- WELCOME TO A LESSON 
ON HOW TO DISPLAY CATEGORICAL
OR QUALITATIVE DATA
GIVEN IN A FREQUENCY TABLE 
AS A BAR GRAPH, PARETO CHART,
PIE GRAPH, AND A PICTOGRAM.
CATEGORICAL OR A QUALITATIVE 
DATA ARE PIECES OF INFORMATION
THAT ALLOW US TO CLASSIFY 
THE OBJECTS UNDER INVESTIGATION
INTO VARIOUS CATEGORIES.
WE USUALLY BEGIN WORKING
WITH CATEGORICAL DATA
BY SUMMARIZING THE DATA 
IN A FREQUENCY TABLE.
WHERE A FREQUENCY TABLE 
IS A TABLE WITH TWO COLUMNS
AS WE SEE HERE, ONE COLUMN LISTS 
THE CATEGORIES
AND THE OTHER FOR THE 
FREQUENCIES WITH WHICH THE ITEMS
IN THE CATEGORIES OCCUR,
MEANING HOW MANY ITEMS 
FIT INTO EACH CATEGORY.
LOOKING AT THE FREQUENCY TABLE,
WE CAN TELL THAT 10 STUDENTS 
RECEIVED AN "A,"
12 STUDENTS RECEIVED A "B," 
15 STUDENTS RECEIVED A "C,"
AND SO ON.
IF WE SUM THE FREQUENCIES, WE 
CAN DETERMINE THE POPULATION,
WHICH WE CAN SEE HERE 
WOULD BE 40.
SO THERE WERE 40 STUDENTS 
IN THE CLASS.
LET'S BEGIN BY DISPLAYING THIS 
INFORMATION AS A BAR GRAPH.
TO CONSTRUCT A BAR GRAPH,
WE NEED TO DRAW A VERTICAL AXIS 
AND A HORIZONTAL AXIS.
THE VERTICAL AXIS WILL HAVE 
A SCALE
AND MEASURE THE FREQUENCY 
OF EACH CATEGORY.
HERE IS OUR VERTICAL AXIS.
NOTICE HOW THE LARGEST FREQUENCY 
IS 15,
AND THEREFORE, THE VERTICAL AXIS 
IS SCALED TO 16 BY TWOS.
THE HORIZONTAL AXIS 
SHOWS THE CATEGORIES.
AGAIN, HERE WE SEE THE LETTER 
GRADES,
AND THE BAR HEIGHT SHOWS 
THE FREQUENCY.
SO FOR "A" THE FREQUENCY IS 10.
NOTICE HOW THE BAR 
HAS A HEIGHT OF 10.
FOR B THE FREQUENCY IS 12.
SO FOR B THE BAR HAS A HEIGHT 
OF 12 AND SO ON.
SOMETIMES YOU ALSO SEE 
THE FREQUENCY LISTED
AT THE TOP OF EACH BAR 
LIKE THIS.
NOW, LET'S TALK ABOUT 
A PARETO CHART.
SOMETIMES OUR CHART MIGHT 
BENEFIT FROM BEING REORDERED
FROM LARGEST TO SMALLEST 
FREQUENCY.
THIS ARRANGEMENT 
CAN MAKE IT EASIER
TO COMPARE SIMILAR VALUES 
IN THE CHART,
EVEN WITHOUT GRIDLINES.
WHEN WE REARRANGE THE CATEGORIES 
IN DECREASING FREQUENCY ORDER
LIKE THIS,
IT IS CALLED A PARETO CHART.
SO HERE'S THE ORIGINAL 
FREQUENCY TABLE.
IF WE WANTED TO REORDER THIS 
FROM LARGEST FREQUENCY
TO SMALLEST FREQUENCY,
WE'D HAVE TO SWITCH THE As 
AND THE Cs
SO THAT THE HIGHEST FREQUENCY 
OF 15 IS FIRST,
FOLLOWED BY 12, 10, 2 
AND THEN 1.
NOW, IF WE USE THIS FREQUENCY 
TABLE TO MAKE A BAR GRAPH,
IT'LL BE A PARETO CHART.
SO THE ORANGE GRAPH 
IS A BAR GRAPH.
THIS PURPLE GRAPH 
IS A PARETO CHART.
AGAIN, 
LOOKING AT THE FREQUENCIES,
NOTICE HOW THEY GO 
FROM LARGEST TO SMALLEST.
SO NOW, THE CATEGORIES ARE 
IN THE ORDER OF C, B, A, D, F,
AND AGAIN, SOMETIMES YOU WILL 
SEE THE FREQUENCY
LISTED AT THE TOP OF EACH BAR.
