Stat 1 chapter 3
S1: Find the Mean, S2: Subtract the mean from each of the measurements, S3: Square each difference, S4: Add together each value, S5: Dividing by "n-1"
What are the steps for sample variance, s^2?
it is less than the mean
What does a negative z-score mean?
it is greater than the mean
What does a positive z-score mean?
It describes the length of the interval that contains the middle 50% of the measurements.
What does the interquartile range describe?
25 percentile
What is the 1st quartile?
50 percentile
What is the 2nd quartile?
75 percentile
What is the 3rd quartile?
100(1-1/k^2)
What is the Chebyshev's Equation?
[u-o,u+o]
What is the empirical rule equation?
Q3-Q1
What is the equation for a interquartile range?
z=x-mean/standard dev.
What is the equation for z-score?
Range
the measurements of the largest measurement minus the smallest measurement
Sample variance
the point estimate of the population variance
What is a normal curve?
A bell shaped curve
Take the root of sample variance
How do you find the sample Standard Deviation?
S1: arrange in order, S2: index, S3: (a) If "i" is not an integer (whole number), round up to next integer. That number decides the pth position. (b) if "i" is a integer(whole number) choose the # and the # after, then find the average.
What are steps for percentiles?
S1: Find the Mean, S2: Subtract the mean from each of the measurements, S3: Square each difference, S4: Add together each value, S5: Divide by "n". S6: Take square root of answer
What are the steps for Standard Deviation?
S1: Find the Mean, S2: Subtract the mean from each of the measurements, S3: Square each difference, S4: Add together each value, S5: Divide by "n".
What are the steps for population variance?
Tolerance Interval
an interval that contains a specified percentage of the individual measurements in a population
The empirical rule
applies to only normally distributed populations , mound-shaped (single peaked) distributions that are not very skewed to the right or left.
Population parameter
is a number calculated using the population measurements that describes some aspect of the population.
Population Standard Deviation
o, is the positive square root of the population variance
Population Variance
o^2, is the average of the squared deviations of the individual population measurements from the population mean.
Chebyshev's Theorem
practical for analyzing non-mound shaped populations since empirical rule will not hold true. Population that is very skewed.
Z-Score
tells the location of a measurement in a population by calculating the number of standard deviations the measurements is from the mean.
