Variable Variety
these are the objects described by a set of data, which can be people, animals, or things.
What are individuals?
This acronym represents the four characteristics used to describe the overall pattern of a distribution of quantitative data.
SOCS (Shape, Outliers, Center, Spread)?
This measure of center is the "midpoint" of a distribution, where half the observations are smaller and half are larger.
What is the median?
This rule identifies an observation as an outlier if it falls more than 1.5 times the IQR above Q3 or below Q1.
What is the 1.5 × IQR rule?
For any density curve, the total area under the curve is always exactly equal to this.
What is 1?
This type of variable places an individual into one of several groups or categories.
What is a categorical variable?
This simple graphical display shows each data value as a point above its location on a number line.
What is a dotplot?
To calculate the Interquartile Range (IQR), you must subtract the first quartile (Q1) from this value.
What is the third quartile (Q3)?
This value, also called a standardized score, tells us how many standard deviations an observation falls above or below the mean.
What is a z-score?
According to the 68-95-99.7 rule, approximately what percentage of observations fall within 1 standard deviation of the mean in a Normal distribution?
What is 68%?
Which of the following is a quantitative variable? A) Zip Code, B) Eye Color, C) Annual Income, D) Gender.
C) Annual Income
When a distribution is described by this term, the right side of the graph (containing the larger values) is much longer than the left side.
skewed to the right
Explain what the standard deviation (sx) represents in the context of a specific data set.
The standard deviation measures the typical (or average) distance of the observations from their mean in that specific context.
This term describes the value in a distribution such that p percent of the observations are strictly less than it.
What is the pth percentile?
The Standard Normal distribution is a specific Normal distribution with a mean (μ) of 0 and a standard deviation (σ) of this.
What is 1?
This term describes the pattern of variation for a variable, specifically what values the variable takes and how often it takes them.
What is the distribution?
These two types of graphs are often preferred over histograms for small data sets because they allow the viewer to see the actual data values.
What are dotplots and stemplots?
This measure of center is calculated by summing all observations and dividing by the total count (n).
What is the mean?
Calculate the z-score for a data point of 10 in a distribution with a mean of 15 and a standard deviation of 2.
What is -2.5? ( z= 10-15 / 2 )
These curves are symmetric, single-peaked, bell-shaped, and described by their mean (μ) and standard deviation (σ).
What are Normal curves?
Which of the following would be considered a quantitative variable? A) Jersey Number, B) Telephone Area Code, C) Number of miles driven to school, D) Student ID number.
C) Number of miles driven to school? (Note: The others are categorical because it does not make sense to find an average Area Code or ID number).
In a histogram, this axis can display either the frequency (count) or this other value, which represents the proportion of data in each class.
What is relative frequency?
Explain why the mean is considered a non-resistant measure of center.
The mean is non-resistant because its value is calculated using the actual numerical value of every observation; therefore, it is pulled strongly toward any extreme values or outliers.
If a student's score on a test results in a z-score of 1.2, provide a full interpretation of this value.
The student’s score is 1.2 standard deviations above the mean score of all students who took the test.
In a Normal distribution, the distance from the mean to the points where the curve changes curvature (the inflection points) is exactly this.
What is one standard deviation (σ)?