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Quantitaive Reasoning > UNIT 4 > Flashcards

UNIT 4 Flashcards

1
Q

Random Variable

A

a quantitative variable whose value depends on chance.

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2
Q

A _____ _____ describes the outcomes of a

statistical experiment in words

A

Random Variable

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3
Q

Discrete Random Variable/ Probability distribution function

A

A listing of the possible

values and corresponding probabilities of a discrete random variable, or a formula for the probabilities

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4
Q

Probability histogram

A

A graph of the probability distribution that displays the possible values of a discrete
random variable on the horizontal axis and the probabilities of those values on the vertical axis.

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5
Q

A discrete PDF (Probability Distribution Function) has ___ characteristics

A

two

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6
Q

Each probability is between _ and _, inclusive, in other words includes zero and one

A

0,1

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7
Q

PDF Function

A

𝟎 ≀ 𝑷(𝑿 = 𝒙) ≀ 1

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8
Q

Sigma Ξ£ means to

A

Sum up

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9
Q

The sum of all probabilities in a distribution is always _

A

1

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10
Q

equation for the sum of all probabilities

A

Ξ£ P(X=x)=1

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11
Q

Expected Value

A

is the long-term average or mean. It is the long term mean of doing
an experiment over and over. It is the expected average.

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12
Q

Variable

A

A characteristic that varies from one person or thing to another

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13
Q

Qualitative Variable

A

A non-numerically valued variable; categorical variable (hair color)

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14
Q

Quantitative Variable

A

A numerically valued variable; numerical variable (weight)

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15
Q

Discrete Variable:

A

A quantitative variable whose possible values can be listed. In particular, a quantitative
variable with only a finite number of possible values is a discrete variable.

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16
Q

Continuous Variable

A

A quantitative variable whose possible values form some interval of numbers

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17
Q

Data

A

Values of a variable.

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18
Q

Qualitative Data

A

Values of a qualitative variable.

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19
Q

Quantitative Data

A

Values of a quantitative variable

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20
Q

Discrete Data

A

Values of a discrete variable; result of counting

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21
Q

Continuous Data:

A

Values of a continuous variable; result of measuring

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22
Q

The number of books in a backpack is ____, the weight of these books is ____.

A

discrete; continuous

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23
Q

Census

A

Collects information from the entire population for which data already exist

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24
Q

Sampling

A

Collect information from a representative part of the population.

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25
Q

Sampling is done when

A

it would be impractical to collect data from the entire population

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26
Q

Experimentation

A

data generated by carefully conducting an experiment

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27
Q

Simple Random Sampling

A

A sampling procedure for which each possible sample of a given size is equally likely to be the one
obtained

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28
Q

Simple Random Sampling With Replacement (SRSWR):

A

: wherein a member of the population can be

selected more than once

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29
Q

Simple Random Sampling Without Replacement (SRS)

A

wherein a member of the population can be

selected at most once

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30
Q

random-number generators

A

software that generates random numbers

31
Q

. Systematic Random Sampling

A

Population/Sample Size rounded down = m

use a generator to generate a number (k) between 1 and m

Select k, k+m k+2m…

32
Q

Clusetr Sampling

A

Divid pop into groups/clusters

obtain random sample from clusters
use all members from step 2 as the sample

33
Q

Stratified Random Sampling with Proportional Allocation

A

Divide Pop unto Strata (subpops)

fom each subpop, create a proportional sample size (strata/population= % sample for each strata)

all members from step two are the sample

34
Q

Convenience Sampling

A

A type of non-random sampling, uses results that are readily available; conducting a study related to
organic food and collecting data from customers as they walk through the doors of Whole Foods

35
Q

You are conducting a survey of students in a
dormitory. You choose your sample by knocking on
the door of every 10th room.

Choosing every 10th room makes this a
______ ______. The sample may be
representative, as long as students were
randomly assigned to rooms.

A

Systematic sample

36
Q

To survey opinions on a proposed new water line,
a research firm randomly draws the addresses of
150 homeowners from a public list of all
homeowners.
The records presumably list all homeowners,
so drawing randomly from this list produces a
_____ _____ _____. It has a good
chance of being representative of the
population.

