Probabilities and Statistics

Last minute GG

1. Intro to stats

Four phases of a statistical study:

1. Data collection
2. Data analysis
3. Data presentation
4. Data interpretation

Definitions:

• population: everyone that you are interested in the study
• sample: some people you pick from population (because you cannot possibly ask everyone)
• variable: a characteristic of the population/sample
• parameter: a characteristic of a population
• statistic: a characteristic of a sample

Distinguish data types:

Level of measurement:

Sampling techniques:

• simple random
  • select randomly out of the whole group. Everyone has the same chance of being selected
• stratified
  • separated population into groups (strata) and random sample people in each group
• cluster
  • separate population into groups based on details (age, sex etc) and
    • randomly select the group (single stage)
    • randomly select the group and then randomly select people in the group (two stage)
• systematic
  • picking people from a list at equal steps, starting from a random point
• convenience (non-probability sampling)
  • use when you are lazy (choose a class to represent the whole school)

all sampling methods except for convenience sampling is considered probability sampling

Chart types:

• bar
• pie
• Pareto
  • both lines and bars
  • bars: individual values
  • lines: cumulative total
• scatter
• histogram
  • like bar chart but for continuous data
• dot
  • display distribution shape
• stem and leaf
  • to compare two samples
• box and whisker
  • display five number summary
  • min, q1, q2 (median), q3, max

You are cooked :(

2. Descriptive statistics

Frequency distribution table: a table of how many occurrences of each value

• ungrouped: use when having little different values
• grouped: use when having too many different values

Steps:

1. Find number of classes (5-20). If too many, use formula $\approx 1 + 3.3\log{n}$
2. Class width
   • $\frac{\text{largest value} - \text{smallest value}}{\text{number of classes}}$ then round up
   • or subtract the lower limit of two consecutive classes
3. Class limits
   • lower limit: choose smallest value in the set then add class width
   • upper limit: subtract one (or appropriate value) from the second class
4. Class boundaries
   • minus 0.5 (or 0.05) on the smallest value, then keep adding class width
5. Class mark (class midpoint)
   • average of lower and upper limit of one class

Frequencies:

• f.: how many times that class happened
• c.f.: keep adding previous f.
• r.f.: divide f. of that class by n
• r.c.f.: keep adding previous r.f.

Three Ms are all on the formula sheet

• Mean

  • Population: $\mu$
  • Sample: $\bar{x}$

• Median: middle value

  • if even, average of middle two

• Mode: most frequent

• Percentile: multiply with n and round up

• Quartile: P25 P50 and P75, round up

• Range: max - min

• Outlier: IQR = Q3 - Q1

  • 1.5 IQR more than Q3 or
  • 1.5 IQR less than Q1

• variance

  • calculate by hand with a table like this

And then population variance = $\sum x^2 P(x) - \mu^2$

Use calculator

Empirical rule is on the formula sheet, ez

3. Linear regression type

Bombed lowkey just read text book its not hard gang