- WELCOME TO A LESSON ON HOW TO DETERMINE
THE MEAN, MEDIAN AND MODE OF A SET OF DATA.
A STATISTIC IS A NUMBER THAT DESCRIBES A SET OF DATA.
THE MEAN, MEDIAN AND MODE ARE THREE STATISTICS
THAT HELP DESCRIBE A SET OF DATA,
AND THEY EACH DESCRIBE DIFFERENT INFORMATION
ABOUT THE SET OF DATA.
THE MEAN IS THE AVERAGE,
WHICH WE'RE PROBABLY MOST FAMILIAR WITH.
SO TO DETERMINE THE MEAN,
WE JUST ADD ALL OF THE NUMBERS
AND THEN DIVIDE BY THE NUMBER OF NUMBERS.
THE MEDIAN IS THE NUMBER IN THE MIDDLE
WHEN THE DATA IS ORDERED FROM LEAST TO GREATEST.
SO TO FIND THE MEDIAN,
WE HAVE TO ORDER THE NUMBERS FROM LEAST TO GREATEST
AND THEN DETERMINE THE NUMBER THAT WOULD BE IN THE MIDDLE,
MEANING HALF THE DATA WOULD BE ABOVE IT
AND HALF THE DATA WOULD BE BELOW IT.
AND IF THERE ARE TWO NUMBERS IN THE MIDDLE,
WE HAVE TO FIND THE MEAN OF THE TWO NUMBERS.
AND THEN LASTLY, THE MODE IS THE NUMBER OR NUMBERS
THAT OCCUR THE MOST OFTEN.
LET'S GO AHEAD AND LOOK AT AN EXAMPLE.
LET'S SAY WE HAVE A SET OF TEST SCORES,
AND WE WANT TO FIND THE MEAN, MEDIAN AND MODE.
WELL, TO FIND THE MEAN,
WE HAVE TO ADD ALL OF THESE NUMBERS UP OR FIND THEIR SUM
AND THEN DIVIDE BY THE NUMBER OF NUMBERS.
SO THERE ARE ONE, TWO, THREE, FOUR, FIVE, SIX, SEVEN, EIGHT,
NINE NUMBERS.
SO WE'LL DIVIDE THIS SUM BY NINE.
LET'S GO AHEAD AND USE OUR CALCULATOR,
AND THE LAST NUMBER WAS 90.
AND WE'RE GOING TO TAKE THIS SUM AND DIVIDE BY NINE,
BECAUSE THERE ARE NINE NUMBERS THAT WE'RE FINDING THE SUM OF.
SO THE AVERAGE OR THE MEAN IS APPROXIMATELY 85.6.
NOW, TO FIND THE MEDIAN,
WE FIRST HAVE TO ORDER THE DATA FROM LEAST TO GREATEST.
I'VE ALREADY DONE THAT HERE IN RED TO SAVE SOME TIME,
AND NOW THAT THE DATA IS IN ORDER FROM LEAST TO GREATEST,
THE MEDIAN WILL BE THE NUMBER THAT'S IN THE MIDDLE,
MEANING WHERE HALF THE VALUES ARE ABOVE,
AND HALF THE VALUES ARE BELOW THAT GIVEN NUMBER.
AND SINCE THERE'S AN ODD NUMBER OF NUMBERS HERE,
88 WILL BE THE MEDIAN,
BECAUSE THERE ARE FOUR NUMBERS ABOVE 88
AND FOUR NUMBERS BELOW 88.
SO OUR MEDIAN IS 88.
THAT ALSO TELLS US THAT HALF OF THE VALUES ARE ABOVE 88
OR 50% OF THE VALUES ARE ABOVE 88,
AND 50% OF THE VALUES ARE BELOW 88.
AND THEN LASTLY, THE MODE
IS THE NUMBER OR NUMBERS THAT OCCUR THE MOST OFTEN.
IT'S OFTEN HELPFUL TO DETERMINE THE MODE
WHEN THE DATA IS IN ORDER FROM LEAST TO GREATEST.
THERE ARE TWO 74s, TWO 83s,
AND THERE'S ONLY ONE OF ALL THE OTHER VALUES.
