Summary

Summary Mathematical Statistics 214

162 views 3 purchases

Course
Mathematical Statistics 214

Institution
Stellenbosch University (SUN)

Digitally summarised notes for Mathematical Statistics 214 at Stellenbosch University for the A1: includes descriptive and exploratory statistics, chapter 3/4, chapter 5 and chapter 6, chapter 7, chapter 8 and chapter 10. These notes are very properly summarised, including all examples done in c...

[Show more]

Preview 4 out of 158 pages

View example

Uploaded on June 24, 2023
Number of pages 158
Written in 2022/2023
Type Summary

math stats 214

Institution
Stellenbosch University (SUN)
Course
Mathematical Statistics 214

miaolivier16

Member since 4 year 654 documents sold

CA$16.25

Added

Add to cart

Add to wishlist

100% satisfaction guarantee
Immediately available after payment
Both online and in PDF
No strings attached

Week 1: 13-17 Feb
Descriptive and exploratory statistics

leaves a tree > e.g. leaf width
POPULATION
, e.g. of

Any of
set
objects, individuals or items with respectto the phenomenon or characteristic thatis

studied, and which forms the whole the objects thatare being studied
or
totality of

>one whole tree

·
defined
by a seto f descriptive conditions

·
has a finite / infinite number of elements

variable:

an observable characteristic a
of
population;e.g. leaf width (random variable X)

be
can
qualitative or
quantative
↓

defined by specifying a

no. of categories:descriptive (observed, notmeasured)

discreet:fixed, isolated values (1, 2, 3, 4 ...)
Quantative

↓
continuous:variable can take on all
possible values within a specific, logical
interval (e.g. age, weight)
amounts thatcan

be counted or measured

measurementof a characteristic

. can be on a nominal, ordinal, interval or ratio scale

-
Nominal:

grouping items into a number categories
of
(only qualitative), e.g. male/female, names,
-
Ordinal: eye colors

ifthe categories can be ordered (e.g. bad, medium, good
-
Interval: e.g. temperature
~>

size the
of difference between any consecutive values (numeric infinitely many values)
e.g. age, temperature, la test

-
RATO?

measurementon the interval scale, butan absolute zero
pointexists
e.g. Kelvin measurements; 100 Kelvin is double so Kelvin;weight, height, distance

, A D

Qualitative Quantative

SAMPLE

subseto felements of the population that is selected to be examined
any
random sample of size ofleaves
e.g.

sampling process -

selecting
of a sample from the population
-
used to make conclusions aboutthe population as a whole

methods
sampling
· random

· stratifiedrandom

·
systematic
· cluster

NOtatiOR

·
population: X random variable
=

leaf-width
-
all
of leaves in particular tree

X -
n(x,08) sample:
E(x) 4
3,5, 3,79...xm 5,53
=

x1 x2
=
= =

var(x) 5 3
0,8 4,07 and
0,72
=
= =

-

,frequency

>
frequency tables 5
A
Discreetn o. of observations
B 3
-
for each value.
for discreetdata: [ 2

grouped frequency table

for continuous data:

Need to items
*
group
into classes

tables for continuous data
frequency

·
Need to
specify intervals for each ofthe classes

range
-

-
no, intervals

-interval widths
-interval limits
-

frequencies

① Range r
largest
=
-

smallestvalue

⑥ No, intervals Typically 6

sturges' rule:1 = 1 +
3.310gion
↑ ↑
no class intervals total no. Observations

③ Interval width preferably equal width

convenient/ sensible

④Internal limits Include all observations

⑥ frequencies No. occurences
of a
of
particular event.

↳

> Interval width
frequencies
-range
no, intervals
12,3] (3,43 (4,5]

(2, 33, interval width is I I 9
(5,6]
10
(3,4],
=>

e.g.

, HISTOGRAM (continuous data)
classification I
grouping
· visual representation
can lead to a loss of

information. (No exact
· area corresponds to
frequency
values of individual items)
· have
equal length intervals
heighta frequencies
->

· bars touch

Frequency distribution: ·
NB:area
corresponds to
frequency crelative

/ data that Area b h frequency)
graph set x
=

shows frequencies then the
equal width,
how ·
If intervals are of
not

are distributed.
the
class
frequencies are not
proportional to

rectangle heights.
CHART
PIE

· Area & Proportion I percentages HEAT MAP

·

Represented on a 360° ·
color indicates observed values (percentages)
circle divided into sectors ·
proportion a color

BAR CHARTS <discreetdata)

·
graphical representation discrete
of and
tables
categorical frequency
·
bars are
separate

FREQUENCY POLYGON

·
figure obtained when heights histogram rectangles
of are
plotted against
midpoints class
of intervals
·
an additional interval is added each
at side (same width) with a
frequency of

o to "anchor" the graph
·
can compare multiple samples STEM AND LEAF DISPLAY

·
similar shape to histogram
CONTINGENCY TABLES ·
Stem:basic interval

·

frequency table for multiple variables ·
leaves:individual observations

2-way tables e.g. 28
-

01076
multiway tables
i
-

00197
·
summaries differenttypes variables
of 15

Stem

fading Dead
Healthy be rounded
· observations can

width < 4 L 0 I
· Stem can be in 19/109/100s etc.
width 4 I 2 2

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller miaolivier16. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for CA$16.25. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

77764 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling

Summary

Summary Mathematical Statistics 214

Document information

Subjects

Written for

Seller

Reviews received

Content preview