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# Displaying data – shape of distributions. Week 3 (1)

## 1. BBA182 Applied Statistics Week 3 (1) Displaying data – shape of distributions

DR SUSANNE HANSEN SARALEMAIL: [email protected]

HT TPS://PIAZZA.COM/CLASS/IXRJ5MMOX1U2T8?CID=4#

WWW.KHANACADEMY.ORG

DR SUSANNE HANSEN SARAL

1

## 2. Histogram of employee completion times Numerical data

Interval (sec.) Frequency230

5

240

8

250

13

260

22

270

32

280

13

290

10

300

7

DR SUSANNE HANSEN SARAL, [email protected]

## 3. Numerical data Employee completion time Cumulative frequency

Intervals (sec.)Frequency

Relative frequency

Cumulative %

230

5

4.5%

4.5%

4.5

240

8

7.3%

11.8%

4.5 +7.3 = 11.8

250

13

11.8%

23.6%

11.8 + 11.8 = 23.6

260

22

20.0%

43.6%

23.6 + 20 = 43.6

270

32

29.1%

72.7%

43.6 + 29.1 = 72.7

280

13

11.8%

84.5%

72.7 + 11.8 = 84.5

290

10

9.1%

93.6%

84.5 + 9.1 = 93.6

300

7

6.4%

100.0%

93.6 + 6.4 = 100

N=

110

DR SUSANNE HANSEN SARAL, [email protected]

## 4. Bar Chart – categorical data

50004000

3000

2000

1000

DR SUSANNE HANSEN SARAL, [email protected]

Surgery

Maternity

Intensive

Care

0

Emergency

1,052

2,245

340

552

4,630

Hospital Patients by Unit

Cardiac

Care

Cardiac Care

Emergency

Intensive Care

Maternity

Surgery

Number

of Patients

Number of

patients per year

Hospital

Unit

## 5. Describing distributions

Once we have made a pictureof our numerical data, the

histogram, what can we say

about it’s shape?

DR SUSANNE HANSEN SARAL, [email protected]

## 6. Describing distributions – what to pay attention to!

Pay attention to:its’ shape

its’ center

Its’ spread

DR SUSANNE HANSEN SARAL, [email protected]

## 7. Describing the shape of distributions

We describe the shape of a distribution in terms of:Modes

Symmetry

Gaps or outlying values

DR SUSANNE HANSEN SARAL, [email protected]

## 8. Mode

Does the distribution have one peak(mode) or several peaks (several

modes)?

Uni-modal: one mode

Bi-modal: Two modes

Multi-modal: More than two modes

DR SUSANNE HANSEN SARAL, [email protected]

## 9. Symmetry

If we can make a mirror image ofthe distribution, we have a

symmetric distribution

DR SUSANNE HANSEN SARAL, [email protected]

## 10. Skewed distribution

The thinner parts of a distribution arecalled tails.

A distribution is skewed, or asymmetric, if

one tail stretches farther out on one side

than on the other side of the center.

A right skewed distribution has a tail that

extends farther to the right.

A left skewed distribution has a tail that

extends farther to the left.

DR SUSANNE HANSEN SARAL, [email protected]

## 11. Right skewed distributions Examples

Employee salaries in a companyWaiting times in a line

DR SUSANNE HANSEN SARAL, [email protected]

## 12. Left skewed distributions Example

Time to finish an examEmployees going home after work

Customers going shopping in a

shopping center on a Saturday

DR SUSANNE HANSEN SARAL, [email protected]

## 13. Outliers

Outliers are extreme data points in a data set that are not close to themajority of the other data points

Example:

Age of 10 people in a restaurant:

24

19

21

65 20

21

23

DR SUSANNE HANSEN SARAL, [email protected]

20 24

25

## 14. Outliers

If you are studying the personal wealth of Americans in 2010 and youhave Bill Gates (Founder of Microsoft) in your sample.

How would the personal wealth of Bill Gates affect the distribution of

personal wealth of Americans in the sample?

DR SUSANNE HANSEN SARAL, [email protected]

## 15. Outliers

Outliers will affect the shape of a distribution:DR SUSANNE HANSEN SARAL, [email protected]

## 16. Outliers

Outliers can affect almost every statistical method we use in Statistics.Therefore we need to look out for them.

