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Data Management > Data Management All Units > Flashcards

Data Management All Units Flashcards

1
Q

100 baby weights studied; 1 baby was 7lbs!

A

variable; baby weights

data; 7lbs

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2
Q

I am 24 years old, Canadian, and size petit.

A

quantitativenumerical; 24 years old
qualitativenon-numerical; Canadian
categorical; petit

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3
Q

I have 1 dog, he is 16kg

A

discrete; 1 dog

continuous; 16 kg

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4
Q

I conducted a research paper, Judy read it and published it on her blog. I published it at the university

A

primary data; I conducted a research paper
secondary data; Judy read it
secondary source; published on her blog
primary source; published it at the university

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5
Q

I want to know how many citizens have allergies. Now I want to know how many since a factory was made.

A

1 variable; allergies

> 1 variable; allergies since a factory was made

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6
Q

A swim race to determine the best is performed three times during the day. There are three timers.

A

inherent variability; three times during the day

measurement variability; three timers

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7
Q

A survey asked university students how they felt about tuition increase, for a paper regarding the general public.

A

sample; university students
population; general public
non-representative sample; university students to represent general public

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8
Q

Picking sixty fish from five spots at the lake, not putting them back in to determine weights.

A

replication; picking 60
randomization; 5 spots
control; not putting them back

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9
Q

Names of family members are placed in a box after picked

A

simple random sample

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10
Q

Names of family on list, sample size divided by the total population = ‘k’ value, every kth member is picked

A

systemic random sample

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11
Q

Names of family members are divided into groups based on similarities, then placed in boxes, mixed, replaced if chosen.

A

stratified random sample

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12
Q

Suburbs within a city, placed in a box and mixed, replaced if picked, all picked are surveyed.

A

clusters; suburbs within a city

cluster random sample

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13
Q

suburbs within a city, placed in a box, and mixed, replaced if picked, all picked are placed in new box and mixed, replaced if picked, final picked are chosen.

A

multi-stage random sample

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14
Q

stand at convenience and ask first 40 people

A

convenience random sample

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15
Q

survey posted on door of convenience store

A

voluntary random sample

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16
Q

in own words

A

open question

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17
Q

choose from alternatives

A

closed question

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18
Q

circle 1

A

information question

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19
Q

rate according to scale

A

rating question

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20
Q

rank alternatives

A

ranking question

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21
Q

choose any number of alternatives

A

checklist question

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22
Q

sample does represent population

A

sampling bias

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23
Q

not all questions are answered

A

non-response bias

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24
Q

disproportionally polled

A

household bias

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25
Q

misleading question

A

response bias

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26
Q

Neighbours are asked the number of plants they own, the responses are sorted into a list, the list is divided into 10 groups, the groups are graphed (number in group=yfrequency, group numbers=xinterval)

A

frequency table; sorted into a list
intervals; 10 groups
histogram; graphed

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27
Q

qualitative graph

A

histogram

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28
Q

quantitative graph

A

bar chart

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29
Q

midpoints of histogram or barchart connected into a line only

A

frequency polygon

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30
Q

interval / total number of data points

A

relative percent frequency

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31
Q

90 degrees / 360 degrees = 0.25 = 25% of the circle graph( ? )

A

pie graph

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32
Q

1, 2, 2, 3, 4, 5, 8

A
  • mode = 2
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33
Q

1, 2, 2, 3, 4, 5, 8

A
  • median = 3
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34
Q

(1, 2, 2, 3, 4, 5, 8) / 7 = 3.5* = x̄

A
  • mean = 3.5
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35
Q

mean, median, mode

A

central tendency

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36
Q

1, 2, 2, 3, 4, 5, 8 -> 8-1 = 7*

A

range

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37
Q

1, 2, 2, 3, 4, 5, 8

|1—–|2–|3———–|5*–|8

A 
2* = Q1 <25% below median, >75% above median
3* = Q2 (median)
5* = Q3 >25% above median, <75% below median
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38
Q

1, 2, 2, 3, 4, 5, 8

20th percentile = 7 x 0.2 = 1.4 number in 2nd place = 20th percentile

A

2 = 20th percentile

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39
Q

σ^2

A

variance

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40
Q

(1, 2, 2, 3, 4, 5, 8) / 7 = 3.5

σ^2 = [(1-3.5)^2 + (2-3.5)^2 + (2-3.5)^2 + (3-3.5)^2 + (4-3.5)^2 + (5-3.5)^2 + (8-3.5)^2 ] / 7 = 4.79

