Download Statistical Reasoning - Palisades High School

Statistical Reasoning
for everyday life
Intro to Probability and
Statistics
Mr. Spering – Room 113
2.1 Data Types and Levels of
Measurements

Qualitative data – consist of values that
describe qualities or non-numerical (i.e.
brand names, letter grades)

Quantitative data – consist of values
representing counts or measurements (i.e.
social security numbers, percentage
grades)
2.1 Data Types and Levels of
Measurements

Four Levels of Measurement:




Nominal – data consisting of names, labels, or categories
only. The data are qualitative and can not be ranked or
ordered
Ordinal – qualitative data that can be arranged in some
order. It generally does not make sense to do computations
with ordinal data. (such as low to high)
Interval – quantitative data which intervals are meaningful,
but ratios are not. Data at this level have an arbitrary zero
point.
Ratio – quantitative data which both intervals and ratios
are meaningful. Data at this level have a true zero point.
2.1 Data Types and Levels of
Measurements

Four Levels of Measurement:

Nominal – Flavors (vanilla comes before chocolate)

Ordinal – Movie ratings ( 3 stars vs. 2 stars)


Interval – temperature (55 degrees is more than 11
degrees, but 55 degrees is not necessarily 5 times hotter
than 11 degrees because 0 does not represent no
temperature i.e. oven bake times)
Ratio – distances (10 miles is twice 5 miles, and 0 miles
means no distance)
2.1 Data Types and Levels of
Measurements
Discrete Versus Continuous Data:
 Continuous – data can take on any value
in a given interval (i.e. fractions etc.)
 Discrete – data can take on only particular
values and not other values in between
(i.e. number of students in the room)

2.1 Data Types and Levels of
Measurements
2.1 Data Types and Levels of
Measurements

Qualitative or Quantitative: Eye color on a dating survey?
Qualitative

Qualitative or Quantitative: Scores on a multiple choice exam?
Quantitative

Qualitative or Quantitative: Flavors of ice cream?
Qualitative

Qualitative or Quantitative: College majors?
Qualitative

Qualitative or Quantitative: Weights of trucks?
Quantitative

Qualitative or Quantitative: Incomes of college graduates?
Quantitative
2.1 Data Types and Levels of
Measurements

Nominal, ordinal, interval, ratio: Numbers on uniforms?
Nominal, no ordering

Nominal, ordinal, interval, ratio: Student rankings of cafeteria food,
excellent, good, fair, poor?
Ordinal, definite order

Nominal, ordinal, interval, ratio: Calendar years of historic events, such
as 1776, 1945, or 2001?
Interval, because dates have no meaningful ratios and zero does not represent
beginning of time

Nominal, ordinal, interval, ratio: Temperatures on the Celsius scale?
Interval, because temperature has no meaningful ratios and zero degrees does
not mean “no heat”

Nominal, ordinal, interval, ratio: Runner’s times in the Boston
Marathon?
Ratio, true zero point

Nominal, ordinal, interval, ratio: Weights of wrestlers?
Ratio, true zero point
2.1 Data Types and Levels of
Measurements

Continuous or discrete: Measurements of time it takes to
walk a mile?
Continuous

Continuous or discrete: Number of calendar years (i.e.
2007)?
Discrete, can not have fractions of a year

Continuous or discrete: Numbers of dairy cows on
different farms?
Discrete

Continuous or discrete: Amount of milk those dairy cows
produce?
Continuous
2.1 Data Types and Levels of
Measurements


HOMEWORK # 5:
pg 57 # 5-51 odd
Qualitative VS. Quantitative