Chapter 2 Flashcards
percentile, z-score, empirical rule
percentile
the percent of data less than or equal to a certain data value
z-score (definition)
how many standard deviations a data point is above/below the mean
z-score (formula)
data point minus mean over standard deviation
positive z-score
above the mean, data value greater than mean
negative z-score
below the mean, data value less than mean
adding or subtracting every data value by a constant
center-add/subtract by constant
spread-same
shape-same
multiplying or dividing every data value by a constant
center-multiply/divide by constant
spread-multiply/divide by constant
shape-same
the normal curve
symmetric, unimodal, bell shaped, mean=median
the empirical rule
within one standard deviation on either side of the mean is 68% of the data, 2 standard deviations 95%, 3 standard deviations 99.7%
empirical rule intervals (min -3, -3 -2… 3 max)
0.15, 2.35, 13.5, 34, 34, 13.5, 2.35, 0.15
normal curve problems
- draw and label curve with mean, standard deviation, ticks
- do calculations (SHOW WORK!)
- answer the question with context
mean of z-scores is…
always 0
standard deviation of z-scores is…
always 1
normalcdf
put in upper/lower bounds and mean/SD (0 and 1 for z-score, real numbers for real numbers) to get area/percentile
invNorm
put in area (percentile, decimal) and mean/SD (0 and 1 for z-scores, real numbers for real numbers) to get equivalent z-score or x value