Stats Final Preparation

Front 1

Individual

Back 1

the objects described by a set of data.

Front 2

variable

Back 2

any characteristic of an individual

Front 3

categorical variable

Back 3

places an individual into one of several groups or categories

Front 4

quantitative variable

Back 4

takes numerical values for which arithmetic operations such as adding or subtracting make sense

Front 5

distribution

Back 5

tells us what values it takes and how often it takes these values

Front 6

rules for a histogram

Back 6

1. The bars of a histogram should cover the entire range of values of a variable. When the possible values of a variable have gaps between them, extend the bases of the bars to meet halfway between the two adjacent possible values

Front 7

describing overall pattern

Back 7

shape, center, spread and check for outliers

Front 8

how to make a stemplot

Back 8

1. separate each observation into stem/leaf 2. Write the stems in a vertical column with smallest at top 3. Write each leaf in the row to the right of its stem in increasing order out 4. For double stems, 0-4 goes on the upper stem and 5-9 goes on the lower stem

Front 9

mean

Back 9

average (x1+x2+x3….)/n

Front 10

resistant measure

Back 10

because the mean cannot resist the influence of extreme observations, it is not a resistant measure. Outliers may pull the mean toward its long tail and skew the mean. The median is resistant. Standard deviation is not resistant either.

Front 11

median

Back 11

midpoint

Front 12

how to find the median

Back 12

1. Arrange all observations in order of size, from smallest to largest 2. If the number of observations, n, is odd, the median is the center. Find the location by counting (n+1)/2. If n is even, average the two center observations

Front 13

relationship between the mean and the median graphically

Back 13

in a symmetric distribution, they are close together. If the distribution is exactly symmetric, the mean and median are exactly the same. In a skewed distribution, the mean is farther out n the long tail than the median

Front 14

How to measure spread:

Back 14

look at the spread of the middle half of the data where there are not outliers, that is look at the quartiles

Front 15

first quartile

Back 15

lies one quarter of the way up the list

Front 16

third quartile

Back 16

larger than 75% of the observations

Front 17

how to make a boxplot

Back 17

take the 5 number summary. Draw horizontal lines at the 3rd quartile, the median and the first quartile. Then draw vertical lines to the maximum and minimum.

Front 18

variance

Back 18

(s squared) of a set of observations is an average of the squares of the deviations of the observations from their mean

Front 19

standard deviation

Back 19

(s) measures spread by looking at how far the observations are from their mean

Front 20

density curve rules

Back 20

1. Always on or above the horizontal axis 2. Has area exactly 1 underneath it… describes the overall pattern of a distribution. The area under the curve and above any range of values is the proportion of all observations that fall in that range

Front 21

median on a density curve

Back 21

equal areas point with half the area under the curve to the left and the remaining to the right

Front 22

mean on a density curve

Back 22

the point at which the curve would balance if it was made of solid material. The mean and median of a symmetric density curve are equal

Front 23

mu

Back 23

the notation for the mean of an idealized distribution

Front 24

Normal distributions

Back 24

normal curves that are symmetric, single-peaked, and bell-shaped.

Front 25

68-95-99.7 rule

Back 25

68% of the observations fall within 1 standard deviation on either side of the mean, 95% of the observations fall within 2 standard deviations on either side of the mean, 99.7% of the observations fall within 3 standard deviations on either side of the mean

Front 26

standardized value

Back 26

z= (x-mu)/alpha also known as Z score

Front 27

z score

Back 27

tells us how many standard deviations the original observation falls away from the mean and in which direction. Observations larger than the mean are positive when standardized and vice versa

Front 28

the standard normal distribution

Back 28

N(0,1) with mean 0 and standard deviation 1. If a variable x has any Normal distribution N(mu, alpha) with mean mu and standard deviation alpha, then the standardized variable is Z

Front 29

response variable

Back 29

measures an outcome of a study aka dependent variables

Front 30

explanatory variable

Back 30

explains or influences changes in a response variable also known as independent variables

Front 31

scatterplot

Back 31

shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each indvidual in the data appears as the point in the plot fixed by the values of both variables for that individual. Always plot the explanatory variable, if there is one, on the horizontal axis of a scatterplot. Explanatory variable = x and response variable = y.

Front 32

how to examine a scatterplot

Back 32

chech for overall pattern, striking deviation, direction, strength, outlier

Front 33

positive association

Back 33

above average values of one tend to accompany above-average values of the other, and below-average values also tend to occur together

Front 34

negative association

Back 34

above average values of one tend to accompany below-average values of the other, and vice versa

Front 35

strength of a stemplot

Back 35

determined by how closely the points follow a clear form

Front 36

correlation

Back 36

r measures the direction and strength of the linear relationship between two quantitative variables ( you are trying to evaluate how closely points lie to a straight line)

Front 37

how to assess correlation

Back 37

1. positive r denotes positive correlation and negative r shows negative correlation. 2. Correlation is always between -1 and 1. Values of r near 0 indicate a weak linear relationship. The strength of the linear relationships increases as r moves toward 1 or -1. -1 or 1 only occur in the case of a perfect linear relationship. 3. Does not describe curved relationships 4. Not resistant

Front 38

If X~N(6, 2)and a sample of n=4 is taken, then x bar is distributed

Back 38

N(6,1) (standard deviation/root n)

Front 39

If X~N (6,2) and a sample of n=4 is taken, (x-6)/2 is distributed

Back 39

N(0,1) equal to Z