Percentiles
Z Scores
Linear Transformations
Empirical Rule
Experiments and Studies
100
If I tell you that you scored at the 55th percentile on your final exam, you would know that...
55% of the class scored the same or worse than you did
OR
You scored the same or better than 55% of the class.
100
What is the formula to find the z-score of a data point?
z = (x - μ ) / σ
100
This feature of a distribution stays the same no matter what linear transformation is applied to the data set.
Shape
100
Another name for the empirical rule is...
The 68-95-99.7 Rule
100
Randomly assigning individuals to treatment distinguishes this from an observational study.
What is an experiment?
200
The 50th percentile is also know as the
median
200
The number of standard deviations x is away from the mean.
What is the z-score of x
200
If you standardize all values in a distribution, what would the new mean and standard deviation be?
Mean: 0
SD: 1
200
What percent of data is within 1 standard deviation from the mean?
68%
200
A fake treatment (like a sugar pill)
What is a placebo?
300
The 75th percentile is also known as...
Q3
300
Rebecca is a 800m runner. Rebecca's time for her last meet had a z-score of 2.76. Interpret Rebecca's z-score.
Rebecca's time was 2.76 standard deviations slower the mean.
300
The distribution of raw scores on a particular achievement test has a mean of 500 and a standard deviation of 80.
If each score is increased by 25, what will be the mean and standard deviation of the distribution of new scores?
Mean: 525
SD: 80
300
What percent of data is within 3 standard deviations of the mean?
99.7%
300
The treatment that the control group receives
None or a placebo
400
If you score a 80% on a test, does this mean you are in the 80th percentile? Why or why not?
No - reasoning may vary...
400
The shaded part of the graph above (mean = 0 and standard deviation = 1) represents this.
What is data that is one or more standard deviations above the mean?
400
The reason that adding a constant to all values in a data set will not effect the standard deviation
Spread is unaffected by shifts.
400
What percent of data is greater than 3 standard deviations away from the mean?
0.3%
400
Give an example of why correlation does not imply causation
Answers may vary...
500
The percentile represents the...
percent of data values that are below.
500
At a local high school, GPAs are normally distributed with a mean of 2.9 and standard deviation of 0.6. What is the z-score for the 80th percentile?
0.84
500
Assume you have a data set with a mean of X. You multiply every value in this dataset by b and then add a to every value. The new mean is
a+bX
500
The height of plants in a certain garden are normally distributed with a mean of 28 inches and a standard deviation of 5 inches.
Use the Empirical Rule to estimate what percentage of plants are greater than 23 inches tall.
84%
500
While useful, why do retrospective observational studies often produce conclusions that are not generalizable?
Multiple answers: -hindsight is 20/20, -lack of random assignment, etc.