One-Variable Descriptive Statistics Flashcards
(101 cards)
1
Q
define population
A
the set of all objects being studied
2
Q
give an example of population
A
studying bolts, the population is all bolts produced
3
Q
define sample
A
a portion (subset) of the population
4
Q
what should a sample be?
A
representative of the population
5
Q
define data
A
information collected on a sample
6
Q
two types of data
A
qualitative and quantitative
7
Q
define qualitative data
A
information collected on a sample that is non numerical
8
Q
give an example of qualitative data
A
hair colour
9
Q
define quantitative data
A
information collected on a sample that is numerical
10
Q
give an example of quantitative data
A
height
11
Q
two types of quantitative data
A
discrete and continuous
12
Q
define discrete quantitative data
A
numerical information collected on a sample that is whole numbers based on counts
13
Q
define continuous quantitative data
A
numerical information collected on a sample that is real numbers based on measurements
14
Q
give an example of discrete quantitative data
A
number of people in a class each day
15
Q
give an example of continuous quantitative data
A
weight
16
Q
4 levels of numerical data
A
nominal, ordinal, interval, ratio
17
Q
define nominal data
A
numbers as labels, no numerical quantity
18
Q
give an example of nominal data
A
numbers on sports jerseys
19
Q
define ordinal data
A
quantities are placed in order like from smallest to largest
20
Q
give an example of ordinal data
A
1st, 2nd, 3rd
21
Q
define interval data
A
arbitrary starting point, differences between quantities have meaning
22
Q
give an example of interval data
A
added or subtracted, not multiplied or divided, like temperature in celsius or farenheit
23
Q
define ratio data
A
all mathematical operations have meaning, fixed starting point
24
Q
give an example of ratio data
A
temperature in kelvins because it starts at absolute zero, a fixed starting point
25
two main types of descriptive statistics
graphical and numerical
26
define descriptive statistics
used to organize and summarize data in order to uncover trends, patterns, make estimates and inferences about the population
27
define graphical descriptive statistics
visual displays used to show trends or behaviour
28
give 4 examples of graphical descriptive statistics
tables, charts, graphs, plots
29
define numerical descriptive statistics
specific mathematical expressions computed using the sample values which describe some aspect of the population
30
6 examples of numerical descriptive statistics
mean, median, mode, range, standard deviation, line of best fit
31
two ways to order samples
notation and ordered
32
example of notation sample
x1, x2, xn
33
example of ordered sample
x(1) < x(2)
34
what do you have to include in stem leaf plots
the value of the stem and leaf
35
for the x interval in a frequency table, what do you have to include?
one has to be equal to or smaller/larger than x
36
what is frequency
the number of leaves in the interval
37
what is relative frequency?
the frequency over n
38
what is percentage?
the percentage of relative frequency
39
what is the cumulative frequency
add up frequencies cumulatively each time
40
in a histogram, what do you plot
frequency vs x interval
41
ways to describe a histogram
uni modal (one peak), gap, spread out
42
when do you use histogram vs bar graph
quantitative vs qualitative
43
in an ogive, what do you plot and what it looks like
cumulative frequencies over x interval; connected dots
44
4 measures of central tendency (location)
sample mean (average), sample median, sample mode, percentiles
45
what is the sample mean also called
arithmetic mean
46
how to calculate sample mean
x bar = sum of x / n where x bar is between or equal to the minimum or maximum
47
what is the sample median and its symbol
x with squiggle; the middle observation in an ordered sample
48
what is the sample mode and its symbol?
most frequently occurring observation in the sample, mode is not unique, may have more than one mode (multimodal) or no mode at all, Mx
49
shape of population distribution when mean is near median?
symmetrical
50
shape of population distribution when mean is greater than the median?
skewed to the right
51
on a population distribution, where is the mean?
on the lower side
52
shape of population distribution when mean is less than median?
