Ch. 2 Stats Vocab

percentile

statistical measure of a distribution; a value for which a given percentage of values may fall

• p% of observations = less than or equal to value

cumulative relative frequency graph/ogive

plots a point corresponding to the percentile of a given value in a distribution of quantitative data; different depiction of histogram’s data

• beginning of first interval = zero

• end of interval = CUMULATIVE y-value

• points are connected with line segments

additive linear constant

x̅_new = x̅_old + C

Sx_new = Sx_old

• no change to shape

• no change to variability

• changes measures of center + location

multiplicative linear transformation

x̅_new = C · x̅_old

Sx_new = C · Sx_old

• no change to shape

• changes to center + location + variability

density curve

graphical representation of a numerical distribution where outcomes are continuous; idealized model for distribution of quantitative variable

• lies above or on horizontal line

• area underneath represents probability

• area under = 1

mean of density curve

balance point: point at which the curve would balance if made of solid material

• influenced by skews

median of density curve

equal-areas point: point that divides the area under the curve in half

• not impacted by skews

mu

mean of population

sigma

standard deviation of population

normal distributions

all types have same characteristics

• shape: bell-shaped, unimodal, symmetric

• mean = median; midpoint of symmetric density curve

• standard deviation is the measure of variability

empirical rule

estimate of the proportion of observations

• 68 - 95 - 99.7 rule

• (0.15% - 2.35% - 13.5 - 68% - 13.5% - 2.35% - 0.15)

• division by multiples of standard deviation

notation for normal curve

N(mean, standard deviation)

z-score/standardized score

how many standard deviations from the mean an observation falls + what direction

• (value - mean)/standard deviation

• MUST ALWAYS INDICATE GREATER OR LESS THAN MEAN

positive z-scores

values larger than mean

negative z-scores

values smaller than the mean

standard normal distribution

a normal curve where

• mean = 0

• standard deviation = 1

proper z-score work

• has a probability statement; P(z < __)

• has a sketch of the normal curve + shaded region of interest

below z-score of

P(z < a) = b

above a z-score of

P(z > a) = b

• 1 - P(z < a) = b

between two z-scores

P(a < z < b) = c

• P(z < b) - P(z < a) = c