Basic Statistics（二）[分享]

**What’s In A Name?
X Y
Mathematics Independent Variable Dependent Variable
Types of Data — “Gappiness”
Whether there are gaps between successively observed values of a variable.

Discrete Variable
gaps exist between observations
obtained by counting

Continuous Variable
no gaps exist between observations
obtained by measuring
Types of Data — Level of Measurement
Deals with preciseness of measurement of the variable.

Nominal Variable
values assumed by a variable indicate different categories

Ordinal Variable
allows not only grouping but also ordering of categories

Interval Variable
meaningful measure of the distance between categories

Ratio or Ratio-Scale Variable
an interval variable that has a scale with a true zero
Statistics — Objectives
Statistics is the branch of science that deals with the collection,
presentation, analysis & interpretation of data for the purpose
of decision-making and problem-solving.
Statistics — An Overview
Descriptive vs Inferential Statistics
Descriptive Statistics
- comprises those methods concerned with collecting and
describing a set of data so as to yield meaning information

Inferential Statistics
- comprises those methods concerned with the analysis of
a subset of data leading to predictions or inferences about
the entire set of data
Descriptive Statistics — An Overview
Numerical Measures
Describes the characteristics of the data set.

Key numerical measures:
measures of location (central tendency)
measures of dispersion (variation)
measures of shape (distribution)
Measures of Location
Mean

Median

Mode

Quartiles
Mean
If the observations in a sample of size n are x1, x2, . . . , xn,
then the sample mean is

The mean is the most common measure of location or center
of the data.
Mean
The pull strength (in gf) of 10 gold bonding wires are
16.85 16.40 17.21 16.35 16.52
17.04 16.96 17.15 16.59 16.57

The sample mean pull strength for the 10 observations is
Mean
The sample mean represents the average value of all
observations in the sample.

For a finite number of observations N, the population mean
(denoted by ) may be determined by

Mean
During Operation Desert Storm in 1991, USAF F-117A pilots
flew 1270 combat sorties for a total of 6905 hours.

Hence, the mean duration of a F-117A mission during this
operation was
Median
Let x (1), x(2), . . . , x(n) denote a sample arranged in increasing
order of magnitude, then the sample median is defined as

The advantage of the median is that it is not influenced very
much by extreme values.
Median
If the sample observations are
1 3 4 2 7 8 6
The sample mean and median are 4.4 and 4 respectively.
Both quantities give a reasonable measure of the central tendency
of the data.

If the last observation is changed so that the data are
1 3 4 2 7 8 2450
The sample mean is 353.6 while the sample median remains
unchanged.
Median
Just as the sample median is the middle value in a sample,
there is a middle value in the population.

The population median is that value at which half the
population lies below it and half lies above.
Mode
The mode is the observation that occurs most frequently in
the sample.

The mode may be unique, or there may be more than 1 mode.
Sometimes, the mode may not exist.
Mode
If the sample observations are
3 6 9 3 5 8 3 4 6 3 1 10
The sample mode is 3, since it occurs four times.

If the sample observations are
3 6 9 3 5 8 3 4 6 3 1 10 6 2 5 6
The sample modes are at 3 and 6, since they both occur four times.

If the sample observations are
1 3 4 2 7 6 8
The sample mode does not exist.
Quartiles
When an ordered set of data is divided into four equal parts,
the division points are called quartiles.

The first or lower quartile Q1 is a value that has approximately 25% of the observations below in value.

The second quartile Q2 is a value that has approximately 50% of the observations below in value. It is also called the median.

The third or upper quartile Q3 is a value that has approximately 75% of the observations below in value.
Quartiles
Twenty ordered observations on the times to failure (in hours)
of electrical insulation material are shown below.
204 228 252 300 324 444 624 720 816 912
1176 1296 1392 1488 1512 2520 2856 3192 3528 3710**