AND NOW, LET'S DISPLAY 
THE SAME DATA AS A PIE CHART.
TO SHOW RELATIVE SIZES, 
IT IS COMMON TO USE A PIE CHART.
A PIE CHART IS A CIRCLE WITH 
WEDGES CUT OUT OF VARYING SIZES
MARKED OUT LIKE SLICES OF PIE 
OR PIZZA.
THE RELATIVE SIZES OF THE WEDGES
CORRESPOND TO THE RELATIVE 
FREQUENCIES OF THE CATEGORIES.
SO HERE'S THE PIE CHART.
THIS WEDGE REPRESENTS THE As.
THIS WEDGE REPRESENTS THE Bs, 
Cs, Ds AND Fs.
NOTICE HOW THIS IS CREATED 
USING SOFTWARE,
WHICH IS VERY COMMON THESE DAYS,
BUT IF WE HAD TO DO THIS 
BY HAND,
ONE CIRCLE REPRESENTS 
360 DEGREES.
SO ONE WAY TO DETERMINE 
THE SIZE OF EACH WEDGE
WOULD BE TO USE A PROTRACTOR, 
WHICH MEASURES ANGLES.
AND BECAUSE THE TOTAL NUMBER 
OF STUDENTS IS 40,
THE SUM OF THE FREQUENCIES, 
AND 10 OF THEM HAVE As,
THE LETTER GRADE OF "A" 
REPRESENTS
25% OF THE TOTAL POPULATION
OR IN THIS CASE, 
25% OF THE CIRCLE.
AND SO IF WE FIND 25% OF 360 
DEGREES, WHICH IS 90 DEGREES,
WE CAN MEASURE OUT 90 DEGREES 
TO CREATE THIS WEDGE.
AND WE CAN DO THE SAME 
FOR THE OTHER LETTER GRADES,
BUT AGAIN, NORMALLY, WE JUST USE 
SOFTWARE TO CREATE PIE CHARTS.
THE LAST GRAPH WE'LL TAKE A LOOK 
AT IS CALLED A PICTOGRAM.
A PICTOGRAM 
IS A STATISTICAL GRAPH
IN WHICH THE SIZE OF THE PICTURE
IS INTENDED TO REPRESENT 
THE FREQUENCIES
OR SIZE OF THE VALUES 
BEING REPRESENTED,
AND THERE ARE SOME VARIATIONS 
OF PICTOGRAMS.
NOTICE HERE INSTEAD OF BARS,
WE'RE USING PICTURES 
OF As, Bs, Cs, Ds AND Fs.
SO IT IS VERY SIMILAR 
TO A BAR GRAPH.
OFTEN YOU WILL SEE THE FREQUENCY
LISTED AT THE TOP 
OF EACH PICTURE.
NOTICE HOW HERE THE IMAGE OF 
EACH LETTER IS THE SAME SIZE.
ANOTHER OPTION IS TO STRETCH 
EACH IMAGE
TO THE CORRECT HEIGHT, 
AS WE SEE HERE.
A LABOR UNION MIGHT PRODUCE THE 
GRAPH TO THE RIGHT OR BELOW HERE
TO SHOW THE DIFFERENCE BETWEEN 
THE AVERAGE MANAGER SALARY
AND THE AVERAGE WORKER SALARY.
LOOKING AT THE PICTURES,
IT WOULD BE REASONABLE TO GUESS 
THAT THE MANAGERS' SALARIES
ARE FOUR TIMES AS LARGE 
AS THE WORKERS' SALARIES,
BECAUSE IT DOES APPEAR 
THE AREA OF THIS LARGER BAG
IS FOUR TIMES AS LARGE 
AS THE AREA OF THE SMALLER BAG.
HOWEVER, THE MANAGERS' SALARIES 
ARE, IN FACT,
ONLY TWICE AS LARGE 
AS THE WORKERS' SALARIES,
WHICH ARE REFLECTED 
IN THE PICTURE
BY MAKING THE MANAGER BAG 
TWICE AS TALL.
SO HERE THIS PICTOGRAM 
CAN BE DECEPTIVE
UNLESS WE PAY CLOSE ATTENTION 
TO THE HEIGHT OF EACH OF THESE
RATHER THAN THEIR SIZE.
LOOKING AT THE SCALING 
ON THE AXES,
NOTICE HOW THIS LARGER BAG 
IS TWICE AS TALL
AS THIS SMALLER BAG,
REPRESENTING THE SALARIES 
ARE ONLY TWICE AS LARGE,
NOT FOUR TIMES AS LARGE.
OKAY. THAT'S GOING TO DO IT 
FOR THIS LESSON.
I HOPE YOU FOUND THIS HELPFUL.
