Z-scores, Z-score indexes and calculating using normal distribution Flashcards
(17 cards)
What are Z-scores?
Z-scores measure the number of standard deviations a datapoint is away from the mean
They apply only to continuous variables.
What do Z-scores help compare?
Individual values in the same or across different distributions
Even when these distributions have different means and standard deviations
How is a Z-score calculated?
Using the formula: z = (Xi - mean) / SD
What is the range of typical Z-scores?
Z-scores usually take values from -3 to +3
Positive indicates greater than the mean, negative indicates smaller than the mean.
What percentage of Z-scores lie between -2 and +2 standard deviations?
95.4%
Values outside this range are considered outliers.
What does standardisation mean in the context of Z-scores?
Putting observations from different distributions on the same scale
What Z-score indicates an outlier?
Z-scores below -3 and above +3
These are typically considered outliers.
What is the process to create a Z-score index?
Transforming variables into z-scores and combining them
This allows countries to be compared based on multiple indicators.
How do you calculate the Z-score index for a country?
Sum all the z-scores for a country and divide by the number of indicators
Invert the sign for negative indicators like income inequality.
What is the relationship between Z-scores and probability under the normal curve?
Z-scores can be used to find probabilities for normally distributed variables
Such as IQ scores.
What is the primary purpose of calculating Z-scores?
To compare scores across different distributions in a standardized way
This helps in understanding relative performance.
What is the first column of the z-score table (normal distribution table) used for?
The integer and first decimal of z-score
What is the first row of the z-score table (normal distribution table) used for?
The second decimal of z-score
True or False: The z-score table only shows positive z-scores.
True
How do you calculate probabilities from z-scores under the normal curve?
Draw a graph and mark the area you are looking for.
Calculate the z-score for both values.
Find both values on the nirmal distribution table.
calculate 1 - (value a + value b)
this is the probalility/proportion
How do you calculate z-scores from probailities under the normal curve?
Draw a graph and mark the area you are looking for.
Find the probability/proportion on the table and find the z-score on the normal distribution table.
Use the rearranged formula: 𝑋𝑖 = 𝑋 + (𝑍𝑖 × 𝑆𝐷)
this is the value the probability/proportion relates to
