Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

History of statistics wikipedia, lookup

Bootstrapping (statistics) wikipedia, lookup

Time series wikipedia, lookup

Transcript
```Section 2.4
Working with Summary Statistics

Measures of Center
 Mean, Median, and sometimes Mode

 Standard Deviation, and Quartiles (Q1 and Q3)
 Remember SD gives an “average” deviation from
the mean.
 The quartiles divide the data into 25% portions.

Lets say we know the mean value of the
homes in a community along with the total
number of homes: \$213,500; 412 homes

We also know the tax rate: 1.5%

How can we use the mean to determine the
total tax dollars received by the community?
 The mean is used to represent the value of every home.

When we describe the center of the annual
income of a group of people, it is typical to use

There are typically a large group of people
clustered around the low end of the scale with a
few having very large incomes. This creates a
distribution that is…..
 Skewed right and therefore the mean gives a measure
that is higher than expected. The median filters out
these extreme values.


Create a dot plot of the following data:
City
Country
Temperature (F)
Algiers
Bangkok
Nairobi
Sao Paulo
Warsaw
Ethiopia
Algeria
Thailand
Spain
Kenya
Brazil
Poland
32
32
50
14
41
32
-22
Now create a dot plot of the distance the
temperature is from freezing (32o). Positive if
above freezing, negative if below.

Recentering a set of data is when we add or
subtract a constant from each data value.
 This shifts the data on the number scale, but does
nothing to change the shape or spread.
 The mean will be shifted by the constant added or
subtracted.

Now use the same data and convert it to celsius.
 Simply multiply the degrees above or below freezing
by 1/1.8.

What happened to your data set?
 Shape
 Mean?
 Standard deviation?


Notice that the mean and SD are multiplied by
1/1.8, but the shape stays the same.
This simply shrinks or if by a number greater
than 1, stretches the distribution.

A summary statistic is resistant to outliers if it is
not changed very much when the outlier is
removed from the data.

A summary statistic is sensitive to outliers if it is
changed significantly when the outlier is
removed from the data.

Remember our discussion of Mean vs Median

Refer to page 77: example of television viewers

Percentile: If a value is at the kth percentile, then k% of
the data is at or lower than this value.

Example: You got a 32 on math portion of the ACT. You
are told this is the 86th percentile.
 That means 86% of the test takers scored at a 32 or
lower.
 It also means that 14% scored above a 32.

This is a measure of where a data value lies
within the data set.


Frequency plot where the plotted points
show you the accumulated percent of data up
to that point.
Example: page 78

Page 80 E47, 49, 53 - 56

Re-Centering happens when you…..??
 What happens to the shape?
 What happens to the center?
 What happens to the spread?

Re-Scaling happens when you….??
 What happens to the shape?
 What happens to the center?
 What happens to the spread?
```
Related documents