Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Understanding Distributions: Shape, Measure of Center, and Measures of Spread, Schemes and Mind Maps of Business Statistics

University of PlymouthBusiness Statistics

An overview of describing distributions, focusing on their shape, measure of center, and measures of spread. Topics include symmetric, skewed left and right, unimodal, bimodal, multimodal, uniform distributions, outliers, gaps, median, mean, and five number summary. Learn how to calculate measures of center and spread, and understand the differences between mean and median.

What you will learn

  • What are the different shapes of distributions?
  • How do you calculate the measure of center for a distribution?
  • What is the difference between the mean and median?

Typology: Schemes and Mind Maps

2021/2022

Uploaded on 09/12/2022

journalyyy
journalyyy ๐Ÿ‡ฌ๐Ÿ‡ง

4.7

(12)

215 documents

1 / 6

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Describing๎˜ƒDistributions
3๎˜ƒTopics:
1. Shape
2. Center
3. Spread
Shape
โ€ขAlways๎˜ƒdescribe๎˜ƒthe๎˜ƒbasic๎˜ƒshape๎˜ƒof๎˜ƒthe๎˜ƒdistribution.๎˜ƒ
โ€ขSymmetric๎˜ƒโ€“left๎˜ƒand๎˜ƒright๎˜ƒside๎˜ƒare๎˜ƒmirror๎˜ƒimages,๎˜ƒor๎˜ƒ
approximate๎˜ƒsince๎˜ƒweโ€™re๎˜ƒdealing๎˜ƒwith๎˜ƒreal๎˜ƒdata
โ€ขSkewed๎˜ƒLeft๎˜ƒโ€“majority๎˜ƒof๎˜ƒthe๎˜ƒdata๎˜ƒis๎˜ƒon๎˜ƒthe๎˜ƒright๎˜ƒside๎˜ƒ
but๎˜ƒtails๎˜ƒout๎˜ƒto๎˜ƒthe๎˜ƒleft
โ€ขSkewed๎˜ƒRight๎˜ƒโ€“majority๎˜ƒof๎˜ƒthe๎˜ƒdata๎˜ƒis๎˜ƒon๎˜ƒthe๎˜ƒleft๎˜ƒside๎˜ƒ
but๎˜ƒtails๎˜ƒout๎˜ƒto๎˜ƒthe๎˜ƒright
โ€ขUnimodal๎˜ƒโ€“one๎˜ƒmajor๎˜ƒmode๎˜ƒwhere๎˜ƒthe๎˜ƒdata๎˜ƒis๎˜ƒcollected๎˜ƒ
around
โ€ขBimodal๎˜ƒโ€“two๎˜ƒmajor๎˜ƒmodes
โ€ขMultimodal๎˜ƒโ€“ multiple๎˜ƒmodes
โ€ขUniform๎˜ƒโ€“data๎˜ƒis๎˜ƒflat๎˜ƒand๎˜ƒfeatureless
pf3
pf4
pf5

Partial preview of the text

Download Understanding Distributions: Shape, Measure of Center, and Measures of Spread and more Schemes and Mind Maps Business Statistics in PDF only on Docsity!

Describing

Distributions

Topics:

1. Shape2. Center3. Spread

Shape

Always

describe

the

basic

shape

of

the

distribution.

Symmetric

  • left

and

right

side

are

mirror

images,

or

approximate

since

weโ€™re

dealing

with

real

data

Skewed

Left

  • majority

of

the

data

is

on

the

right

side

but

tails

out

to

the

left

Skewed

Right

  • majority

of

the

data

is

on

the

left

side

but

tails

out

to

the

right

Unimodal

  • one

major

mode

where

the

data

is

collected

around

Bimodal

  • two

major

modes

Multimodal

  • multiple

modes

Uniform

  • data

is

flat

and

featureless

Also

mention

any

unusual

features

Outliers

  • observations

away

from

the

main

distribution.

Can

be

some

of

the

most

informative

and

interesting

Gaps

  • spaces

between

clumps

of

data

Median or

Mean

Measure

of

Center

the

middle

observation

Arrange

the

data

in

order

from

least

to

greatest

If

an

odd

number

of

obs.

find

the

middle

number

If

an

even

number

of

obs.

find

the

average

of

the

middle

two

numbers

Median

Arithmetic

average,

add

all

observations

together

and

divide

by

the

number

of

observations.

If

there

are

n

observations

which

are

labeled

as

The

mean

is

Read

as

โ€œx

barโ€

Must

be

written

with

the

bar!!!!

Mean

1

2 ,^

,...,

n

x

x

x

1

1

=

=

n

i^

n

i

i

i

x

x

x

n

n

`

The

mean

is

affected

by

outliers

and

the

median

is

resistant

to

outliers Ex.

AGE

`

When

the

data

is

symmetric

with

no

major

outliers

use

the

mean

`

When

the

data

is

skewed

or

has

major

outliers

use

the

median

Numeric

description

of

the

distribution

  1. Minimum2. 1

st

Quartile

(Q

1

  • Middle

number

of

the

bottom

half

of

the

data

  1. Median 4. 3

rd

Quartile

(Q

3

  • Middle

number

of

the

top

half

of

the

data

  1. Maximum

Number

Summary

Put

data

in

order

2

2

3

4

5

5

6

6

7

7

7

7

7

8

9

9

9

10

11

12

14

16

19

27

35

Number

Summary

Min

=

2

Q

= 1

Med

=

7

Q

3 =^

Max

=

35

Range

  • difference

between

the

highest

and

lowest

values

Range

Max

  • Min

Interquartile

Range

  • difference

between

the

percentile

and

percentile

Range

of

the

middle

of

the

data

IQR

Q

3

โ€“ Q

1

Measures

of

Spread

Standard

Deviation

is

a

number

that

describes

how

much

data

vary

or

spread

out.

Uses

difference

of

each

data

value

from

the

mean.

Measure

of

Spread

(

) 2

1

=

โˆ‘

n

i

i

x

x

s

n

The

higher

the

number

the

more

the

data

is

spread

out.

Can

never

be

negative

If

s

all

the

values

in

the

data

set

are

equal.

The

square

of

the

standard

deviation

is

call

the

variance.

(s

2

var)

Standard

Deviation

facts

Two

machines

are

set

to

cut

a

piece

of

metal

that

should

weigh

15

grams.

A

random

sample

of

50

pieces

from

each

machine

is

taken

and

the

weights

are

measured.

Both

are

centered

at

15

grams.

s 1

=

g

s 2

=

g

If

you

use

the

mean,

use

st. dev.

If

you

use

the

median,

use

the

IQR

Describing

Distributions:

20.434.

20.031.

x s medIQR

= =

= =

With

Upper

Outlier

Without

Upper

Outlier

19.842.

20.031.

x s medIQR

= =

= =