STAT 210 Ch 4

mean

the most often used measure of central location

Since all subjects of the population are rarely known, the population standard deviation is usually _________ and must be estimated by the sample standard deviation, denoted ___.

unknown; S

xn =

value of nth (last) observation

IQR

The lower and upper quartiles enclose the middle 50% of the data and hence the IQR measures the range of this middle half of the data

The population mean is estimated by the sample mean, denoted by

X (read "X-bar")

Standard deviation

a measure of variability around the mean

The mean is highly influenced by

outliers

Variance

A measure of spread around the mean that is related to the standard deviation

Interquartile range (IQR).

A measure of spread around the median; Measures variability around the median. Therefore the IQR is resistant to outliers and may be a better measure of spread than the standard deviation if the distribution is skewed; can be considered the "middle quartile", such that 50% of the data is less than it and 50% of the data is greater than it

Long-tailed distribution

A symmetric boxplot with long whiskers or several outliers at each end indicate that the data may come from a distribution with long tails

Statistical Inference

All subjects of the population are rarely known. Hence the population parameter of interest can rarely be determined and must be estimated using a sample statistic. The statistics are denoted using regular letters, such as X, s, and p

Boxplot

Displays quantitative data by giving info on the shape of a distribution, on the center and spread of a distribution and on the concentrations of data values in the tails of a distribution (outliners)

Lower fence=

Q1 - 1.5 IQR

Upper fence=

Q3 + 1.5 IQR

IQR=

Q3 - Q1

Population mean is denoted by the Greek letter m (read "mu")...

and is the sum of all observations divided by how many individuals that there are in the population.

Outliers

any observation less than the lower fence value or greater than the upper fence value

The population median is usually denoted by the Greek letter and is estimated by the sample median, denoted by

h (read "eta"); M

Deviation

is the amount that an observation differs from the mean: x - X

Upper adjacent value

largest observation that remains in the data set

Range= ______________. It is heavily __________ by outliers.

maximum value - minimum value; influenced

Dispersion parameter

measure the spread or variability around the center

If, however, all the values are _____ ___ ____, then the characteristic is called a ______ and of interest is to measure the amount of spread (or dispersion or variability) around a central value

not the same; variable

n=

number of observations in the sample

Lower Quartile

observation with 25% of the data less than it and 75% of the data greater than it. Denoted as Q1

Upper Quartile

observation with 75% of the data less than it and 25% of the data greater than it. Denoted as Q3

The median is more _________ to outliers than the mean

resistant

The population standard deviation is denoted by ___________.

s (read "sigma")

For symmetric distributions the mean and median will be nearly the _______.

same

If all the values of a characteristic are the _______ then the characteristic is a _______, and both the mean and median are the constant value. There is no spread in the data.

same; constant

Population mean is estimated by the

sample mean

since the entire population is usually unknown the population variance is estimated using the ___________.

sample variance s2

Lower adjacent values (aka whisker)

smallest observation that remains in the data set