Comparing Data Distributions Practice

Answer 1

1. Normal Distribution vs. Skewed Distribution:
- A normal distribution is symmetric and bell-shaped, with the mean, median, and mode all being equal. In contrast, a skewed distribution is asymmetrical, with the tail pointing towards the side with fewer data points.
- Examples of normal distributions include heights of people in a population, while examples of skewed distributions include income levels or exam scores.
- In a normal distribution, approximately 68% of data falls within one standard deviation of the mean, while in a skewed distribution, this might not hold true due to the skewness.

2. Discrete Distribution vs. Continuous Distribution:
- A discrete distribution consists of discrete random variables with finite or countable outcomes, while a continuous distribution consists of continuous random variables with an infinite number of possible outcomes.
- Examples of discrete distributions include the number of students in a class or the number of outcomes on a dice, while examples of continuous distributions include weight or height measurements.
- Probability mass function (PMF) is used to describe a discrete distribution, while probability density function (PDF) is used to describe a continuous distribution.

3. Uniform Distribution vs. Exponential Distribution:
- A uniform distribution has a constant probability over a defined range, where all outcomes are equally likely. In contrast, an exponential distribution describes the time between events in a Poisson process.
- An example of a uniform distribution is rolling a fair dice, where each outcome has an equal probability of occurring. An example of an exponential distribution is the time between goals scored in a soccer match.
- The probability density function for a uniform distribution is a horizontal line, while the probability density function for an exponential distribution is skewed to the right.