With Statistics Workshop with Statistics Workshop FunFunFunFun

with Statistics

Workshop

Fun

Temasek Polytechnic • School of Informatics & IT

How the workshop works

• 3 hours @ Temasek Polytechnic

– First 1.5 hours workshop on statistics

– next 1.5 hours to create an interesting infographic to tell a story using the data.


Why attend this workshop?

• Learn key statistics concepts that will help you make better decisions

• Pick up useful Microsoft Excel Skills

• Win attractive prizes!


Stats in Action!

http://www.youtube.com/watch?v=tyVFGpg17hw&feature=player_embedded#at=13


Examples of Infographic

http://www.whoishostingthis.com/blog/wp-content/uploads/2013/01/awesome_datacenters_nowatermark.jpg



http://www.datacenterreports.com/data-center-design/~/media/Files/Data%20Center%20Reports/Defending%20the%20Death%20Star%20with%20a%20Little%20Data%20Center%20Design%20-%20Full%20Size.ashx



http://thumbnails.visually.netdna-cdn.com/a-whos-who-of-the-minions_51d54556b6828.jpg


What is Statistics ?

Statistics is the study of the Collection Organization Analysis Interpretation of data


Why Study Statistics?

1. Numbers are everywhere!

2. Statistical techniques are used to make decisions that effect our daily lives

3. How can stats affect you?


Types of Statistics

Statistics

DescriptiveStatistics

InferentialStatistics


Definition

Descriptive Statistics – Methods of organizing, summarizing, and presenting data in an informative way.Examples: (Mean, Median, Mode), Frequency distribution table, Charts (Bar Chart, Line Chart), graphs (Histogram, Box-and-Whisker Plot) etc.

Inferential Statistics – The methods used to estimate a property of a population on the basis of a sample.Example: Sampling


Inferential Statistics

a research firm observes that women are twice as likely as men to shop impulsively.

an accountant observes that the current year’s total sales of $60 million represents a 20% increase compared to last year’s total sales.

Which type of statistics is involved when ...

ANSWER :

ANSWER : Descriptive Statistics


Population and Sample

Samplerefers to a portion of the population.

Populationrefers to a set or collection of all possible observations of some specific characteristics.


Population Sample(a) Weekly allowances of all students of

Singapore Primary School.(b) A group of 5 employees selected

from Ace Company Ltd to representit at a conference.

(c) Volume of sales generated by all 30salesmen of Trustworthy Trading.

(d) Monthly expenditure on clothes for50 persons.

(e) Life span of 100 batteriesmanufactured by EverlastingCompany.

(f) Salaries of all employees of RafflesBank.


Types of Variables

Types of Variables

Qualitative (Categorical responses)

Quantitative (Numerical responses)


Variable Definition1. Qualitative variable: When the characteristic being studied is nonnumeric, it is called a qualitative variable. Examples are gender, state, country etc. It is discrete

2. Quantitative variable: When the variable studied can be reported numerically, the variable is called a quantitative variable. Examples are age, amount, no. of children etc. can be either discrete or continuous

(a) Discrete variable: Individually separate and distinct. can only assume certain values and there are usually “gaps” between values. Example: Children in a family, number of students, number of employees etc.

(b) Continuous variable: can assume any value within a specified range. Example: Amount, height, temperature etc.


Qualitative (Discrete)

Quantitative Discrete Continuous

(a) Records of number of sick leave of employees.

(b) Number of vehicles sold this month in Singapore.

(c) Time taken to travel from home to TP.

(d) Amount of rainfall in the month of January.

(e) Total Diameter of rings produced.

(f) Types of credit card used.(Master, visa, diners)

(g) Monthly income of employees.


Levels of Measurement

There are four levels of data:• Nominal • Ordinal• Interval• Ratio


Definition

1. Nominal: variables which are classified into categories and order will be meaningless. Example: Race, Gender, Religious affiliations etc.

Nominal level variables must be:

(a) Mutually exclusive An individual object, can only belong to one category at a time. Not possible to have 2 categories at a single time. Can you be both F and M?

(b) Exhaustive Each individual object must belong to either a F or M


2. Ordinal: Ordinal level variables are arranged in some order and the categories have some relationship among them. Example: Student’s grade, customer’s rating, military rank.

Definition


3. Interval: Similar to the ordinal level, but there is a meaningful difference between values. 0 ≤ x ≤ 1 is an interval which contains 0 and 1, as well as all numbers between them

Example: Temperature, Dress size, time

Definition


4. Ratio: Practically all quantitative data is recorded as ratio level of measurement. Similar to the interval level, but has an absolute zero (0). Example: Number of employees, distance etc.

Definition


M.E.A.N M.E.D.I.A.N

M.O.D.E


Mean

the average value of the data set.

the most important and most frequently used measure of central tendency. computed as the sum of all observed values divided by the total number of observations.


Example

The following shows the net profits of 12 branches of

Evergreen Florist Shop on Mother’s Day.

Net Profits ($)

903 1745 1883 863 1204 16241698 957 1041 1138 1354 1802

Compute the mean net profit

• assuming that data are from a population.


Solution

Population Data

Population Mean

903+1745+1883+863+1204+1624+1698+957+1041+1138+1354+1802 12

N

X

Population Size

16212 12$1,351

=

=

=

sum of all observed values

1


Median

Compute the median for the following odd number of observations.

903 1745 1883 863 1204 16241698 957 1041 1138 1354

First arrange the data in an array ( in ascending order )

863 903 957 1041 1138 1204 1354 1624 1698 1745 1883

= $1,204

Median= th observation in data array) (n + 1 2

) ( 11+ 1 2

Median = th observation

= 6 th observation

Net Profits ($) of Evergreen Florist

Middle value in the data set


Example

Compute the median for the following even number of observations.

