Quantitative Data Analysis

DOT DIAGRAMS

IT IS THE PLACEMENT OF THE AVAILABLE PRICES IN A LINEAR SECTION

* IT IS SUITABLE FOR A SMALL NUMBER OF OBSERVATIONS

SOME OBSERVATIONS

• THE AVERAGE CONSUMPTION PER GALLON OF GASOLINE IS VERY CLOSE FOR THE 3 CARS

• THE VARIABILITY OF GASOLINE CONSUMPTION IN CAR 3 IS SMALLER

TOO MANY VALUES MAKE THESE GRAPHS WITH REDUCED SIMPLICITY AND INEFFICIENT

STEAM AND LEAF PLOTS

• Good way to describe the distribution of data.
• Good first step in constructing a frequency distribution or histogram.

PROCEDURE

• We divide each number into 2 parts (stem and leaf)

• We create a vertical line -> stem on the left, leaf on the right

EXAMPLE

# SCORE IN A TEST (MAXIMUM 100):

63,73,76,63,58,92,51,68,74,55,87,65,78,81,52

(STEM)     |   (LEAF)

  5                | 1258

  6                | 3358

  7                | 3468

  8                | 17

  9                | 2

• The division into tens (stem) and units (leaf) is obvious – the division is not always obvious.

• What happens when we have thousands?

THESE DIAGRAMS GIVE A GOOD PICTURE AND A CONCISE PRESENTATION OF THE DATA

GRAPHICS FOR EXPRESSING QUALITATIVE DATA

EXAMPLE: We asked 300 basketball journalists, team officials, and former players which team will win next year’s EuroLeague. The table below shows their answers, followed by a pie chart.

TEAM	# OPINIONS OF CONQUEST	% OPINIONS OF CONQUEST
CSKA	90	30%
BARCELONA	80	27%
FENERBAHCE	50	17%
REAL MADRID	40	13%
ANADOLU EFES	25	8%
OTHER TEAM	15	5%
TOTAL	300	100%

PIE CHART

A circle that is subdivided into circular sectors, each representing a category.

NOTES

o Area -> proportional to the % corresponding to the specific circular sector.

o Effective when the purpose is to clearly show the differences in the sizes of the categories.

o Often used to present economic figures.

Used for comparison at different times.

BAR CHART

A graph that is represented by rectangular bars, each representing a category.

NOTES

o Height or width of bar -> Proportion of the % corresponding to the specific category.

For more complex comparisons, alternative forms of (grouped, stacked) are used

STACKED BARCHART

If we have to capture new information.

HERE -> OPINIONS BY CATEGORY OF RESPONDENTS (for each group)

GROUPED AND STACKED BARCHART

If we have to capture new information. HERE -> OPINIONS BY CATEGORY OF RESPONDENTS (for each group)