A

*4.79 = variance

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41
Q

(1, 2, 2, 3, 4, 5, 8) / 7 = 3.5

σ^2 = [(1-3.5)^2 + (2-3.5)^2 + (2-3.5)^2 + (3-3.5)^2 + (4-3.5)^2 + (5-3.5)^2 + (8-3.5)^2 ] / 7 = 4.79

σ = square root (4.79) = 2.19*

A

*2.19 = standard deviation

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42
Q

4-7 | 14 | 2 | 4 | 20 |
———————————————–
8-12 | 10 | 4 | 6 | 20 |
———————————————–
13-18| 5 | 10 | 5 | 20 |
———————————————–
Total | 29 | 16 | 15 | 60 |

A

contingency table* typically categorical data

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43
Q

A line that goes through as much data as possible on a graph

A

line of best fit* regression line

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44
Q 
y= dependent / response variable
x= independent / explanatory variable
A

scatter plot

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45
Q

dots tend to increase left -> right and upwards looking like an arrow

A

correlation coefficient r = 1 positive slope

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46
Q

dots tend to increase left -> right and upwards looking like a stretched oval

A

correlation coefficient r = 0.8 (r > 0 [max = 1], increase in one increases the other)

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47
Q

dots tend to decrease left -> right and downwards looking like an arrow

A

correlation coefficient r = -1 negative slope

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48
Q

dots tend to decrease left -> right and downwards looking like a sphere

A

correlation coefficient r = -0.4 (r < 0 [max = -1], increase in one decreases the other)

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49
Q

dots look like a w

A

correlation coefficient r = 0 no linear correlation, change in one, does not change the other

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50
Q

dots look like a circle

A

correlation coefficient r = 0 no linear correlation, change in one, does not change the other

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51
Q

dots look like a horizontal line

A

correlation coefficient r = 0 no linear correlation, change in one, does not change the other

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52
Q

dots look like a circle outline

A

correlation coefficient r = 0 no linear correlation, change in one, does not change the other

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53
Q

0 | 3 | 0 | 0 | 9 |
———————————————–
3 | 5 | 15 | 9 | 25 |
———————————————–
6 | 10 | 60 | 36 | 100 |
———————————————–
8 | 11 | 88 | 64 | 121 |
———————————————–
11 | 17 | 187 | 121 | 289 |
———————————————–
12 | 19 | 228 | 144 | 361 |

y=mx + b

m = [n(Σxy) - (Σx)(Σy)] / n(Σx^2) - (Σx)^2 = [6(578) - (40)(65)] / [6(374) - (40)^2] = 1.35

b = (Σy)/n - [m (Σx/n)] = 65/6 - 1.35 (40/6) = 1.85

y=1.35x+1.85

A

regression line (line of best fit) equation

54
Q

coefficient of determination

A

how much y varies based on x

r^2 = [n(Σxy)-(Σx)(Σy)]^2 / [n(Σx^2)-(Σx)^2][n(Σy^2)-(Σy)^2]

55
Q

correlation coefficient

A

rootr^2

aka square the coefficient of determination

56
Q

residual point

A

point that is not the same as the predicted value
substitute residual x-value into regression equation to get expected y value, subtract from actual y value
ay - py = res

57
Q

outlier point

A

point that is a large residual point, away from line of best fit

58
Q

causation

A

1 variable changes the other

59
Q

percentage change

A

(new value - old value)/old value x 100%

60
Q

polling bias

A

leading questions, sample problems

61
Q

small sample bias

A

extreme data values in sample

62
Q

hidden sample patterns

A

patterns (seasonal purchases, bus use during school season, etc.)

63
Q

scale bias

A

when the x or y axis is made longer to make the overall graph appear larger or smaller in it’s increase/decrease

64
Q

bias in starting points of the axis

A

when the y axis starts at a value other than 0 to illustrate better growth or decline

65
Q

data mining

A

using statistical analysis on large data sets to uncover hidden patterns

66
Q

combinatorics

A

how many ways can I get to work (the study of how many ways through combination and permutations)

67
Q

tree diagram

A

home
/ \
main (1) side (2)
/ \ / \
bus (1) bike (2) bus bike
2 x 2 = 4 possible ways*multiplicative counting principle

68
Q

permutation

A

pick 3/10 girls for relay team

a = 1 ≠ a = 2

69
Q

combination

A

pick 3/10 girls for track team

a=1=a=2

70
Q

ordered pair

A

[a, b] ≠ [b,a]

