Download population

Statistics
Descriptive Statistics
Collecting, summarizing, and
describing data
 Collect data
ex. Survey
 Present data
ex. Tables and graphs
 Characterize data
ex. Sample mean
Inferential Statistics
Drawing conclusions and/or making
decisions concerning a population
based only on sample data
Estimation
ex. Estimate the population mean
weight using the sample mean
weight
Hypothesis testing
ex. Test the claim that the
population mean weight is 120
pounds
POPULATION
A population consists of all the items or individuals about
which you want to draw a conclusion.
SAMPLE
A sample is the portion of a population selected for analysis.
PARAMETER
A parameter is a numerical measure that describes a
characteristic of a population.
STATISTIC
A statistic is a numerical measure that describes a characteristic
of a sample.
Sample statistics versus population parameters
Measure
Population
Parameter
Sample
Statistic
Mean

X
Variance
2
S2
Standard
Deviation

S
2-1
Data Summary and Display
Sample Mean
Population Mean
For a finite population with N measurements, the mean is
The sample mean is a reasonable estimate of the population mean.
Sample Variance and Sample Standard Deviation
Population Variance
When the population is finite and consists of N values, we may define the
population variance as
The sample variance is a reasonable estimate of the population variance.
The sample variance is
The sample standard deviation is
Percentile (= Quantile)
•
•
For any whole number P (between 1 and 99), the Pth percentile of a distribution is a
value such that P% of the data fall at or below it.
The percent falling at or above the Pth percentile will be (100 – P)%.
Quartiles
•
•
•
•
Percentiles that divide the data into fourths
Q1 = 25th percentile
Q2 = the ” median ”= 50th percentile
Q3 = 75th percentile
25%
25%
Q1
25%
Q2
25%
Q3
Five-Number Summary of Data
 The five numbers that describe the spread of data are:
 Minimum
 First Quartile (Q1)
 Median (Q2)
 Third Quartile (Q3)
 Maximum
Range = Maximum-Minimum
Inter-quartile range
IQR  Q3  Q1
2-2
Stem-and-Leaf Diagram
Steps for Constructing a Stem-and-Leaf Diagram
2-2
Stem-and-Leaf Diagram
2-2
Stem-and-Leaf Diagram
Note:
1Minitab orders the leaves from smallest to
largest on each stem
2The left column shows
• a count of the observations at and
above each stem in the upper half
• a count of the observations at and
below each stem in the lower half
• at the middle stem (16), the number
of observations at this stem.
2-3 Histograms
A histogram is a more compact summary of data than a stem-and-leaf diagram. To
construct a histogram for continuous data, we must divide the range of the data into
intervals, which are usually called class intervals, cells, or bins. If possible, the
bins should be of equal width to enhance the visual information in the histogram.
Constructing a histogram
•
•
•
•
Make a frequency table
Place class boundaries on the horizontal axis
Place frequencies or relative frequencies on the vertical axis
For each class draw a bar whose width extends between corresponding
class boundaries. The height of each bar is the appropriate frequency
or relative frequency.
2-3 Histograms
2-3 Histograms
2-4 Box Plots
• The box plot is a graphical display of the fivenumber summary of data.
• Box plot describes several important features of a
data set, such as center, spread, departure from
symmetry, and outliers.
• Outlier: an observation that lie unusually far from the
bulk of the data
2-4 Box Plots
2-5
Time Series Plots
• A time series or time sequence is a data set in which the
observations are recorded in the order in which they occur.
• A time series plot is a graph in which the vertical axis
denotes the observed value of the variable (say x) and the
horizontal axis denotes the time (which could be minutes, days,
years, etc.).
• When measurements are plotted as a time series, we
often see
•trends,
•cycles, or
•other broad features of the data
2-5
Time Series Plots
Graphical Errors:
Compressing the Vertical Axis
Bad Presentation

Quarterly Sales
$
$
200
50
100
25
0
0
Q1 Q2
Q3 Q4
Good Presentation
Quarterly Sales
Q1
Q2
Q3
Q4
Graphical Errors: No Relative Basis
Bad Presentation
Freq.
A’s received by
students.
300

Good Presentations
%
30%
A’s received by
students.
20%
200
100
0
10%
0%
FR SO
JR
SR
FR SO JR SR
FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior