Narrator: BACK IN 1988, THREE BROTHERS WITH A LOVE OF SURFING
AND MEXICAN FOOD STARTED A SMALL TACO STAND THAT CATERED
TO BEACH-GOERS IN ORANGE COUNTY, CALIFORNIA.
Wing Lam: WAHOO’S TACOS STARTED OUT
IN SOUTHERN CALIFORNIA AS A PLACE WHERE SURFERS
COULD HANG OUT AFTER THEY WENT SURFING.
WAHOO’S IS A PLACE THAT YOU WENT TO REFUEL
AFTER THE DAY’S ACTIVITY.
Narrator: USUALLY DRESSED IN FLIP-FLOPS,
BOARD SHORTS, AND A T-SHIRT,
WAHOO’S CO-FOUNDER WING LAM ISN’T YOUR NORMAL ENTREPRENEUR.
Lam: AS LONG AS THERE’S WAVES, I’M OUT THERE SURFING.
Narrator: TO MANAGE THEIR EXPANDING BUSINESS,
LAM AND HIS TEAM PRODUCE DATA ON EVERY ASPECT OF RESTAURANT OPERATIONS,
FROM SQUARE FOOTAGE COSTS RIGHT DOWN
TO THE POUNDS OF TOMATOES, CILANTRO,
AND JALAPENO PEPPERS USED EACH WEEK.
THE DATA HELP THEM ENSURE THE QUALITY OF THEIR PRODUCT
AND GIVE THEM A GOOD SENSE OF THEIR FOOD COSTS,
STAFFING, AND INVENTORY NEEDS.
ONE INDICATOR OF WAHOO’S SUCCESS AT
ANY OF ITS LOCATIONS IS NET SALES DATA.
NET SALES ARE WHAT IS EARNED BEFORE
DEDUCTING THE COSTS OF LABOR,
FOOD, RENT, ADVERTISING, AND SO ON.
HERE’S SOME EXAMPLE DATA, FROM
THE SOUTH COAST PLAZA LOCATION IN SOUTHERN CALIFORNIA.
WAHOO’S GATHERS THESE DATA ON EACH STORE EVERY FOUR WEEKS.
DATA LIKE THESE, WITH FEW OBSERVATIONS,
CAN EASILY BE PRESENTED AS A STEMPLOT.
THIS STEMPLOT SHOWS THE SALES FOR
EACH FOUR-WEEK PERIOD DURING ONE YEAR,
IN THOUSANDS OF DOLLARS.
WE SEE A SINGLE-PEAKED DISTRIBUTION
CENTERED AROUND $127,000,
A GAP SPANNING THE 150,000 AND 160,000 STEMS,
AND AN UNUSUALLY HIGH VALUE— AT $177,000.
IN ADDITION TO PICTURES, WAHOO’S MANAGEMENT
NEEDS NUMBERS TO QUANTIFY
IN DOLLARS HOW MUCH EACH STORE
TYPICALLY BRINGS IN OVER A YEAR,
AND HOW FAR EACH STORE’S SALES VARY FROM WHAT’S TYPICAL.
STATISTICALLY SPEAKING, THEY NEED
A MEASURE OF CENTER AND A MEASURE OF SPREAD.
THE MOST COMMON MEASURE OF THE CENTER OF A DISTRIBUTION IS THE MEAN,
WHICH IS THE AVERAGE OF ALL VALUES OF
THE VARIABLE X IN THE DATA SET.
WHEN THE VALUES IN THE DATA SET REPRESENT
THE ENTIRE POPULATION,
THE MEAN IS SYMBOLIZED BY THE GREEK LETTER “MU.”
WHEN THE VALUES REPRESENT
A PORTION OF A POPULATION, OR SAMPLE,
THE MEAN IS REFERRED TO AS X-BAR.
THE SALES DATA FROM WAHOO’S SOUTH COAST PLAZA
IS A SAMPLE OF ONE YEAR.
FINDING X-BAR FOR THESE DATA IS SIMPLY
A MATTER OF ADDING UP ALL THE ACTUAL VALUES
OF X AND DIVIDING BY THE NUMBER OF
OBSERVATIONS N IN THE SAMPLE—THIRTEEN BECAUSE
A YEAR CONSISTS OF THIRTEEN FOUR-WEEK PERIODS RATHER THAN 12 MONTHS.
FOR THESE DATA, X-BAR EQUALS A LITTLE OVER $130,000.
SOME PERIODS ARE LOWER AND SOME ARE HIGHER,
BUT THAT’S THE AVERAGE NET SALES FOR THIS STORE.
NOW THEN, THE CENTER IS JUST ONE MEASURABLE
ASPECT OF A DISTRIBUTION.
HAVING A NUMERICAL WAY TO DESCRIBE THE VARIABILITY,
OR SPREAD, IS EQUALLY IMPORTANT.
A KEY MEASURE OF THE SPREAD OF A DISTRIBUTION IS THE STANDARD DEVIATION.
THE STANDARD DEVIATION MEASURES HOW FAR THE SALES FIGURES
TYPICALLY DIFFER, OR DEVIATE, FROM THE MEAN SALES FIGURE.
IN FACT, TO COMPUTE THE STANDARD DEVIATION (OR “S.D.”),
YOU BASICALLY JUST AVERAGE UP ALL OF THE SQUARED DIFFERENCES
OF THE SAMPLE OBSERVATIONS FROM THEIR MEAN, X-BAR,
THEN TAKE THE SQUARE ROOT.
YOU’LL SEE MORE DETAILS IN CLASS OR YOUR TEXTBOOK.
IF THE STANDARD DEVIATION REFERS
TO THE SPREAD OF DATA IN A POPULATION,
IT IS WRITTEN AS THE GREEK LETTER SIGMA.
IF IT REFERS TO THE SPREAD OF A SAMPLE – THE USUAL CASE --
IT IS WRITTEN AS S IN MATH NOTATION.
FOR THE SAMPLE DATA FROM THE SOUTH COAST PLAZA STORE,
THE STANDARD DEVIATION IS JUST OVER $17,000.
THUS, WE CAN SAY THAT “MOST” PERIODS HAVE
NET EARNINGS WITHIN ABOUT
$17,000 OF THE MEAN VALUE OF ABOUT $130,000.
THE “CENTER” OF A DISTRIBUTION TELLS US ABOUT
WHERE OUR DATA TENDS TO BE LOCATED.
MEANWHILE, THE “SPREAD” OF A DISTRIBUTION TELLS
US ABOUT HOW VARIABLE THE DATA ARE AROUND THEIR CENTER.
BOTH ARE IMPORTANT CHARACTERISTICS, AS, FOR EXAMPLE,
TWO DISTRIBUTIONS COULD HAVE THE SAME CENTER
BUT DIFFERENT SPREADS, OR VICE-VERSA.
FINALLY, NOTE THAT THE MEAN IS JUST ONE MEASURE OF CENTER,
AND THE STANDARD DEVIATION IS JUST ONE MEASURE OF SPREAD...
THERE ARE ALTERNATIVES FOR EACH THAT MAY BE
MORE APPROPRIATE IN CERTAIN SITUATIONS.
YOU’LL LEARN MORE ABOUT THIS IN CLASS.