Econo test 1

mean

the average of a set of numbers

Median (even sample size)

Median (odd sample size)

Mode

Most frequent occurring number

Finding percentile of a value

Quartile value

Interquartile Range (IQR)

IQR= Q3 - Q1

Empirical Rule (for bell-shaped, symmetric data)

Multiplication Rule (Joint Probability

Nominal

Pure labels, categories, or names. No inherent order, and numbers are just identifiers.

University degree name, hair color, school attended

ordinal

Categories with a meaningful rank or order, but the numerical distance between them is not defined.

• Examples: Product ratings (1 = Poor, 2 = Average, 3 = Good), class standing (Frosh, Soph, Junior, Senior), survey satisfaction.

Discrete variable

Discrete values have gaps between them.

• They are almost always whole numbers ($0, 1, 2, 3\dots$). You cannot have fractions or infinite decimals in between.

• The Test: Ask yourself, "Can this value be 2.37841?" If that makes no sense, it is discrete.

• Examples from your exam & real life:

  • Number of customer complaints in a day (you can have 1 or 2 complaints, but never 1.47 complaints).

  • Number of cars sold by a dealership.

  • Number of students in a lecture hall.

  • Number of defective light bulbs in a box.

Continuous variable

Measurable values that can take on decimals/fractions over an interval.

• Continuous values have no gaps. They can take on any value within a range or interval—including infinite decimals.

• They depend on how precise your measuring tool (stopwatch, scale, ruler) is.

• The Test: Between any two numbers (like 5 and 6), can you always find another number in between (like 5.5, 5.55, 5.555)? If yes, it is continuous.

• Examples from your exam & real life:

  • Time: Time spent waiting in a drive-thru (e.g., $4.25$ minutes, $4.258$ minutes).

  • Money / Financial amounts: Monthly electricity bill ($142.36), stock return percentages ($3.14\%$).

  • Physical measurements: Height, weight, distance, temperature.

Histogram graph

Pareto Diagram

Chebyshev's Theorem

Z-scores

Covariance

Correlation Coefficient (r)

Expected value of a discrete random variable $X$

right skew

right is the tail and the bump is left side (mean>median> mode

Left skew

The tail is the left side the bump is the right (mean<median<mode

Empirical Rule

What does the sample correlation coefficient ($r$) measure, and how do you interpret its value?