midterm 1

Question 1

what are the 4 meanings of the word “statistics”?

Answer 1

1) data
2) functions of data (ex: mean and range)
3) techniques for collecting, analyzing and interpreting data for subsequent decision making
4) the science of creating and applying these techniques

Question 2

4 categories of users of statistics

Answer 2

1. people who need to be able to read/understand statistical presentations used in their field. *
2. people who need to select, apply, and interpret statistical procedures in their work. *
3. applied statisticians
4. mathematical statisticians

Question 3

population

Answer 3

a collection of all people, objects, or events that share one or more specified characteristics
(ex from ch3 hw: white women students in the university)

Question 4

concrete population

Answer 4

population that has a finite number of elements (all the people listed in a telephone directory)

Question 5

conceptual population

Answer 5

population that has an infinite number of elements (flipping a coin for eternity)

Question 6

element

Answer 6

an element is a single person, object, or event of the population (ex from ch 3 hw: a white women student)

*there is either a finite or infinite number of elements within a population

Question 7

observation (datum)

Answer 7

the observation is the number or label used to represent an element of the population.
-this is a measurable characteristic of the element

(ex from ch 3 hw: career ambivalence)

Question 8

sample

Answer 8

a subset of a population

Question 9

descriptive statistics

Answer 9

tools for depicting or summarizing data so that they can be more readily comprehended
(reduces data into a comprehendible number, and induction)

Question 10

induction

Answer 10

a process in which the researcher reasons from a sample to draw a general conclusion about a population

Question 11

inferential statistics

Answer 11

tools for inferring the properties of one or more populations by inspecting samples of the population
(makes it easier to draw conclusions despite variations in observations)

Question 12

variations can be due to:

4 possibilities

Answer 12

1. inherent variability in the phenomenon being observed/differences among participants
2. errors of measurement
3. undetected changes in conditions
4. combination of the 1st 3

Question 13

random sampling

Answer 13

method of drawing samples from a population so that every possible sample has an equal chance of being selected

Question 14

non random sampling

Answer 14

method of sampling based on haphazard or purposeless choices (this is not good for making inferences about a population)

Question 15

large sample of a population

Answer 15

the larger the sample, the closer it becomes to resembling the population.

Question 16

variable

Answer 16

characteristic that can take on different values

represented by a letter @ end of alphabet

range- set of elements for which the variable stands
value- each element of the range

Question 17

constant

Answer 17

characteristic that does not vary

represented by a letter @ beginning of alphabet

range of a constant consists of a single element

Question 18

2 classifications of variable

Answer 18

qualitative variable and quantitative variable

Question 19

qualitative variables

Answer 19

symbol whose range consists of attributes or non quantitative characteristics of people, objects or events

-these variables are mutually exclusive, and collectively exhaustive

(can be ordered or unordered)

Question 20

ordered variables

Answer 20

categories suggest an order or rank

(freshman, sophomore, junior, senior)

Question 21

unordered variables

Answer 21

categories do not suggest an order or rank

(race categories or gender( men and women)

Question 22

quantitative variables

Answer 22

symbol whose range consists of a count or a numerical measurement of a characteristic.

these can be discrete or continuous

Question 23

discrete variables

Answer 23

range can assume only a finite number of values or a number of values that is countably infinite. (measurements are exact)

Question 24

continuous variables

Answer 24

range is uncountably infinite (measurements are approximations)

Question 25

what are the four levels of measurement? (keyword levels)

Answer 25

nominal ordinal interval ratio

Question 26

nominal measurement

Answer 26

elements assigned to mutually exclusive/exhaustive equivalence classes properties: distinctness (each element is different from one another) transformation: one-to-one - you can substitute element labels without changing the meaning of the classes

Question 27

ordinal measurement

Answer 27

elements are assigned to mutually exclusive and exhuastive equivalence classes that are ranked or ordered with respect to one another label properties: distinctness and order (denoted by numbers or other ordered symbols transformation: strictly increasing monotonic (new labels must retain rank/order of the classes)

Question 28

interval measurement

Answer 28

assigning elements numbers that denote equal differences as the differences in magnitude of the elements -numbers have the properties of distinctness, order, and equivalence of intervals. transformation: positive linear (a variables value can be multiplies by a positive constant and then added by a constant and still retain its meaning X' = a+bX

Question 29

ratio measurement

Answer 29

similar to interval except that the origin of the scale represents the absence of the measured characteristics properties: distinctness, order, equivalence of intervals, and zeros as the absence of measurement transformation: multiplication by a positive constant (transformation that preserves all the properties of a ratio scale)

Question 30

national statistics- oldest of the three types

Answer 30

- enumerative and descriptive in character - used to keep records of taxes and other state resources - caesar ordered all citizens to report to the tax collector - john graunt kept records of birth and death statistics - first work to summarize and interpret data

Question 31

probability theory (more info on history in notes)

Answer 31

earliest traces found in the orient concerning the gender or the expected child

Question 32

experimental statistics (historical people in notes)

Answer 32

statistical procedures and principles that help guide the design of experiments.

Question 33

graphs for qualitative variables

Answer 33

bar graph | pie chart

Question 34

graphs for quantitative variables

Answer 34

histogram frequency polygon cumulative polygon stem and leaf display(tukey)

Question 35

frequency distribution

Answer 35

tables showing the equivalence classes and the frequency with which their score values occur

Question 36

equivalence class for a single score value (quantitative)

Answer 36

is ungrouped

Question 37

equivalence class for a collection of scores (quantitative)

Answer 37

is grouped

Question 38

equivalence class for a qualitative category

Answer 38

is ungrouped

Question 39

class intervals

Answer 39

are the equivalence classes of a frequency distribution

Question 40

problems with frequency distributions

Answer 40

qualitative information is lost

Question 41

advantage of grouped frequency distributions for quantitative variables

Answer 41

they are easier to interpret than ungrouped frequency distributions when theres a large amount of data

Question 42

nominal limits (upper and lower)

Answer 42

used to represent the class intervals.

Question 43

real limits

Answer 43

-used to show that there are no gaps between the class intervals. -used to compute class interval size upper limit= .5 above nominal upper limit lower limit= .5 below nominal lower limit

Question 44

7 guidelines for constructing a frequency distribution

Answer 44

1. class intervals should be mutually exclusive 2. for quantitative variables , there should be no gaps between the class intervals 3. all quantitative class intervals should have the same width or size 4. the distribution should have 10 to 20 class intervals unless the number of scores is very small 5. preferred class interval sizes are 1, 2, 3, 5, 10, 15, 20... 6. nominal lower limit of each quantitative class interval should be divisible by the class interval size 7. the class interval containing the largest score value should be placed at the top left. - for qualitative variables, the order of the class intervals should reflect the order inherent in the variable - if variable is unordered they can be ordered alphabetically

Question 45

grouping scores results in

Answer 45

loss of information | -grouped distributions are typically used if the spread of the scores is large.

Question 46

relative frequency distributions

Answer 46

a distribution that shows the proportionate or percentage frequency for each class interval ``` proportionate frequency (prop f) propf= f/n ``` percentage (%f) %f= f/n x 100

Question 47

why are relative frequency distributions useful

Answer 47

they are useful for comparing two frequency distributions with different sample sizes (n)

Question 48

cumulative frequency distribution

Answer 48

shows the number, proportion, or percentage of scores that occur below the real upper limit of each class interval

Question 49

equivalence classes are ordered alphabetically if

Answer 49

there is no inherent order to the variables