STAT 151 > Module 2 > Flashcards

Module 2 Flashcards

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1
Q

What is frequency?

A

the counts or number of observations that fall into a given class/category of a variable or that have a given value of the variable

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2
Q

What relative frequency?

A

the ratio of the frequency of a class/category (of a certain value) to the number of observations
frequency/sum of all

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3
Q

What is relative percent frequency?

A

frequency/sum of all x 100

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4
Q

What are pie charts?

A

require the calculation of degrees of the circle that represent each category

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5
Q

What is a simple bar graph?

A 
shows the frequencies of categories for one variable
leaves spaces (gaps) between bars
can show the same information as a pie chart
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6
Q

What is area principle?

A

area under the graph must equal the variable (frequency, percentage) being presented

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7
Q

What is a multiple bar graph?

A

shows the frequencies of categories for two variables at the same time
thus, can show more information than a pie chart

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8
Q

What are marginal distributions?

A

frequency distribution for each variable

total frequency for category/grand total x 100

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9
Q

What are joint distributions?

A

frequency distribution of joint events

frequency of joint event/grand total x 100

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10
Q

What are conditional distributions?

A

frequency distributions for one category of a variable

frequency of event/total frequency for category x 100

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11
Q

What are segmented bar graphs (stacked bar graphs)?

A

similar to multiple bar graph, except segments are piled on top of each other

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12
Q

What are three aspects of describing the distribution of quantitative variables?

A

shape

center: the middle of the distribution
spread: variation or dispersion of the distribution

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13
Q

What is limit grouping?

A

often best for tables

example: 70-79, 80-89, 90-99, etc.

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14
Q

What is cutpoint grouping?

A

best for graphs

example: 70-under 80, 80-under 90, 90-under 100

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15
Q

What is a histogram?

A

like a bar graph, but no space between bars
used for quantitative data (both discrete and continuous)
x axis shows classes of quantitative variable
y axis shows frequency or relative frequency or relative percent frequency

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16
Q

What are the pros and cons of using a histogram?

A

Pros: shows the shape, summarizes large data sets
Cons: cannot see individual data

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17
Q

What is a dot plot?

A

useful for showing the relative positions of the data, which are not shown in histograms
can be used to compare two or more populations or groups

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18
Q

What are the pros and cons of using a histogram?

A

Pros: see detail of numbers
Cons: cannot show big groups of data

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19
Q

What is a stem plot?

A

easy to construct

the first one or two digits of the observations are considered the stems, while the last digit is considered as the leaf

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20
Q

What are the pros and cons of using a stemplot?

A

Pros: see detail of numbers
Cons: cannot show big groups of data, limited to comparing two sets of data

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21
Q

What is population distribution?

A

the distribution of population data

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22
Q

What is sample distribution?

A

the distribution of sample data

if you take several samples from the same population, every sample will have slightly different shape or distribution

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23
Q

What does a symmetrical graph look like?

A

a distribution that can be divided into two parts such that one is a mirror image of the other

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24
Q

What does a skewed graph look like?

A

distribution that has one tail of the distribution longer than the other

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25
What does a left skewed graph look like?
negatively skewed | left tail is longer than right tail
26
What does a right skewed graph look like?
positively skewed | right tail is longer than left tail
27
What is a J-shaped graph?
special type of negatively skewed distribution that has no right tail
28
What is a Reverse J-shaped graph?
special type of positively skewed distribution that has no left tail
29
What is modality?
refers to the number of peaks in the distribution
30
What is a unimodal graph?
one peak (or one mode)
31
What is a bimodal graph?
two peaks that are approximately the same height
32
What is a multimodal graph?
three or more peaks
33
What is the formula for population mean?
summation of all items in the population/population size
34
What is the formula for sample mean?
summation of all observations in a sample/sample size
35
What is a median?
the middle observation in a distribution divides the area under the curve into two equal halves is a resistant measure best measure of center for skewed distributions
36
What is a mode?
one or more points in a frequency distribution that have the greatest frequency is the only measure of center that can also be used for qualitative data
37
What is a mean?
the center of the gravity of the distribution (histogram) is not a resistant measure, seriously affected by skewed graphs the best measure of center for symmetrical distributions
38
What is the range of a graph?
max-min = difference between the highest and lowest observations in a data set a biased measure of variation
39
What is the formula for sample variance?
sum of squared deviations from the mean/sample size - 1
40
What is the formula for sample standard deviation?
positive square root of the sample variance
41
What are degrees of freedom (df)?
df is the number of independent observation | df = n - 1
42
What are percentiles?
divide a data set into 100 equal parts
43
What are deciles?
divide a data set into 10 equal parts
44
What are quartiles?
divide a data set or distribution into 4 equal parts
45
What is the first quartile on a graph?
the median of that part of the data set that lies below the median of the entire data set
46
What is the second quartile on a graph?
the median of the entire data set
47
What is the third quartile on a graph?
the median of that part of the data set that lies above the median of the entire data set
48
What is the interquartile range (IQR)?
the difference between the first and third quartiles
49
What is a five number summary?
Min, Q1, Q2, Q3, Max
50
What are outliers?
observations that lie outside the overall pattern of the data
51
What are adjacent values?
the most extreme observations that still lie within the lower and upper limits
52
What are the pros of boxplots?
can summarize large amounts of data
53
What are the cons of boxplots?
cannot show detail, that is, each number or observation
54
How do you use mean and median to determine the shape of a distribution?
if mean > median then right skewed if mean < median then left skewed if mean = median then possibly (but not definitely) symmetric
55
How do you use quartiles to determine the shape of a distribution?
if Q3 - Q2 > Q2 - Q1 then right skewed if Q3 - Q2 < Q2 - Q1 then left skewed if Q3 - Q2 = Q2 - Q1 then possibly (but not definitely) symmetric
56
What is the best choice for measures of center and spread for symmetric distributions?
mean and standard deviation
57
What is the best choice for measures of center and spread for skewed distributions?
median and IQR
58
What is a density curve?
a model for a frequency distribution whereby the areas (or density) under the curve represents relative frequencies as well as probabilities
59
What is the continuous probability model?
form a smooth curve used for continuous quantitative variables assigns probabilities as areas under a density curve
60
What is a z score?
tells us the number of standard deviations a particular measurement is from the mean thus, it is a measure of the relative standing of an observation among all observations on a particular data set can be applied to any type of distribution, but it is commonly applied to normal distributions
61
What is a normally distributed variable?
a variable that follows a normal, bell-shaped distribution and forms a normal curve most populations are approximately normal, rather than completely normal
62
What are the characteristics of the normal curve?
bell shaped centered at the mean is completely defined by it's mean and standard deviation the total area under the normal curve = 1 the measures of center all coincide extends indefinitely in both directions follows the empirical rule
63
What is the empirical rule?
68. 26% lie within one standard deviation 95. 44% lie within two standard deviations 99. 74% lie within three standard deviations
64
How do you assess normality?
if the plot is roughly linear, you can assume that the variable is approximately normally distributed if the plot is not roughly linear, you can assume that the variable is not approximately normally distributed guidelines should be applied loosely for small samples and strictly for large samples
65
What are linear transformations?
involve adding, subtracting, multiplying, or dividing a constant for each data value
66
What is shifting data?
adding (or subtracting) a constant results in shifting the measures of position spread and shape do not change
67
What is rescaling data?
multiplying or dividing by a constant results in all measures of position being multiplied by the same constant all measures of spread are multiplied by the same constant shape does not change
STAT 151
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