71
Q

ordered triple

A

[a,b,c] ≠ [c, a, b]

72
Q

ordered N-tuple

A

[a, b,c,d, e] ≠ [a, c, b, d, e]

73
Q

factorial notation

A

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

74
Q

factorial notation for permutations

A 
10_P_3 = P(10, 3) = 10!/(10-3)! = 10! / 7! = 10 x 9 x 8 = 720
nPr = P(n,r)
P(n,0) = 1 always regardless of n
75
Q

factorial notation for combinations

A 
10_C_3 = C(10, 3) = 10! / (10-3)! x 3! = 10! / 7! x 3! = 120 
nCr = C(n,r) = (n/r)
76
Q

permutation with repetition

A

1234567
rearrange success = 7! / 3!x2!x1!x1! = 420
1233411
P(7,4) = 7!/(7-4)! = 7!/3! = 420

77
Q

mutually exclusive

A

choose 2/4 boys or 2/5 girls
C(4,2) = 4!/(4-2)!x2! = 6
C(5,2) = 5!/(5-2)!x2! = 10

6+10 = 16 ways* additive counting principle

78
Q

direct approach

A

in a group of 4 boys and 5 girls, choose group of 4 with > or = 2 girls
C(5,2) x C(4,2) = P(5,2)/2! x P(4,2)/2! = 10 x 6
C(5,3) x C(4,1) = P(5,3)/3! x P(4,1)/1! = 10 x 4
C(5,4) x C(4,0) = P(5,4)/4! x P(4,0)/0! = 5 x 1

=60 + 40 + 5 = 105 ways

79
Q

indirect approach

A

C(9,4) - [C(5,0) x C(4,4)]- [C(5,1) x C(4,3)]
= P(9,4)/4! - [P(5,0)/0! x P(4,4)/4!] - [P(5,1)/1! x P(4,3)/3!]
= 126 - (1 x 1) - (5x4) = 105 ways

80
Q

combination with all possible sizes

A 
How many communities can 9 people form?
with 1 = C(9,1) = 9
with 2 = C(9,2) = 36
with 3 = C(9,3) = 84
with 4 = C(9,4) = 126
with 5 = C(9,5) = 126
with 6 = C(9,6) = 84
with 7 = C(9,7) = 36
with 8 = C(9,8) = 9

9+36+84+126+126+84+36+9+1(with 9 people) = 511 + 1(no communities) = 512
2^9 = 512

81
Q

venn diagram

A

A + B = A∩B intersection
A & B = A∪B union
S (the box around the venn diagram) universal set

82
Q

inclusion-exclusion principle

A 
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(A∩C) - n(B∩C) + n(A∩B∩C)
83
Q

pascal’s triangle

A

row 0 *1
row 1 *1 1
row 2 *1 2 1
row 3 *1 3 3 1
row 4 *1 4 6 4 1
row 5 *1 5 10 10 5 1
row 6 *1 6 15 20 15 6 1
*AKA position ‘0’

84
Q

pascal’s identity

A

t_n,r + t_n, r+1 = t_n+1, r+1

85
Q

pascal’s triangle in relation to combinations

A 
t_n,r = C(n,r) = (r/n)
t_6,3 = C(6,3) = 6! / (6-3)! x 3! = 20
86
Q

sum of row

A

row 0 1 sum 2^0 = 1
row 1 1 1 sum 2^1 = 2
row 2 1 2 1 sum 2^2 = 4
row 3 1 3 3 1 sum 2^3 = 8
row 4 1 4 6 4 1 sum 2^4 = 16
row 5 1 5 10 10 5 1 sum 2^5 = 32
sum of row = #n = 2^n

87
Q

pascal’s triangle with routes

A 
|1 \_\_\_5\_\_\_15\_\_\_35\_\_\_70\_\_\_B126|
|1\_\_\_4\_\_\_10\_\_\_20\_\_\_35\_\_\_\_\_56|
|1\_\_\_3\_\_\_6\_\_\_\_10\_\_\_15\_\_\_\_\_\_21|
|1\_\_\_2\_\_\_3\_\_\_\_4\_\_\_\_5\_\_\_\_\_\_\_6|
|A\_\_\_1\_\_\_2\_\_\_\_3\_\_\_\_4\_\_\_\_\_\_\_5|

t_n,r = C(n,r) = (r/n)
t_9,5 or t_9,4
C(9,5) or C(9,4)
9!/(9-5)!x5! or 9!/(9-4)!x4!
=126 =126

