- 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.