skewed to the left
53
define percentile
the location in an ordered sample that is larger than that percentage of the observations
54
which measure of location is a percentile and which percentile is it?
median is p50
55
5 intervals for box and whisker plot
minimum, first quartile = p25, second quartile =median=p50, third quartile = p75, max
56
when middle bar is closer to right and whisker is shorter, what is the shape of the population distribution for a box and whisker plot?
skewed to the right
57
when middle bar is closer to the left and whisker is shorter, what is the shape of the population distribution for a box and whisker plot?
skewed to the left
58
range on box and whisker plit
between min and max
59
inter-quartile range for box and whisker plot
between first quartile and third quartile
60
what does a box and whisker plot mean?
25% of the sample is between each quartile
61
define range
the difference between the largest and smallest observations in a sample
62
define the interquartile range
the difference between q3 and q1, represents the middle 50% of the observations in a sample
63
define sample variance
the average squared distances away the observations in a sample are from the mean
64
define standard deviation
the average distance away the observations in the sample are from the mean
65
what would the z score be of an observation one standard deviation above or below the mean?
above = 1, below = -1
66
value of interval between mean - standard deviation < x < mean plus one standard deviation
66% of observations are within this interval
67
value of interval between mean - 2 standard deviations < x < mean plus two standard deviations
75% of observations are within this interval
68
value of interval between mean - 3 standard deviations < x < mean plus 3 standard deviations
99% of observations are within this interval
69
define outlier
an unusually large or small value in the sample
70
3 possible sources of outliers
measurement error, data entry error, observations from a different population have been included
71
what does CS stand for?
pearson coefficient of skewness
72
when cs is larger than 1, what does this mean?
distribution is significantly skewed to the right
73
when cs is less than -1, what does this mean?
distribution is significantly skewed to the left
74
when cs is between or equal to -1 and 1, what does this mean?
the distribution is symmetrical and there is no significant skew
75
midpoint for grouped data
middle of interval
76
what does adding frequencies for grouped data tell us?
the sample size
77
how to find grouped median
can be approximated by the midpoint of the interval in which the median would fall
78
how to find modal class (mode for grouped data)
not possible to estimate mode, but can state interval with highest frequency of observations
79
how to find range for grouped data
difference between first interval and last interval ignoring equal to signs
80
population: μ, sample:
x bar
81
population: σ, sample:
s
82
population: σ^, sample:
s^
83
in order for the inference step to produce good results about the population, what myst be sample be?
representative of the population (all aspects and features in the population must be represented in some way)
84
3 properties of a good, representative sample
reliable, valid, unbiased
85
define a reliable sample
repeated samples from the same population give the same conclusion
86
define a valid sample
measurements must be determining of the aspect of the population you are interest in, not some other aspect of the population
87
define an unbiased sample
sample does not favour any portion of the population over any other portion (estimated mean approaches actual mean as sample increases)
88
define random sample
a sample chosen without any preset pattern or scheme - cannot predict if a certain member of the population will be chosen or not
89
6 sampling methods
simple random sample, sequential sample, stratified sample, proportional sample, cluster sampling, multi-stage sampling
90
define simple random sample
each member of the population has an equal chance to be selected for the sample
91
give an example of simple random sample
names in a hat
92
define sequential sample
members of the population are ordered in some way, members are chosen at some pre-determined interval
93
give an example of sequential sample
assembly line
94
define stratified sampling
population is naturally grouped in layers or strata, random sample from each group
95
define proportional sampling
each group in sample is proportional to the population
96
define cluster sampling
population is divided into clusters, sample is taken from each cluster
97
define multi-stage sampling
population is clustered, random sample chosen from each cluster, random sample then chosen from that sample
98
what 2 sampling methods do not result in a representative sample?
self-directed sample, convencience sample
99
define self-directed sample
members of the population can choose to be part of the sample of not
100
2 examples of self-directed sample
ad, questionnaire
101
define convenience sample
use the part of the population that is easily at hand
