2.8 Distributions and Probability Flashcards
What are the learning outcomes for the Psych 1B lecture?
Students should be able to:
* Identify a normal distribution and diagnose different types of skew
* Understand basic probability theory and the link with distributions
* Calculate basic probabilities
Learning outcomes outline the skills and knowledge students are expected to acquire by the end of the lecture.
What are the four levels of measurement?
The four levels are:
* Nominal: Non-ordered categories
* Ordinal: Ordered categories like Likert scale responses
* Interval: Continuous data with meaningful intervals but no true zero
* Ratio: Continuous data with meaningful intervals and a true zero
Levels of measurement define the nature of data and the statistical techniques applicable.
Define the term ‘mean’ in statistics.
The average value
* Sensitive to outliers
The mean is calculated by summing all values and dividing by the number of values.
What is the median in statistics?
The middle data point
The median is the value separating the higher half from the lower half of the data set.
What does the mode represent in a dataset?
The most frequent data point
* Very crude measure
The mode is useful for categorical data where we wish to know which is the most common category.
What is standard deviation?
On average, how much each score differs from the mean
* Square root of the variance
Standard deviation is a measure of the amount of variation or dispersion in a set of values.
True or False: A positive skew indicates that most values are clustered at the high end of the scale.
False
A positive skew indicates that most values are clustered at the low end of the scale.
What does skewness measure in a distribution?
Asymmetry in distributions
Skewness indicates the direction and degree of distortion from the symmetrical bell curve of a normal distribution.
What is the difference between platykurtic and leptokurtic data?
Platykurtic data: More dispersed distribution
Leptokurtic data: More peaked distribution
Kurtosis describes the shape of a distribution’s tails in relation to its overall shape.
What is the probability range in statistics?
Probability runs from 0 to 1
* 1 indicates 100% probability
* 0.5 indicates 50% probability
* 0.05 indicates 5% probability
Probability quantifies the likelihood of an event occurring.
Fill in the blank: The probability of a new Pokémon trainer choosing Squirtle is _______.
1/3 = 0.33 = 33.33%
This example illustrates how to calculate basic probability in a given scenario.
What is the empirical probability of a randomly selected Psych 1B student being taller than Emily?
89.72%
This probability is calculated based on the number of students taller than Emily in the sample.
What does a normal distribution look like?
A mathematically defined, theoretical distribution with a bell shape (Gaussian distribution)
* Symmetrical on its middle axis
* Mean, median, and mode are the same
Normal distributions are common in statistics and many natural phenomena.
What percentage of scores lie within -1 SD and +1 SD in a normal distribution?
68%
* 68.26% to be precise (34.13% + 34.13%)
This is a key property of the normal distribution that helps in understanding standard deviations.
True or False: In a negatively skewed distribution, the mean is less than the median.
True
In a negatively skewed distribution, the mean is pulled towards the lower end of the scale.
What does the central limit theorem state?
As sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution
This theorem is fundamental in statistics, allowing for the use of normal probability techniques.
What is the probability of the first trainer choosing Bulbasaur and the second trainer choosing Squirtle without replacement?
1/3 * 1/2 = 0.17 = 17%
This calculation demonstrates the concept of conditional probability.
List the key terms related to distributions and probability.
Key terms include:
* Normal distribution
* Skew
* Positive skew
* Negative skew
* Kurtosis
* Leptokurtic
* Platykurtic
* Empirical probability
Understanding these terms is essential for grasping statistical concepts.
