Levels of Measurement
The amount of calories someone consumes in a morning.
What is ratio?
The symbol for population mean.
What is μ (mu)?
Events that cannot occur at the same time.
What are mutually exclusive events?
The type of statistics that makes predictions or generalizations.
What is inferential statistics?
The five-number summary consists of these values.
What are the minimum, Q1, median, Q3, and maximum?
A student ranking system (1st, 2nd, 3rd) is an example of this level of measurement.
What is ordinal?
The symbol for sample standard deviation.
What is s?
If P(A) = 0.4 and P(B) = 0.3 and they are mutually exclusive, what is P(A or B)?
What is 0.7?
If a normal distribution has a mean of 50 and a standard deviation of 5, what range contains the middle 95% of data (use empirical rule)?
What is 40 to 60? (Mean ± 2σ → 50 ± 10)
Find the IQR given Q1 = 25 and Q3 = 75.
What is 50? (IQR = Q3 - Q1 = 75 - 25 = 50)
This level of measurement includes zero as a meaningful absence of quantity.
What is ratio?
The symbol for population standard deviation.
What is σ (sigma)?
The sum of probabilities for all events in a sample space always equals this.
What is 1?
The difference between mean, median, and mode tells us about this property of a dataset.
What is skewness?
How do you determine outliers using IQR on a boxplot?
What is Q1 - 1.5 × IQR and Q3 + 1.5 × IQR?
This type of variable is purely categorical with no ranking.
What is nominal?
The symbol for sample variance.
What is s² (s squared)?
A bag has 3 red, 5 blue, and 2 green balls. What is the probability of picking a blue ball?
What is 5/10 or 0.5?
Chebyshev’s theorem is useful for datasets that are not this shape.
What is normally distributed?
When should you use IQR instead of standard deviation or range?
What is when data has outliers?
Temperature in Celsius is an example of this level of measurement.
What is interval?
The symbol for population variance.
What is σ² (sigma squared)?
Given P(A) = 0.6 and P(B) = 0.2, find P(A or B) if they are not mutually exclusive and P(A and B) = 0.1.
What is 0.7? (P(A or B) = P(A) + P(B) - P(A and B))
Experimental studies manipulate variables, while this type does not.
What is observational?
Given Q1 = 30, Q3 = 90, and an outlier threshold of 1.5 * IQR, find the lower and upper bounds for outliers.
What are -60 and 180? (Lower Bound = Q1 - 1.5×IQR, Upper Bound = Q3 + 1.5×IQR)