Shifting data and what it affects
Adding or subtracting constant to every data value
Affects center and position (mean, median, ,in, max, Q1, Q2, Q3)
Rescaling data and what it affects
Multiply or divide data values by constant
Affects center, position, spread (mean, SD, median, range, min, max, Q1, Q2, Q3)
Calculate z-score / standardization
(y-μ) divided by σ
No units
Meaning of positive and negative and 0 z-score value
Positive –> ___ SD above mean
Negative –> ___ SD below mean
0 –> observation exactly on mean (no
deviation)
What does z-score affect
Changes spread (SD=1) and center (mean=0)
What does the total area between horizontal axis and under density curve equal to?
One
Is P(x=a) = 0 true with continuous or discrete variables?
Continuous variables
Empirical (68-95-99) rule
68% observations fall within 1 σ of mean μ
95% observations fall within 2 σ of mean μ
99% observations fall within 3 σ of mean μ
Finding area under standard normal curve
Given z = number
Look at z-table and find required number
Finding area under standard normal curve when given number has three places after decimal
- Find required number using third decimal place
- Find required number using second decimal place
- Add answers from step 1 and 2 and divided by 2
When given number not on z-table?
Lowest possible value
When to change inequality sign?
When finding right side of standard normal curve
If positive change to negative and vic versa
Finding area under standard normal curve between two numbers
- Find both numbers on z-table
- Subtract numbers
Finding area under standard normal curve between two large numbers
P (a < y < b)
= P (a-μ / σ < a-μ / σ < a-μ / σ)
= P (a* < z < b)
= P (z < b) - P (z < a*)
- (y-μ) divided by σ for both numbers
- Find numbers on z-table and subtract them
Given probability, not z-score and determining smallest percentage for normal standard distribution
Find corresponding z-score by finding probability number in z-table
Given probability, not z-score and determining largest percentage for normal standard distribution
- Switch > to <
- Determine new probability
–> 1 - decimal of
percent - Find two closest numbers to new probability on z-table
- Add both numbers up found on z-table and divide by 2
Given probability, not z-score and determining middle percentage for normal standard distribution
- Determine new probability
–> 1 - decimal of
percent / 2 - Find closest number to new probability on z-table
- Invert sign (switch negative to positive)
Given probability, not z-score and determining smallest percentage for NOT normal standard distribution
- Find corresponding z-score by finding probability number in z-table
- y = μ + zσ
