn
Professor Berthold Lausen (



External examiner

No external examiner information available for this module.
Available via Moodle
Of 47 hours, 30 (63.8%) hours available to students:
17 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information
Mathematical Sciences

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