Unit 4 Flashcards
density curves
mathematical models representing the distribution of our variables values
what can a smooth curve tell us?
the proportion of observations that fall below a certain value
what are the two important properties of density curves?
a density curve is always positive
(never falls below the x- axis, can have (-) y values)
has an area of 1 underneath it
(represents 100% of the data)
what is a uniform distribution between 0 and 1?
a density curve for which each number between 0 and 1 is equally likely
what is proportion?
area of a rectangle (normally in %)
how do you calculate the area of a triangle?
area = 0.5bh
what are 5 characteristics of a normal distribution?
bell shaped
symmetric
heavy in the middle and light on the ends
density curves, therefore never falls below the x-axis
has an area underneath equal to 1
how do you calculate the area of a triangle?
area = 0.5bh
what is a parameter?
any mathematical calculation performed on a population
what are the two parameters?
mean and standard deviation
what is μ?
mean (the center)
what is σ?
population standard deviation (how concentrated the distribution is about the mean
what are the two parameters?
mean and standard deviation
what is a statistic?
a mathematical calculation performed on a sample
the two parameters correspond to two statistics, what are they?
X̄ and s
what is X̄?
the sample mean that corresponds to μ
what is s?
the sample standard deviation that corresponds to σ
what is a big difference between μ and σ?
μ value can take any positive or negative value
σ value cannot be negative
how is this read?
X ~ N(μ, σ)
X is normally distributed with a mean of μ and a standard deviation of σ
what is the 68%, 95% and 99.7% rule?
a normal density curve will have approximately
68% of its data falling within 1 standard deviation from the mean
95% of its data falling within 2 standard deviations from the mean
99.7% of its data falling within 3 standard deviations from the mean
what does the standard normal table do?
gives us the area or proportion of observations from negative infinity to some value z, which is called a z-score
when an area is to the right, how do we write that proportion?
P(Z > z)
what will the proportion of observations at a certain point be?
ALWAYS ZERO
(lines don’t have any area)
