3.1 Flashcards
symmetric distributions
shows mirror symmetry about the centre
uniform distribution
each outcome has a similar frequency, each outcome appears equally likely to occur, distribution is symmetric, no mode, median/mean in the middle
mound shaped distribution (normal, bell, gaussian)
each outcome has a decreasing frequency from the middle or interval with the greatest frequency, distribution is symmetric, median mean mode all in middle
u shaped distribution
frequencies are greater at the end intervals (bimodal) distribution is symmetric, a bimodal distribution may suggest another population group within the larger group, median/mean in middle, mode at the ends
skewed distribution
asymmetrical distribution where the direction denotes skew type, right skewed has a tail to the right, left skewed has a tail to the left, mode doesn’t have have to be on the opposite tail
right skewed
mode at peak, mode then median then mean, tail to the right, x̅ > med
left skewed
mode at peak, mean then median then mode, tail to the left, x̅ < med
pearsons index of skewness
PI = [3(x̅ - median)]/s
sample stdev
s = √(∑(x-x̅)^2)/n-1
if |PI| ≥ 1
then the data is significantly skewed
if PI ≥ 1
then the data is right skewed
if PI ≤ - 1
then the data is left skewed
PI ≈ 0
means x̅ ≈ med, symmetric, not normal recess, could be uniform, mound, u-shaped
outlier
data value is considered an outlier if the value is 1.5(IQR) below Q1 or 1.5(IQR) above Q3
IQR
interquartile range, the difference between Q3 and Q1
reason for outliers
valid data obtained by chance, mistake in data process (measurement or observation error), sample size not large enough, improper sampling (incorrect population), recording error/transposition error
outlier for normal distribution
outlier if it’s 3 or more stdev away from the x̅
