Stats Key Info

Question 1

Population

Answer 1

Entire set of items (sampling units) in the group being studied.

Question 2

Census

Answer 2

Measuring every member of a population

Question 3

Evaluation - Census

Answer 3

+ Accurate
- Expensive
- Some testing destroys the item

Question 4

Sampling frame

Answer 4

List of sampling units

(It is not always possible to create this, thus can be a disadvantage of some techniques)

Question 5

Simple Random Sampling

Answer 5

Equal chance of being selected - done using random number generator/ lottery sampling alongside sampling frame.

Type of RANDOM Sampling

Question 6

Evaluation - Simple Random Sampling

Answer 6

+ Bias-free
- Sampling frame required

Question 7

Systematic Sampling

Answer 7

Taking every k^th unit (k = population / sample), pick random number between 1 and k for start point

Type of RANDOM Sampling

Question 8

Evaluation - Systematic Sampling

Answer 8

+ Quick to use
- Sampling frame required

Question 9

Stratified Sampling

Answer 9

Sample is proportionally representative of the strata (groups) of the population.
Formula: Sample / population x strata (for each strata)
(use either simple random/systematic to fill groups)

Type of RANDOM Sampling

Question 10

Evaluation - Stratified Sampling

Answer 10

+ Reflects Population
- Need clearly classified strata (groups) for population

Question 11

Opportunity Sampling

Answer 11

Sample based on who/what is available at the time.

Type of NON-RANDOM Sampling

Question 12

Evaluation - Opportunity Sampling

Answer 12

+ Easy, cheap
- Unlikely to be representative

Question 13

Quota Sampling

Answer 13

Similar to stratified sampling, but strata are filled by the researcher using opportunity sampling, thus are not necessarily representative of the population.

Type of NON-RANDOM Sampling

Question 14

Evaluation - Quota Sampling

Answer 14

+ No sampling frame needed
- Not random, potential bias

Question 15

Data Types

Answer 15

Qualitative: Non-numerical
Quantitative: Numerical

Types of Qualitative:
Discrete: Can only take certain values (often integers) => e.g. shoe size
Continuous: Can take any value in a range, must be grouped. => e.g. foot length

Question 16

Median (Location)

Answer 16

LQ: n/4 th term
Median: n/2 th term
UQ: 3n/4 th term

xth percentile = x/100 n th term
Decile = 10% Chunk = Percentile/10

Question 17

Mean (Location)

Answer 17

x̄ = ∑fx / ∑f (or ∑x / n)

Question 18

Variance (Spread) σ^2

Answer 18

(∑f)(x^2) / ∑f) - x̄^2
MSMSM
Mean of the Squares Minus Square of the Mean
(Also = Sxx / n)

Question 19

Coding

Answer 19

If y = ax + b…
then mean of y
= a(mean of x) + b

AND
σ of y = a x (σ of x)

Question 20

Linear Interpolation (Location)

Answer 20

Using the assumption that all data values are evenly spread throughout each class, using proportion to find how far through each class the data value should be.

Remember to add on the lower-class boundary after finding the correct data value.

e.g.
Class Limits: 12.5 Q1 15.5
|——–|—–|
Cumulative Freq.: 5 10 13

12.5 + (10-5 / 13 - 5) x 3 = 14.375 = Q2

Question 21

Sampling Units

Answer 21

Individuals of a population

Question 22

Finding Quartiles (Location)

Answer 22

n/4 or n/2 or 3n/4
If decimal: round UP ALWAYS
If whole number, find midpoint with next value.

Question 23

Outlier Boundaries (Representation)

Answer 23

Q1 - 1.5(IQR) or Q3 + 1.5(IQR)
(USUALLY)

Question 24

Interquartile Range (Spread)

Answer 24

Q3 - Q1
+ Ignores extremes

Question 25

Interpercentile Range (Spread)

Answer 25

e.g. 10th to 90th IPR P90 - P10

Question 26

Histograms

Answer 26

- Continuous Data - No gaps

Question 27

Frequency Density (Histograms)

Answer 27

Frequency / Class Width

Question 28

Area (Histograms)

Answer 28

Frequency x k

Question 29

Comparing Diagrams

Answer 29

3 Features Compare... 1) 1 measure of Location 2) 1 measure of Spread Use... 3) Context from question

Question 30

PMCC (Correlation)

Answer 30

Measure strength and +/- of correlation -1 ≤ r ≤ 1

Question 31

Regression Line

Answer 31

i.e. Line of best fit e.g. y = a + bx a = y when x = 0 b = how much y changes with x

Question 32

Interpolation (Regression)

Answer 32

Estimating inside the data range (usually using regression line) + Usually more reliable

Question 33

Extrapolation (Regression)

Answer 33

Estimating outside the data range (usually using regression line) - Usually less reliable

Question 34

Exponential/ Non-Linear Models

Answer 34

y = ab^x lny = lna + xlnb y = ax^n lny = lna + nlnx

Question 35

Normal Distribution

Answer 35

X~N(μ , σ^2) μ = Pop. Mean = np σ = SD = np(1-p) [For reference: BD: X~B(n, p)]

Question 36

Binomial Distribution

Answer 36

X~B(n, p) Rules: - Fixed number of trials, n - Trials are independent - Fixed probability of success, p - 2 possible outcomes (usually success/failure)

Question 37

Standard Normal Distribution

Answer 37

Z ~ N (0, 1^2) Z = (X - μ) / σ (Z = No. of SDs above mean)

Question 38

Z Distribution

Answer 38

-1 <=> 1 SD = 68% -2 <=> 2 SD = 95% -3 <=> 3 SD = 99.7%