Business statistics Week 4

Geometric Mean

A multiplicative average of a data set

Calculating the pth Percentile

A.First arrange the data in ascending order (smallest to largest). B.Locate the approximate position of the percentile by calculating Lp: Lp=(n+1)p100, where Lp indicates the location of the desired pth percentile and n is the sample size; for the population percentile, replace n with N. For example, we set p=50 for the median because it is the 50th percentile. B.Once you find the value for Lp, observe whether or not Lp is an integer: If Lp is an integer, then Lp denotes the location of the pth percentile. For instance, if L20 is equal to 2, then the 20th percentile is equal to the second observation in the ordered data set. If Lp is not an integer, we need to interpolate between two observations to approximate the desired percentile. So if L20 is equal to 2.25, then we need to interpolate 25% of the distance between the second and third observations in order to find the 20th percentile.

How can we find the mean of a data set?

Add up the values of all the data points and divide by the number of data points in the population or sample.

Box Plot (Box and Whisker Plot)

-A graphical display of the minimum value, quartiles, and the maximum number of a data set. -Convenient way to graphically display the five-number summary of a data set

Mode

-Measure of central location that is the most occurring value in the data set -Most frequently occurring value in a data set. A data set may have no mode or more than one mode

For a qualitative data set , the most meaningful measure of central location is the _______________.

Mode

The arithmetic mean is usually not a good measure of central location if an_____________ exists.

Outlier

Median

The middle value of a data set

Covariance

The numerical measure that reveals only the DIRECTION of the linear relationship between two variables, but not the strength of the linear relationship, is referred to as the ___________________.

The pth percentile

The pth percentile divides a data set into two parts: approximately p percent of the observations have values less than the pth percentile and approximately (100 - p) percent of the observations have values greater than the pth percentile.

An urn contains 12 balls, five of which are red. Selection of a red ball is desired and is therefore considered to be a success. If three balls are selected, what is the expected value of the distribution of the number of selected red balls?

https://www.youtube.com/watch?v=p0F5SlbTOSI

Arithmetic Mean

primary measure of central location (AKA: Mean or Average) -Additive Average of a set