PETE 404 Lecture 4 Questions

Interpreting Quartile Skew Coefficient

1) Qs = 0: symmetric 2) Qs < 0: left tail longer 3) Qs > 0: right tail longer

Properties of CDF

1) bounded between 0 and 1 2) limits of 0 and 1 3) increasing 4) continuous 5) intervals

Important characteristics for every set of measurements

1) central/typical value 2) spread about central value 3) symmetry

What are the 3 measures of shape

1) coefficient of skewness 2) quartile skew coefficient 3) coefficient of kurtosis

Two types of random variables

1) discrete 2) continuous

Interpreting coefficient of kurtosis in regards to gaussian distribution

1) k = 3: gaussian distribution 2) k < 3: less peaked than 3) k > 3: more peaked than

Measures of location or central tendency

1) mean 2) median 3) mode

The _______ of a continuous distribution corresponds to the point on which ____ is attained

1) mode 2) maximum probability

Three properties of a PDF

1) non-negative 2) unit area under f(x) 3) intervals

5 common measures of spread

1) range 2) variance 3) standard deviation 4) coefficient of variation 5) interquartile range

4 Steps to generating a PDF

1) sort data in ascending order 2) divide data range in convenient/reasonable intervals (bins) 3) count number of points, i, in each bin to calculate probability of each bin Pi(fi) 4) plot bin mid-range versus Pi

Results if dx is too small or too large

1) too small= pdf is too bumpy 2) too large= pdf has low resolution

A ______ defines the probability of finding a value of a r.v, X, that is less than or equal to a specified value x

Cumulative distribution function

Why is a CDF preferred over a PDF

PDF is dependent on bin size

Equation of probability for each bin

Pi = fi/n

Random Variable

a real valued function that assigns a value to each outcome in a sample space

A CDF defines what about a random variable

all probabilistic properties; complete statistical characterization

What part of the PDF defines probability

area under the curve

Shape of PDF is a function of ______

bin size

In practice only generate continuous through fitting data to ____ CDF functions

closed form

Measure of how peaked (or fat) a distribution is

coefficient of kutosis

Describes the measure of asymmetry of the histogram

coefficient of skewness

What is a normalized measure of dispersion

coefficient of variation

Continuous CDF

continuous within limits of 0 and 1

Mild Outlier

deviates more than 1.5 times the iqr from median

Extreme Outlier

deviates more than 3 times the iqr from the median

Discrete CDF

discontinuous at xi and constant in between

What is equation for determining bin intervals (dx)

dx = (xn-x1)/n

Rule of thumb for calculating bin intervals

dx = 5(xn-x1)/n

Negative Skewness

elongated tail to left; mass of data on right -mean<median

Positive Skewness

elongated tail to the right; mass of data on left -mean>median

Histogram is a graphical representation of a ________

frequency table

Which type of curve do we typically use for risk analysis

inverse cumulative histogram

______ is sensitive to erratic values

mean

On a CDF, the ______ is the value on the x-axis that corresponds to P50 on the y-axis

median

_______ is often the class with the tallest bar on the histogram

mode

Advantage to using PDF over CDF

more intuitive and shows spread of probability more clearly

When working with order statistics, the number of boundaries is always _____ than the number of partitions

one less

Mode is sensitive to _______

only to the value with the highest frequency

Variance is very sensitive to _____

outliers

We obtain _______ each time an experiment is performed

realization of a random variable

Quartile Skew Coefficient

serves same purpose as coefficient of skewness but is only sensitive to central part of distribution

Range is a poor descriptor for _____ samples

small

Percentiles

split into hundredths

Quartiles

split into quarters

Deciles

split into tenths

Quantiles

splitting data into any fraction

What is the average squared difference of data about the mean

variance

Low Kurtosis

variance due to frequent modest size deviation

High Kurtosis

variance mainly due to infrequent extreme deviations

When should variance divide by n-1 rather than just n

when sample sizes <30