Chapter 2 - Describing Location in a Distribution

Question 0

add the counts in the frequency column for the current class and all classes with smaller values of the variable

Answer 0

cumulative frequency column

Question 1

value with p percent of the observations less than it

Answer 1

pth percentile

Question 2

divide the entries in the cumulative frequency column by the total number of individuals. multiply by 100 to convert to a percent

Answer 2

cumulative relative frequency column

Question 3

divide the count in each class by the total number of individuals. multiply by 100 to concert to a percent

Answer 3

relative frequency column

Question 4

plot a point corresponding to the cumulative relative frequency in each class at the smallest value of the next class

Answer 4

cumulative relative frequency graph

Question 5

standardized score when x is an observation from a distribution that has known mean and standard deviation find the

Answer 5

z score

Question 6

subtracting the same positive number from each value in a data set shifts the distribution to the left by that number

Answer 6

effect of subtracting a constant

Question 7

shift the distribution to the right by that constant

Answer 7

effect of adding a constant

Question 8

• 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

Answer 8

effect of multiplying or dividing by a constant

Question 9

• always on or above the horizontal axis
• has area of exactly 1 underneath it

describes overall pattern of distribution.

Answer 9

density curve

Question 10

“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

Answer 10

median of a density curve

Question 11

“balance point” of a distribution

-pulled away from median in the direction of the long tail

Answer 11

mean of a density curve

Question 12

the ____ and ____ of a symmetric density curve are equal

Answer 12

mean and median

Question 13

used to represent standard deviation of a density curve

Answer 13

o greek letter sigma

Question 14

changing mew without changing o moves the normal curve along the horizontal axis without

Answer 14

changing it’s spread

Question 15

standard deviation o controls the spread of a

Answer 15

normal curve

Question 16

point at which this change of curvature takes place are located at a distance o on either side of mean mew

Answer 16

locating o by eye on a normal curve

Question 17

• described by a normal density curve

- specified by mean mew and sx o

Answer 17

normal distribution

Question 18

• 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

Answer 18

normal curve

Question 19

• 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)

Answer 19

68-95-99.7 rule

use mew +/- n(o)

Question 20

-in any distribution, the proportion of observations falling within k standard deviations of the mean is at least 1- (1/ksquared)

Answer 20

chebyshevs inequality

Question 21

• 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

Answer 21

standardize the variable

z=(x-mew)/o

Question 22

• 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

Answer 22

standard normal table

Question 23

• 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

Answer 23

how to find the area in any normal distribution

Question 24

• 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

Answer 24

finding values from areas in any normal distribution

Question 25

a graph is not normal when

Answer 25

• data is clearly skewed
• has multiple peaks
• isn’t bell shaped

Question 26

provides a good assessment of whether a data set follows a normal distribution

Answer 26

normal probability plot

Question 27

how interpret a normal probability plot

Answer 27

• 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

Question 28

right skewed distribution in a normal probability plot

Answer 28

largest observations fall distinctly to the right of a line drawn through the main body of points

Question 29

left skewed distributiocin a normal probability plot

Answer 29

largest observations fall distinctly to the left of a line drawn through the main body of points