Chapter 2 - Describing Location in a Distribution Flashcards
add the counts in the frequency column for the current class and all classes with smaller values of the variable
cumulative frequency column
value with p percent of the observations less than it
pth percentile
divide the entries in the cumulative frequency column by the total number of individuals. multiply by 100 to convert to a percent
cumulative relative frequency column
divide the count in each class by the total number of individuals. multiply by 100 to concert to a percent
relative frequency column
plot a point corresponding to the cumulative relative frequency in each class at the smallest value of the next class
cumulative relative frequency graph
standardized score when x is an observation from a distribution that has known mean and standard deviation find the
z score
subtracting the same positive number from each value in a data set shifts the distribution to the left by that number
effect of subtracting a constant
shift the distribution to the right by that constant
effect of adding a constant
- multiples or divides measures of center and location (mean, median, quartiles, percentiles) by b
- multiples or divides measures of spread (range, iqr, sx) by b
- does not change shape of distribution
effect of multiplying or dividing by a constant
- always on or above the horizontal axis
- has area of exactly 1 underneath it
describes overall pattern of distribution.
density curve
“equal areas point” where half the area under the curve is to It’s left and the remaining half of the area to It’s right
median of a density curve
“balance point” of a distribution
-pulled away from median in the direction of the long tail
mean of a density curve
the ____ and ____ of a symmetric density curve are equal
mean and median
used to represent standard deviation of a density curve
o greek letter sigma
changing mew without changing o moves the normal curve along the horizontal axis without
changing it’s spread
standard deviation o controls the spread of a
normal curve
point at which this change of curvature takes place are located at a distance o on either side of mean mew
locating o by eye on a normal curve
- described by a normal density curve
- specified by mean mew and sx o
normal distribution
- where the mean of a normal distribution can be found at the center in a symmetric distribution
- sx is distance from the center to the change of curvature points on either side
- symmetric, single peak, bell shaped
normal curve
- applies only to norma distributions
- approximately 68% of observations fall within o and mean mew (middle of curve)
- approximately 95% of observations fall within 2o and mean mew
- approximately 99.7% of observations fall within 3o and mean mew (outers of curve)
68-95-99.7 rule
use mew +/- n(o)
-in any distribution, the proportion of observations falling within k standard deviations of the mean is at least 1- (1/ksquared)
chebyshevs inequality
- normal distribution with mean 0 and sx 1
- if variable x has any normal distribution N(mew, o) with mean mew and sx o, you must
standardize the variable
z=(x-mew)/o
- table of areas under the standard normal curve
- table entry for each value z is the area under the curve to the left of z for less than problems
- table entry for each value z is the area under the curve to the right of z for greater than
standard normal table
- state distribution and the values of interest: draw a normal curve with the area of interest shaded and the mean, sx, and boundary values identified
- either a) computer z score for each boundary value and use table a or technology or b) use the normalcdf command and label each of the inputs
how to find the area in any normal distribution
- draw normal curve with the area of interest shaded and the mean, sx, and unknown boundary identified
- either a) use table a or technology to find value of z with the indicated area under the standard normal curve, then unstandardize to transform back to original distribution or b) use the invnorm command and label each input
finding values from areas in any normal distribution
a graph is not normal when
- data is clearly skewed
- has multiple peaks
- isn’t bell shaped
provides a good assessment of whether a data set follows a normal distribution
normal probability plot
how interpret a normal probability plot
- if points on normal probability plot lie close to a straight line, plot indicates the data is normal
- systematic deviations from a straight line indicate a non normal distribution
- outliers appear as points that are far away from the overall pattern of the plot
right skewed distribution in a normal probability plot
largest observations fall distinctly to the right of a line drawn through the main body of points
left skewed distributiocin a normal probability plot
largest observations fall distinctly to the left of a line drawn through the main body of points
