Standardizing Data and the Normal Distribution Part 1 by David Spade, PhD

About the Lecture

The lecture Standardizing Data and the Normal Distribution Part 1 by David Spade, PhD is from the course Statistics Part 1. It contains the following chapters:

Standardizing Data and the Normal Distribution
Shifting Data
Rescaling Data
The Normal Distribution
The Empirical Rule
The Z-Table
Using the Z-table in reverse

Included Quiz Questions

What is an example of a shift in a data set that was provided in the video?

A shift of a data set means adding the same constant to each observation.
A shift of a data set means that each observation is multiplied by the same constant.
A shift of a data set means that each observation is squared.
A shift in a data set is the addition of a constant followed by the subtraction of a variable number.
A shift in a data set is the addition of a variable number.

Why do we standardize data?

We standardize data in order to ensure that all variables are on the same scale.
We standardize data in order to make the distribution more symmetric.
We standardize data in order to get rid of outliers.
Data standardization is common practice.
We standardize data in order to ensure that no variables are on the same scale.

What does the empirical rule tell us?

The empirical rule tells us that for data that comes from a normal distribution, about 68% of the data lie within one standard deviation of the mean.
The empirical rule tells us that for any data set, about 68% of the data lie within one standard deviation of the median.
The empirical rule tells us that all data come from a normal distribution.
The empirical rule states that 95% of the data lie within three standard deviations.
The empirical rule states that 68% of the data lie within three standard deviations.

What describes an appropriate use of the z-table?

The z-table is used to find probabilities associated with the normal distribution by finding the z-score in the margins of the table and looking up the probability in the associated cell in the body of the table.
The z-table is used to find probabilities associated with any data set after the data values have been standardized.
The z-table is used to find probabilities associated with the normal distribution by finding the z -score in the body of the table and then looking for the probability in the margin.
The z-table is a way to standardize data.
The z-table is used to evaluate skewed data set by finding the z-score and looking at the probability in the margin.

How can we assess whether our data are roughly normally distributed?

A unimodal, symmetric histogram with a linear probability plot is roughly normal.
We can look at a histogram, and if the histogram is skewed or has multiple modes, we can conclude our data are normal
We can look at a normal probability plot, and if the plot shows a non-linear pattern, we can conclude our data are normal.
We can look at a normal probability plot, and if the plot shows random scatter, we can conclude our data are normal
A logarithmic probability plot is roughly normal.

Suppose the mean STAT score is 80 and the standard deviation is 10. What is the z-score for a STAT score of 75?