88
Q

pascal’s triangle with restrictions

A

To spell ‘EUCLID’
E 1 -> = ‘0’
U U 2 2^n -> 2^5
C C C 3 =32 possible ways
L L L L 4
I I I I I 5
D D D D D D 6

89
Q

trial

A

I tossed a coin to decide on supper (tossing of the coin is the trial)

90
Q

possible outcome

A

heads = fish, tails = tofu

aka element* an item contained in a set or sample space

91
Q

sample space
compound experiment
discrete sample space

A

*I watched to see how many girls came with a girl or a guy

92
Q

continuous sample space

A

I wanted to see ~how many~(event~) female puppies weighed more than maleM), (M>F)}

93
Q

theoretical probability

A

p(A) = n(A) / s(A)
n(A) [success]
s(A) [total possible]

94
Q

grid

A 
|1 \_\_\_2\_\_\_3\_\_\_4\_\_\_5|
|1| 
|2|\_\_\_\_\_\_10\_\_\_20\_\_\_\_\_56|
|3|\_\_\_3\_\_\_6\_\_\_\_10\_\_\_15\_\_\_\_\_\_21|
|4|\_\_\_2\_\_\_3\_\_\_\_4\_\_\_\_5\_\_\_\_\_\_\_6|
|5\_\_\_1\_\_\_2\_\_\_\_3\_\_\_\_4\_\_\_\_\_\_\_5|
95
Q

odds

A 
There's a 70% chance of rain, odds are 7:3 it will rain, and 3:7 it won't.
p(A) = it will
p'(A) = it won't
A = p(A) + p'(A)
1-70% = p'(A)
96
Q

cardinality

A

the number of possible outcomes in a probability experiment

97
Q

mutually exclusive event

A

I need to decide on going to an event at the library, or staying home to do something else. *see disjoint sets

98
Q

disjoint sets

A

p(A or B) = p(A) + p(B)

p(A∪B) = p(A) + p(B)

99
Q

non-mutually exclusive event

A

I want to pick a playlist for a road trip; I like jazz and rock, my Dad likes heavy metal and rock.
p(A or B) = p(A) + p(B)
p(A∪B) = p(A) + p(B) - p(A∩B)

100
Q

independent events

A

I want to know the probability of my dog having to pee in 4 hours, and a salad being available at work.
p(A∩B) = p(A) x p(B)
p(A∩B∩C) = p(A) x p(B) x p(C)

I want to know the probability of my dog not having to pee in 4 hours and a salad being available at work.
P(A’) = 1 - p(A)
P(A’∩B) = p’(A) x p(B)

I want to know the probability of my dog not having to pee in 4 hours and a salad not being available at work.
P(A’) = 1 - p(A)
P(A’∩B’) = p’(A) x p’(B)

101
Q

dependent event

A

I went to a cafe but the hostess was rude, so I don’t think I’ll go back.

102
Q

conditional probability of B occuring, given A has occured

A

P(B|A)
P(A∩B) = p(A) x p(B|A)

I want to pick my name 2x in a row from a draw of 15, without putting it back (My name’s only in twice)
A = 2/15 B = 1/14
P(A∩B) = 2/15 x 1/14 = 2/210 = 1/105

If the first name isn’t my name…
p’(A) = 1 - 2/15 = 13/15
p(A’∩B) = p’(A) x p(B|A’) = 13/15 x 1/7* = 13/105
* since name wasn’t drawn, of 14 names left, 2 are mine 2/14

103
Q

probability distribution diagram

A

graph that shows probability as y axis, outcomes on x axis

i.e. heads 50% or tails 50% for coin toss* discrete random variables

104
Q

probability distribution diagram

A

graph that shows probability as y axis, outcomes on x axis

i.e. shoe size* continuous random variables

105
Q

probability of possible outcome

A 
X | p(x)
 1 | 1/6 u.p.d.*
2 | 1/6
3 | 1/6
4 | 1/6
5 | 1/6
6 | 1/6
X = random variable
p(x) = probability of possible outcome
u.p.d.* uniform probability distribution p(x) = 1/n
106
Q

weighted mean

A

5 students received 0, 3 = 50, 1 = 75 and 1 = 100
x̄_w = (5x0 + 3x50 + 1x75 + 1x100)/10 = 32.5*
*aka expected value

107
Q

binomial probability distribution

A

I will go to knitting club, or I won’t.

