Statistics Test Preparation

Types of Data

 Qualitative (categorical):  Data that a number can not describe

Nominal: named categories with no order
Ordinal: ordered, named categories 

Quantitative (numbers): Data that can be represented by a number value

Discrete: data that is based on observation and counting. Example: 3 cats, 7 dogs, 8 snakes.

Continuous: data that is collected by measuring. It can contain any numbers within a range. Examples: weight, height, temperature, and length.





⚠ The One Exception to Watch Out For Numerical Data

Just because a graph features numbers doesn't automatically make it numerical data. If the numbers are just labels or codes that can't be added or averaged, it is actually categorical data.

  • Examples of "Fake" Numerical Data: Zip codes (e.g., 90210), jersey numbers on athletes, or phone numbers. You can't mathematically add two zip codes together to get a meaningful number, so they act like categories or names.

How do outliers affect the data?

1. Mean (Average)

  • How it is affected: Heavily influenced.

  • Why: The mean adds up every single number in the dataset. Because an outlier is extremely high or extremely low, it drags the overall sum up or down. High outliers pull the mean higher; low outliers pull the mean lower.

2. Median (Middle Value)

  • How it is affected: Resistant / barely changes.

  • Why: The median only cares about the physical middle position of the data when it is lined up in order. Changing or adding an extreme value at the very top or bottom usually only shifts the median slightly (or not at all). 

3. Mode (Most Frequent Value)

  • How it is affected: Remains unchanged (usually).

  • Why: The mode is the number that appears the most times. Since an outlier is, by definition, an unusual, rare value, it is rarely the most frequently occurring number in the set. (Note: If an extreme value happens to be repeated multiple times, it could theoretically become the mode, though this is rare).

4. Range (Maximum minus Minimum)

  • How it is affected: Drastically increased.

  • Why: The range is calculated by subtracting the lowest number from the highest number (Max-Min). If the outlier is a high maximum or a low minimum, it instantly widens the distance between the top and bottom bounds of the dataset.

Number Peaks In Data                                

Unimodal, bimodal, and multimodal refer to the number of modes (the most frequently occurring values) in a set of numbers or data.

Unimodal

  • Definition: A distribution with one clear peak or mode where most data points cluster.

  • Real-Life Example: Heights of a specific group of adults, or exam scores where the majority of students earn a "B".

  • Meaning: The data represents a single, uniform population or a consistent behaviour. 

Bimodal

  • Definition: A distribution with two distinct peaks or modes representing two high-frequency groups.

  • Real-Life Example: Restaurant customer traffic with peaks at lunch and dinner, or software task times split between beginners and experts.

  • Meaning: The dataset combines two different underlying groups, populations, or patterns.

Multimodal

  • Definition: A distribution containing three or more peaks or modes.

  • Real-Life Example: E-commerce checkout completion times spread across mobile, tablet, and desktop users, or urban traffic peaking during morning commute, school pickup, and evening rush hour.

  • Meaning: The data reflects multiple distinct subgroups, behaviours, or preferences with no single dominant trend. 

Spot the ‘tricky’ words for the test

Mean: Average, shared equally

Median: Number in the middle, midpoint, halfway point of the sorted data

Mode: Frequency, most common/frequent, typical

Range: Difference, spread