# MATH07038 2019 Statistics and Numerical Methods

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**Description**

Apply statistical and probability techniques to present and analyse data. Use numerical techniques to find approximate solutions.

This module will be approximately 8 weeks in duration due to work placement.

### Learning Outcomes

*On completion of this module the learner will/should be able to;*

**1.**

Compute the mean, median, mode, range, interquartile range, standard deviation and variance of data

**2.**

Calculate the probability of simple events and the probability associated with normal and binomial distributions

**3.**

Use sampling techniques to form confidence intervals and carry out hypothesis tests

**4.**

Plot a mean and range control chart and use it to test for statistical control

**5.**

Find correlation coefficients and regression equations

**6.**

Construct a function to fit data points using interpolation and extrapolation.

**7.**

Approximate the area under a curve

**8.**

Find numerical solutions of equations using the Newton-Raphson method

### Indicative Syllabus

Organisation and presentation of data

Measurement of central tendency: mean, median, mode

Measurement of dispersion: range, interquartile range, variance and standard deviation

Cumulative frequency curve

Probability Laws: independent and dependent events, addition and multiplication laws.

Probability distributions including normal and binomial distributions

Sampling Theory

Control Charts

Regression analysis and correlation

Curve Fitting

Numerical solutions of equations using Taylor's theorem, Newton-Raphson method

Approximate the area under the curve

### Coursework & Assessment Breakdown

**Coursework & Continuous Assessment**

**End of Semester / Year Formal Exam**

### Coursework Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
---|---|---|---|---|---|---|

1 | Continual Assessment | Continuous Assessment | Assessment | 20 % | OnGoing | 1,2,3,4,5,6,7,8 |

### End of Semester / Year Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
---|---|---|---|---|---|---|

1 | Final Exam Written Examination | Final Exam | Closed Book Exam | 80 % | End of Term | 1,2,3,4,5,6,7,8 |

### Full Time Mode Workload

Type | Location | Description | Hours | Frequency | Avg Workload |
---|---|---|---|---|---|

Lecture | Flat Classroom | Theory | 5 | Weekly | 5.00 |

Tutorial | Not Specified | Tutorial | 1 | Weekly | 1.00 |

Independent Learning | UNKNOWN | Review Course Work | 4 | Weekly | 4.00 |

### Part Time Mode Workload

Type | Location | Description | Hours | Frequency | Avg Workload |
---|---|---|---|---|---|

Lecture | Flat Classroom | Theory | 5 | Weekly | 5.00 |

Tutorial | Not Specified | Tutorial | 1 | Weekly | 1.00 |

Independent Learning | Not Specified | Review course work | 4 | Weekly | 4.00 |

### Module Resources

**Non ISBN Literary Resources**

James Reilly, Using Statistics, Gill and Macmillan

Stroud: "Engineering Mathematics", any edition

**URL Resources**

James Reilly Applied Statistics e-book:

http://www.statisticalsolutions.ie/wp-content/uploads/2013/03/APPLIED-STATISTICS-ebook.pdf

**Other Resources**

www.mathcentre.ac.uk

www.khanacademy.org

IT Sligo Maths Support Centre