A

Simple Random sample

37
Q

Agricultural inspectors for Jefferson County check
the levels of residue from three common pesticides
on 25 ears of corn from each of the 104 cornproducing farms in the county.
Each farm may have different pesticide use,
so the inspectors consider corn from each
farm as a subgroup (stratum) of the full
population. By checking 25 ears of corn from
each of the 104 farms, the inspectors are
using _____ _____. If the ears are
collected randomly on each farm, each set of
25 is likely to be representative of its farm.

A

Stratified sampling

38
Q

Anthropologists determine the average brain size
of early Neanderthals in Europe by studying skulls
found at three sites in southern Europe.
By studying skulls found at selected sites,
the anthropologists are using a
_______ _____. They have little
choice, because only a few skulls remain
from the many Neanderthals who once lived
in Europe. However, it seems reasonable to
assume that these skulls are representative
of the larger population.

A

Convenience sample

39
Q

Sampling Bias

A

occurs when a sample is collected from a population and some members of the population are
not as likely to be chosen as others

40
Q

Sampling bias can lead to

A

incorrect conclusions being drawn about the population being

studied

41
Q

Sampling Errors

A

are those that occur in the actual sampling process; such as the sample not being large
enough

42
Q

Non-Sampling Errors

A

are tied to factors not related to the sampling process such a defective
counting device

43
Q

A sample can ____ __ an exact representative of the population (unless the sample is exactly equal to the
population) so there will always be some ____ ____.

A

never be;sampling error

44
Q

Distribution of a Data Set

A

is a table, graph, or formula that provides the values of the observations and
how often they occur

45
Q

Unimodal

A

one peak

46
Q

bimodal

A

two equal peaks

47
Q

multimodal

A

many equal peaks

48
Q

Symmetrical distributions can be shaped as

A

bell, triangular, rectangular

49
Q

Skewed Ditributions skew ___ or ___

A

right or left

50
Q

Reverse J Shaped distribution

A

swoop down left to right

51
Q

Population Data

A

The values of a variable for the entire population

52
Q

Sample Data:

A

The values of a variable for a sample of the population

53
Q

The distribution of population data is called the

A

Population Distribution, or the distribution of the variable.

54
Q

The distribution of sample data is called a

A

Sample Distribution

55
Q

Truncated/Non-Truncated Graphs

A

By truncating the scale on the vertical axis it gives the impression that the
differences between the bars are far greater than they really are.

56
Q

Improper Scaling

A

Number of homes this year will be double last year, so the developer doubled the width
and height, which makes it look like four times the number of homes will be built.

57
Q

Random Variable

A

is a quantitative variable whose value depends on chance

58
Q

describes the outcomes of a

statistical experiment in words

A

Random Variable

59
Q

Typically, upper case

letters such as X or Y are used to represent

A

Random Variables

60
Q

Continuous Random Variable

A

a random variable whose possible values form some interval or range of
numbers

61
Q

Continuous Random Variables Represent

A

values that are measured such as baseball batting averages, IQ scores, the length
of time a long-distance phone call lasts, SAT scores,

62
Q

Probability Density Function pdf:

A

A curve representing the probability distribution of a continuous random
variable.

63
Q

function of graphs

A

f(x)

64
Q

Cumulative Distribution Function cdf:

A

Area under the curve used to evaluate probabilities

65
Q

The area under the curve is always equal to

A

1

66
Q

𝑷(𝒄 < 𝑿 < 𝒅) is the probability that

A

the random Variable (X) falls between values c and d on the x axis

67
Q

Probability is found for ____ of x-values and NOT for _____ x-values

A

intervals ;individual

68
Q

𝑷(𝑿 = 𝒄) =0

A

the probability that X equals a specific value is zero

69
Q

Uniform Distribution

A

a distribution that has constant probability since all events are equally likely to occur

70
Q

Almost all the observations in any data set lie within _____ standard
deviations to either side of the mean

A

three

71
Q

Number of Standard Deviations is more commonly

referred to as the _____

A

z-score

72
Q

Z Score =

A

(𝑫𝒂𝒕𝒂 𝑽𝒂𝒍𝒖𝒆 βˆ’ 𝑴𝒆𝒂𝒏)/

𝑺𝒕𝒂𝒏𝒅𝒂𝒓𝒅 π‘«π’†π’—π’Šπ’‚π’•π’Šπ’n

73
Q

ΞΌ

A

mu=mean of population

74
Q

Οƒ

A

= standard deviation

Quantitaive Reasoning (3 decks)

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