  • The sum of all probabilities in an experiment = 1
  • I want to know the probability of a weighted coin tossing 2 heads in a row/3 trials. 2/3 x 2/3 x 1/3
               vs.

-I want to know the probability of a tail being tossed at all in 3 tosses.
2/3 x 2/3 x 1/3 = 4/27 x 3 -> 1/3 x 2/3 x 2/3 or 2/3 x 1/3 x 2/3 or 2/3 x 2/3 x 1/3

108
Q

direct method

A 
p(x) = C(n,x) (p^x)(q^n-x)
x = number of success 
n = independent trials
q = probability of failure on each trial
p = probability of success on each trial

p(1) = C(3,1)(1/3)^1(2/3)^2 = 3!/(3-1)!x1! x (1/3)^1 x (2/3)^2 = 4/9 = 44.4%

109
Q

indirect method

A

I order 25 cookies, with a 1% estimate of a broken cookie. What is the probability of at least 5 being broken?

p=0.01
q=1-0.01 = 0.99
p(x>/=5) = 1 - p(x<5)
= 1 - p(x=0) - p(x=1) - p(x=2) - p(x=3) - p(x=4)

p(x>/=5) = 1 -C(25,0)(0.01)^0(0.99)^25 - C(25,1)(0.01)^1(0.99)^24 - C(25,2)(0.01)^2(0.99)^23 - C(25,3)(0.01)^3(0.99)^22 - C(25,4)(0.01)^4(0.99)^21

p(x>/=5) = 1 - 0.777821359 - 0.196419535 - 0.023808429 - 0.00184375 - 0.00010243 = 0.00004497 = 0.0004%

110
Q

expected value

A

E(X) = n x p
expected value = number of trials x probabilities of success

or

E(X) = n x a/N

111
Q

hypergeometric probability

A 
p(x) = [C(a,x) C(N-a, n-x)]/C(N,n)
a = number of possible successes
x= actual number of success in experiment
N = population in experiment
n = number of objects being sampled
112
Q

continuous random variable

A

I want to know the temperature

113
Q

uniform distribution

A

p(x=25) = 1/infinity
=0 (because 25.001)
rectangle graph

114
Q

unimodal distribution

A

normal distribution aka bell curve

mean = mode = median

115
Q

bimodal distribution

A

Like a unimodal distribution on both sides (2 humps)

116
Q

unimodal-negatively skewed

A

mode > median > mean

117
Q

unimodal-positively skewed

A

mode < median < mean

118
Q

measures of central tendency

A

mean, median and mode

119
Q

measures of spread

A

range, percentile, standard deviation

120
Q

mesokurtic distribution

A 
z = (x - μ)/σ
z = number of standard deviations variable is away from mean
x = variable
μ = mean
σ = standard deviation
121
Q

platykurtic distribution

A

scores are spread out, top looks flat

122
Q

leptokurtic distribution

A

data is close to mode, top is pulled like a stretched pile

123
Q

area under normal bell curve

A

area = 1, sum of all possibilities

124
Q

z score equaling an exact number

A

probability = 0% (because 0.33)

125
Q

+ z score

A

greater than mean μ
p(z>0.67) = p(zz>0) = p(0>z>0.4)
p(z

126
Q
  • z score
A

less than mean μ
p(z>-0.67) = p(z<0.67)
with normal bell curve,
p(-0.4y) = 0.5 - y (equivalent from table)

127
Q

continuity correction

A

modification of discrete data in order to use with z-score table 1/2 below and above given value

(try to find 36 -> 35.5 and 36.5)
z = (36.5 - 35)/4 = 0.38
z = (35.5 - 35)/4 = 0.12
p(35.5 < x < 36.5) = p(0.12 < z < 0.38)

36.5 - 35.5 -> 0.38 - 0.12 -> 0.1480 - 0.0478 (table numbers) = 0.1002 = 10.2%

128
Q

binomial distribution probability

A

p(X) = C(n,x) (p^x)(q^n-x)

129
Q

expected value

A

E(x) = np
aka mean of data
aka μ = np

130
Q

standard deviation equation

A 
σ = root(npq)
n = number of possible trials
p = success
q = fail

np and nq >/= 5 for normal approximation of binomial distribution

131
Q

time series graph

A

variable (i.e. population) y-axis

timeline x axis

132
Q

percentile

A

value turns into z-score which tells the probability aka the percentile

Data Management (1 decks)

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