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AP Stats [Ch.2]
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What is a density curve?
a curve that is always on or above the x-axis and has area exactly 1 underneath it
What does the area under a density curve represent?
the proportion of all observations that fall in that range
Where is the median of a density curve located?
median is the equal-areas point. Half the area under the curve is to the left, the other half of the area is to the right
Where is the mean of a density curve located?
mean is the balance point of the density curve
What is the difference between the randInt and rand commands on the TI-83?
randint(a, b) returns a random integer between a and b ; rand returns a random number between 0 and 1
How would you describe the shape of a normal curve?
Symmetric, single-peaked, bell-shaped
Where on the normal curve are inflection points located?
at ± σ. (These are the points where the curve changes concavity.)
Explain the 68-95-99.7 rule
This rule states that for a normal curve, 68% of the data lies between ± 1 σ, 95% of the data lies between ± 2 σ, and 99.7% of the data lies between ± 3 σ.
What is a percentile?
the value such that p% of the observations fall at or below it ; used when we are most interested in seeing where an individual observation stands relative to the other individuals in the distribution
Is there a difference between the 80th percentile and the top 80%? Explain.
Yes, The 80th percentile means 80% of the data values are equal or below. The top 80% means 80% of the values are equal or above
Is there a difference between the 80th percentile and the lower 80%? Explain.
No, these are the same
Explain how to standardize a variable
z-score = (x - u) / σ
What is the purpose of standardizing a variable?
tells us how many standard deviations the original observation falls away from the mean, and in which direction
What is the standard normal distribution?
A normal distribution with mean 0 and standard deviation 1
What information does the standard normal table give?
The table entry for each value z is the area under the curve to the left of z
Describe two methods for assessing whether or not a distribution is approximately normal
1) Construct a frequency histogram or stemplot. See if the graph is approximately bell-shaped and symmetric about the mean.
2) Construct a normal probability plot. If the data distribution is close to normal, the plotted points will lie close to a straight line. (Nonnormal data will show a nonlinear trend)
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