FINAL EXAM:
Chapter 10
:
Statistics
•
Understand the purpose of descriptive statistics
o
Statistics
: mathematical methods to collect, organize, summarize, and analyze data.
1) Describe the data.
2) Describe the estimated accuracy of the data in representing the sampled population.
3) Describe how variables are related (this part comes in chapter 12).
o
Descriptive statistics
:
Intended to reduce data sets to allow for easier interpretation.
These statistical methods allow organize data into some type of ordered fashion.
We will be dealing with two types of descriptive statistics: data distribution and
summary statistics.
•
Understand data distribution and summary statistics (pp. 267279)
o
Data distribution
is most frequently in the form of tables and graphs.
A distribution
is simply a collection of numbers.
Frequency distribution
– a table of each score, ordered according to magnitude,
and its actual frequency of occurrence.
The sum of the frequency column is the number (N) of persons or items that
make up the distribution.
Some frequency distributions include the cumulative frequency (cf).
•
Cumulative frequency
– adding the number of scores in one interval to the
number of scores in the intervals above it.
o
Sometimes it is best to present the data is graph form:
•
Histogram/ bar chart:
frequencies are represented in vertical bars.
•
Frequency polygon
: If a line is drawn from the midpoint of each interval at
its peak along the yaxis to each adjacent midpoint/peak.
•
Frequency curve
: similar to a frequency polygon except the points are
connected by a continuous, unbroken curve instead of a line.
o
Normal curve
: a symmetrical bellshaped curve.
o
Skewness
: the concentration of scores around a particular point on the x
axis.
If the tail trails off to the right it is known as a
positive skew
, and
if the tail trails off to the left, it is known as a
negative skew
.

abscissa
: xaxis (horizontal)

ordinate
: yaxis (vertical)
o
Summary Statistics: Central Tendency
o
**
Summary statistics
: help make data more manageable by measuring two basic
tendencies of distribution: central tendency and dispersion, or variability.
Central Tendency
: describes a “typical” score.
•
Mode
= most frequently occurring score.
•
Median
= the score in the midpoint of the distribution.
•
Mean (M)
= the average of all the scores in a distribution.
o
Outliers
: pull the mean toward their direction
*Level of Distribution affects usefulness of central tendency
measures (Nominal: Mode; Ordinal: Mode and Median;
Interval/Ratio: Mode, Median, and Mean).
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Summary Statistics: Dispersion
Dispersion
measures describe the way scores “spread out” away from the central
tendency.
•
Range
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 Spring '11
 IVORY
 Statistics, Normal Distribution, Standard Deviation, Descriptive statistics, Summary statistics

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