903 1745 1883 863 1204 16241698 957 1041 1138 1354 1895

First arrange the data in an array ( in ascending order )

863 903 957 1041 1138 1204 1354 1624 1698 1745 1883 1895

= $1,279

Net Profits ($) of Evergreen Florist

Median= th observation in data array) (n + 1 2

Median = 6.5= 1204 + 1354 /2

2


Mode

Determine the mode for the following data :

Since the value occurs most frequently,

Mode =

$100,000 $5,000 $10,000 $20,000 $30,000 $50,000 $100,000

$100,000

$100,000

the value that occurs most frequently.


Example

No ModeRaw data: 8 6 7 9 2 5

One ModeRaw data: 8 8 7 9 2 8

More Than One ModeRaw data: 8 8 7 9 2 9

Answer :

Answer :

Answer :

No Mode

8

8 and 9

3


Comparison of Mean, Median & Mode modemedianmean

modemedian

mean

mode median

meanDistribution Skewed to Right or Positively SkewedMean > Median

Distribution Skewed to Left or Negatively SkewedMean < Median

Symmetrical Distribution or Normal Distribution

Mean = Median = Mode

For skewed distributions, the is the best measure as it lies between the mean and mode.

MEDIAN

4


Range

The following shows the net profits of 12 branches of Evergreen Florist Shop on Mother’s Day.

903 1745 1883 863 1204 16241698 957 1041 1138 1354 1802

Find the range for the net profit.

Range = Largest Value - Smallest Value

Range = =

1883 - 863$1,020

5


1. Variance

the average of the squared distances of the observations from the mean.

22

2 N

X

1n

xnxs

222

Population Variance

Sample Variance


What’s the difference?

What is the difference between the 3 curves?

Curve A

Curve B

Curve C

They have same mean

but different amount of spread (variability).

So how far iseach data valuefrom the mean?


Standard Deviation

most important and most commonly used measure of dispersion.

defined as the square root of variance, i.e. the square root of the average of the squared distances / deviations of the observations from the mean.

6


Graphical Presentations of Data


Histogram a graphical presentation of a frequency distribution.

is constructed by (i) marking class intervals on the x-axis, and (ii) drawing rectangles whose heights correspond to the class frequencies.


Histogram with 1 category

Sales 10 to 19 20 to 29 30 to 39 40 to 49 50 to 59 60 to 691 4 3 5 9 8


Histogram with 2 categories (Group)Sunshine hours Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecLondon 52 71 113 153 204 204 205 195 148 111 69 48Barcelona 146 156 187 204 248 267 308 270 207 181 145 143


Histogram with 4 categories (Stacked)Sunshine hours Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecLondon 52 71 113 153 204 204 205 195 148 111 69 48Barcelona 146 156 187 204 248 267 308 270 207 181 145 143

7


Frequency Polygon (Line Chart)

is formed by letting the midpoint of each class represents the data in that class and then connecting the sequence of midpoints at their respective frequencies.

10 to 19 20 to 29 30 to 39 40 to 49 50 to 59 60 to 69

Histogram Showing Daily Sales Turnover

0

1

2

3

4

5

6

7

8

9

10

Sales Turnover (in $'000)

Num

ber o

f Day

s

10 to 19 20 to 29 30 to 39 40 to 49 50 to 59 60 to 69

Sales(in $’000)

Frequency(No. of Days)

10 – 1920 – 2930 – 3940 – 4950 – 5960 – 69

143598

Frequency polygon showingdaily sales turnover.


Line chart with 1 categoryYear 1870 1913 1950 1973 2003Western Europe $367 $902 $1,396 $4,096 $7,857


Line chart with 6 categoriesYear 1870 1913 1950 1973 2003Western Europe $367 $902 $1,396 $4,096 $7,857USA $98 $517 $1,455 $3,536 $8,430Japan $25 $71 $160 $1,242 $2,699China $189 $241 $244 $739 $6,187India $134 $204 $222 $494 $2,267Africa $45 $79 $203 $549 $1,322

8


Area chart with 6 categoriesYear 1870 1913 1950 1973 2003Western Europe $367 $902 $1,396 $4,096 $7,857USA $98 $517 $1,455 $3,536 $8,430Japan $25 $71 $160 $1,242 $2,699China $189 $241 $244 $739 $6,187India $134 $204 $222 $494 $2,267Africa $45 $79 $203 $549 $1,322

9


Pie Chart

Ethnic Group Frequency DegreesChinese 2240 269ºMalay 400 48ºIndian 230 28ºOthers 130 15º

Total: 360º

Number of Degrees Relative Value For Each Category of the Category

360o

circular display divided into sections based on the number of observations. useful in showing proportional relationships, such as market share & budgets.

Total = 3000


Example

Pie Chart Showing the Ethnic Composition of Residents in ABC New Town

Others (130)

Chinese(2240)

Malay(400)

Indian(230)

10


Pictogram Showing the Ethnic Composition of Residents in ABC New Town

Chinese

= 100 residents130

230

400

a display that uses pictures or symbols to represent frequencies.

Malay

Indian

Others

2240

Pictogram

11


Scatter & Bubble Plot

12

Showing relation based on 2 dimensions

Showing relation based on 2 dimensions


Infographic (http://infogr.am/beta/)

http://infogr.am/beta/


A Short Survey

https://docs.google.com/forms/d/1kXw0_RvLI-A5S-O6oTHC4svOsCtTtgU_DNz63mrgBqw/viewform?usp=sharing&edit_requested=true






Thanks!

Documents

With Statistics Workshop with Statistics Workshop FunFunFunFun