An outlier can be the most informative part in your data or it may just be an

error.

No matter what it is, you need to look at it critically and judge if it is important

for our analysis.

DR SUSANNE HANSEN SARAL, [email protected]

## 17. Graphs to Describe Time-Series Data

A histogram can provide information about the distribution of a variable, butit cannot show any pattern of the data over time.

Sometimes we need to analyze data over time.

A graph of values against time is called a times series plot

DR SUSANNE HANSEN SARAL, [email protected]

## 18. Graphs to Describe Time-Series Data

A time-series plot is used to show the values of a variable ordered over time.Time is measured on the horizontal axis

The variable of interest is measured on the vertical axis

Used to monitor the evolution of a certain item of interest, such as evolution of the price of

gas, annual interest rates, daily closing prices for shares of common stock, evolution of home

prices in a certain region, exchange rates (Euro-TL, TL-$), etc.

DR SUSANNE HANSEN SARAL, [email protected]

## 19. Line Chart (time series plot) One variable

DR SUSANNE HANSEN SARAL, [email protected]## 20. Line Chart (time series plot) Two variables

DR SUSANNE HANSEN SARAL, [email protected]## 21. Line Chart (time series plot) Two variables

DR SUSANNE HANSEN SARAL, [email protected]## 22. Presenting statistical charts and graphs

When presenting data for an audience or a manager your charts and graphsMUST give as clear and accurate picture of the data as possible.

The graphs and charts must be:

Convincing

Clear

Truthful

DR SUSANNE HANSEN SARAL

## 23. Manipulation of data

Data can be manipulated in graphical techniques in such a way that they lookmore/less favorable than they are in reality. This gives misleading information

about the data.

You need to be critical whenever you are presented a graph, pie-chart,

histogram, etc.

You should also be careful not to construct misleading information with

graphical techniques.

3/22/2017

## 24. Manipulation of data

DR SUSANNE HANSEN SARAL## 25. Identical data - different graph How is this possible?

DR SUSANNE HANSEN SARAL## 26. Manipulation of data

DR SUSANNE HANSEN SARAL## 27. Manipulation of data

Annual Earnings report62,5

62

61,5

61

Earnings

60,5

60

59,5

59

1 Qtr

2 Qtr

3 Qtr

DR SUSANNE HANSEN SARAL

4 Qtr

## 28. Manipulation of data What does this graph say about the data?

Earnings100

90

80

70

60

50

Earnings

40

30

20

10

0

1 Qtr

2 Qtr

3 Qtr

DR SUSANNE HANSEN SARAL

4 Qtr

## 29. Manipulation of data

EarningsEarnings

62,5

100

90

62

80

61,5

70

60

61

Earnings

50

Earnings

60,5

40

60

30

20

59,5

10

59

1 Qtr

2 Qtr

3 Qtr

0

4 Qtr

1 Qtr

DR SUSANNE HANSEN SARAL

2 Qtr

3 Qtr

4 Qtr

## 30. Histogram with equal interval width

## 31.

Data Presentation Errors(continued)

Do not make a histogram of categorical data

Unequal histogram interval widths

Label the x-axis and y-axis clearly (identify

variables clearly)

Compressing or distorting the vertical axis

Do not calculate numerical summaries of categorical data,

such as code, telephone numbers, etc.

DR SUSANNE HANSEN SARAL

## 32. Contingency table Class exercise

A survey of the entering MBA students at a university in the US reported thefollowing data on the gender of their students in their two MBA programs:

What are the two variables under study?

Gender

Type of program

Two-year Evening

Men

116

66

Women

48

38

Total

164

104

Total

182

86

268

## 33. Contingency table How many students are surveyed?

A) How many of all MBA students are women?B) How many of Two-year MBAs are women?

C) How many of Evening MBAs are men?

D) How many of all MBAs are men?

Gender

Type of program

Two-year Evening

Men

116

66

Women

48

38

Total

164

104

Total

182

86

268

## 34. Contingency table How many students are surveyed?

Calculating the percent/probability of absolute frequencies:P=