Shift and Scale
Adding 5 to the mean would change the median by this value.
5
This percentile is the value below which 50% of the data fall.
50th percentile.
The Z-score tells how many “blank” the observed value is from the mean.
Standard deviation(s).
In any density curve, this is always the total area under the curve.
1
A normal model is called a normal model because its values are ___?
Approximately normally distributed
A teacher records the quiz scores (out of 10 points) for a class and then decides to adjust all the scores by adding 2 points to each student’s original score. What statistic of the test scores will increase?
The center.
This term is used to describe the range between the 25th and 75th percentile.
IQR (inner quartile range)
If you have a sample mean of 20, observed mean of 10, and a SD of 5 in a given distribution, this would be the z-score.
-2
If the distribution is approximately normally distributed. What measure of variation should we use?
What are two essential characteristics of a normal model?
Bell-shaped and symmetrical
If we have a set table of values and we add or subtract from the original values. The distribution will look ______
True or False: If we add or subtract to the original value, the percentile will change.
False
A student scores 82 on a test with a mean of 75 and a standard deviation of 5. What is the z-score?
z = 1.4
If the distribution is skewed, what center should we use?
Median.
Name all three major percentages in the normal model (aka the empirical rule).
68%, 95%, 99.7%
This type of transformation changes both the center and spread of a distribution.
Multiplying or dividing by a constant.
A high school administered a standardized math test to 500 students. The scores were approximately normally distributed with a mean of 72 and a standard deviation of 8. How many students scored above the 90th percentile?
50 students.
The heights of adult women in a population are approximately normally distributed with a mean of 64 inches and a standard deviation of 2.5 inches. A woman who is 68 inches will yield a z-score of 1.6. What does this mean (interpret)?
She is 1.6 standard deviations above the mean.
What is the point that divides the area under the curve in half called?
The median.
In a normal model, this is the percentage of the distribution that lies outside of 3 standard deviations.
About 0.03%.
This transformation technique is often used to make a distribution with skewed data more symmetric.
Taking the log.
Scores: 40, 40, 42, 50, 65, 71, 73, 84, 91, 93
If Bob scored a 65 on the test, what percentile is he in?
50th percentile.
Assume test scores are normally distributed with a mean of 75 and a standard deviation of 10. What percentage of students scored above 85?
15.9% of students.
What is always true for a density curve?
The total area under the curve is 1.
What theorem is used to see if a normal model can be used?
The central limit theorem.