STP 420 Midterm #1

noise

EXPECTED variability

signal

variability due to certain CHARACTERISTICS

cases

objects or subjects described by a data set; WHERE your info came from

ex: 5 students being surveyed on their age/major

variable

a characteristic of a person/thing that can be assigned a number or category

-ex: age, major

value

the actual OUTCOMES of that variable (ex: 19 years old, Mathematics BA)

quantitative variable

a variable that records the AMOUNT of something (numerical) (speed limit, age, etc.)

categorical variable

records which of several groups or categories an individual belongs to (ex: hair color, zip codes, phone numbers)

numbers can be categorical variables when

the numbers do not actually have a meaning when on a continuum/not a measurement (ex: phone numbers, zip codes, etc.)

in a bar chart, the vertical bars are kept

SEPARATE

bar charts can display frequency or

relative frequency

relative frequencies should add up to

1.0

you cannot leave out certain categories in a pie chart because

it would not be a complete circle (100%)

stemplots can have ______ lines per stem

one OR two

purpose of having two lines per stem

might need to "zoom" in deeper and break the stem into pieces to see the distribution/spread of data

stem

ALL but the final digit

leaf

the final digit

histogram

a bar graph depicting a frequency distribution (frequency or relative frequency)

advantage of stem & leaf plot

displays all outcomes

disadvantage of stem & leaf plot

will not be very informative if the data set is too large (histogram will be more organized)

single value grouping

each vertical bar of the histogram represents a SINGLE possible value

single value grouping is rarely used and is best for

a small data set or small range of values

limit grouping

Use when the data are expressed as whole numbers and there are too many distinct values to employ single-value grouping

limit grouping only works on _______ variables

DISCRETE

-ex: number of used textbooks bought = [0-3], [4-7], [8-11], [12-15]

interval width for limit grouping

(upper limit - lower limit + 1)

-ex: the interval [4, 7] actually has a width of 4 (4, 5, 6, 7)

cutpoint grouping is used on __________ variables

CONTINUOUS

ranges of cutpoint grouping is expressed as

"[number] to under [number]"

ex: "54 to under 56"

[54, 56)

discrete variables

values that can be counted; a FINITE number of possible outcomes; integers only

-ex: # of books, # of people, etc.

continuous variables

can assume an infinite number of values between any two specific values; goes off into DECIMALS

-ex: weight, time, etc.

Patterns of Data:

1) shape (modality & symmetry/skewness)

2) center (central tendency)

3) spread (SD, range, interquartiles, etc.)

4) outliers

unimodal distribution

A distribution with one peak

bimodal distribution

a distribution with two modes

multimodal distribution

two or more peaks in a distribution curve

symmetric distribution

a distribution in which the data values are uniformly distributed about the mean; the mean is the best measure of center

left skew

mean > median

-clusters on the right

-long tail is on the left

right skew

mean < median

-clusters on the left

-long tail is on the right

in left and right skewed distributions, the _________ is the best measure of center

MEDIAN

measures of center

1) mean

2) median

3) mode

measure of center for categorical data

MODE

how many times must a value occur in a data set to be a mode?

TWICE

resistant measure

extreme values have little to no influence on its outcome

-not sensitive; does not respond strongly to outliers or changes in a few observations

range =

largest observation - smaller observation

-measures SPREAD of data

-NOT a resistant measure

deviation

difference between an observation and the mean

the SUM of all deviations from the mean

is always equal to zero

sample standard deviation

the AVERAGE of all deviations

sample standard deviation (s) tends to __________ population standard deviation

underestimate

quartiles

divides a set into 4 equal parts

(Q1, Q2, Q3)

interquartile range

Q3 - Q1

-RESISTANT

finding quartiles:

1) rearrange the data in ascending order

2) Q2 = median

3) Q1 = the median of the LOWER HALF of observations

4) Q3 = the median of UPPER HALF of observations

if you are finding the quartiles on a set with an odd number of observations,

you can either include or NOT include the median, but expect different results. include the median in your upper and lower halfs for exam

5 Number Summary

1) minimum value

2) Q1

3) Q2/median

4) Q3

5) maximum value

Outliers

lower fence = Q1 -1.5(IQR)

upper fence = Q3 + 1.5(IQR)

boxplot

displays distribution of a data set using 5 number summary

advantage of boxplot

clearly shows outliers and skew

z score

the number of standard deviations a particular score is from the mean