Lecture 11: Statistics Theory

Question 1

What does Statistic Mean?

Answer 1

It is the branch of mathematics associated with:

• collecting and analysing data to describe things
• interpret things
• predict things

Question 2

Who uses statistics and why??

Answer 2

People who purposefully collect data, and want to understand the information they have collected.

1. Government: Collect for population info.
   
   1. size, structure and distribution
   2. changes in these values over time (birth, migration, age)
2. ​Scientists: related to experiments and use to try to understand situations
   
   1. ​relationships between treatments and outcomes
   2. correlation between causes and effects
3. Engineers: regarding performance of a material under certain conditions
   
   1. mean time to failure
   2. stress testing/ load rating
   3. reliability
4. Managers: to make informed decisions
   
   1. return on investments
   2. rostering

Question 3

What are the two main branch of statistics?

Answer 3

1. Inferential
2. Descriptive

Question 4

Explain Descriptive Statistics

Answer 4

• Statistics used to summarise or describe the main characteristics or a set of data
• e.g. average daily temperatures (max/min)
• useful for analysing sets of data to understand what the data shows or to enable comparisons

Question 5

Inferential statistic

Answer 5

• useful for decision making when a data for the entire population is unavailable
• make conclusions about characteristics of a population based on characteristics of a “random sample” selected
• e.g. aim: quality assurance - proportion of defective items in a batch estimated based on results of a selected sample

Question 6

What does the term Variable mean?

Answer 6

A characteristic of interest that can take different values. Can be either Discrete or continuous.

Question 7

What is Discrete variable?

Answer 7

the set of possible outcomes is countable

Question 8

what is continuous variable?

Answer 8

the outcomes can take values on a continuous scale

Question 9

What does the term population mean?

Answer 9

all members of the group

Question 10

What does the term parameter mean?

Answer 10

a numerical characteristic of a population

Question 11

What does the term sample mean?

Answer 11

a subset of the population

Question 12

What does the term subsample mean?

Answer 12

a subset of the sample

Question 13

What does the term statistic mean?

Answer 13

a characteristic of a sample or subsample

Question 14

Explain Descriptive Statistic

Answer 14

How do you organise large data?

1. Organise Data
   
   1. a frequency distribution table
   2. high and low value are easy to distinguish
   3. common values are obvious
   4. easy to perform calculations
   5. frequency values might indicate the shape of the distribution
2. Graphic representation
   
   1. bar chart
   2. table
   3. frequency polygon

Question 15

What is the formula for probability distribution?

Answer 15

Relative frequency = score frequency / total number of scores

Question 16

Describing Distributions. What are some terms to consider?

Answer 16

• Measures of central tendancy
  
  • arithmetic mean (average)
  • median
  • mode
• measures of dispersion
  
  • range
  • variance
  • standard deviation
• common shapes of distribution
  
  • symmetric
  • skewed

Question 17

Explain all three Central Tendencies.

Answer 17

1. Mean: add all elements/ total of elements
2. Median: middle number
   
   1. if there are two: add and divide by 2
3. Mode: Most occurring
   
   1. bimodal: two number occur same amount

Question 18

Explain Dispersion terms:

Answer 18

Dispersion: how dispersed data is

• range: Large - smallest. the difference
• variance: calculates how much each value deviates from mean
• deviation: difference between a score X and mean
• standard deviation: the square root of a variance

Question 19

What is symmetric? List the three examples of symmetric shapes.

Answer 19

Symmetric: shape can be folded along a vertical axis so the two sides coincide

• rectangular
• uniform
• bell-shaped

Question 20

What is skewed? give examples.

Answer 20

Skewed: a non symmetric shape

• J curve
• Gamma distribution

If positive skewed. Mean is greater then Median

if Negative skewed. Mean is Less then Median

Question 21

List two main common distributions. Give a brief explanation.

Answer 21

1. Binomial - applies to discrete variables
   
   1. family distribution where:
      
      1. n = number of samples
      2. p = probability of success
2. Normal - applies to continuous random variables
   
   1. family distribution
      
      1. mean
      2. standard deviation

Question 22

Principles of inferential statistics.

Answer 22

we begin with a sample of data points and try to determine the distribution of the rest of the population.

Question 23

what does estimation mean

Answer 23

is the process of summarising a sample to only describe it wih a characteristic

Question 24

confidence intervals:

Answer 24

are used to quantify how confident we are about our estimations

Question 25

hypothesis testing

Answer 25

uses a sample data to evaluate the credibility of a claim about the population

• is an assumption about the population parameters
• it might not be true - we use experimental data to decide.