SO THERE ARE TWO MODES IN THIS CASE, 74 AND 83.
LET'S GO AHEAD AND CONSIDER A SIMILAR SITUATION
WHERE WE HAVE A BUNCH OF TEST SCORES,
AND WE WANT TO DETERMINE THE MEAN, MEDIAN AND MODE.
HERE WE HAVE 12 DATA VALUES.
SO WE'RE GOING TO GO AHEAD AND FIND THE SUM
AND THEN DIVIDE BY 12 TO DETERMINE THE MEAN.
SO LET'S GO AHEAD AND GO STRAIGHT TO THE CALCULATOR,
AND THE LAST TWO VALUES WERE 90 AND 92.
SO WE'RE GOING TO TAKE THIS SUM,
AND BECAUSE THERE ARE 12 TEST SCORES,
WE'LL NOW DIVIDE BY 12 TO DETERMINE THE MEAN.
SO NOW, THE AVERAGE OR MEAN IS APPROXIMATELY 80.7.
TO FIND THE MEDIAN,
WE FIRST HAVE TO PUT THE DATA IN ORDER FROM LEAST TO GREATEST.
I'VE ALREADY DONE THAT HERE IN RED,
AND NOW, WE NEED TO DETERMINE THE NUMBER OR NUMBERS
IN THE MIDDLE.
WELL NOW, BECAUSE WE HAVE AN EVEN NUMBER OF DATA ITEMS,
THERE WILL BE TWO NUMBERS IN THE MIDDLE.
83 AND 88 ARE BOTH IN THE MIDDLE,
BECAUSE THERE ARE FIVE VALUES ABOVE THOSE TWO NUMBERS,
AND THERE ARE FIVE VALUES BELOW THOSE TWO NUMBERS.
SO IF THERE ARE TWO MIDDLE NUMBERS,
WE HAVE TO FIND THE MEAN OR AVERAGE OF THESE TWO NUMBERS.
SO THE MEDIAN WILL BE 83 + 88 DIVIDED BY 2.
THAT'S GOING TO GIVE US 85.5 FOR OUR MEDIAN.
SO AGAIN, WHAT THAT MEANS IS 50% OF THE CLASS SCORED ABOVE 85.5,
AND 50% SCORED BELOW 85.5.
NOW, LET'S GO AHEAD AND DETERMINE THE MODE.
AGAIN, IT'S OFTEN HELPFUL TO DETERMINE THE MODE
WHEN IT'S IN ORDER FROM LEAST TO GREATEST.
WE HAVE TWO 74s.
NOTICE WE HAVE THREE 83s,
AND SINCE 83 OCCURS MORE OFTEN THAN 74,
WE ONLY HAVE ONE MODE THIS TIME. THE MODE WOULD BE 83.
NOW, LET'S GO BACK TO THE PREVIOUS PROBLEM
JUST FOR A MOMENT.
NOTICE HERE THE MEAN AND MEDIAN WERE PRETTY CLOSE IN VALUE,
AND IN THIS EXAMPLE
THE DIFFERENCE BETWEEN THE MEAN AND THE MEDIAN IS LARGER.
THE REASON THE MEAN IS SO MUCH LOWER
IS BECAUSE IF YOU LOOK AT THE TEST SCORES,
THIS TEST SCORE RIGHT HERE IS REALLY LOW,
AND IT HAS A VERY LARGE IMPACT ON THE MEAN,
BUT IT DOESN'T HAVE AS MUCH OF AN IMPACT ON THE MEDIAN.
AND THAT'S ONE OF THE REASONS WHY IT'S SO IMPORTANT
TO HAVE MORE THAN ONE STATISTIC TO DESCRIBE A SET OF DATA.
THE VALUES THAT ARE REALLY LARGE OR REALLY SMALL
FROM MOST OF THE OTHER VALUES
ARE SOMETIMES CALLED OUTLIERS,
AND THEY CAN HAVE A MUCH LARGER IMPACT ON THE MEAN
THAN THEY DO THE MEDIAN.
AND TO ILLUSTRATE THIS,
LET'S GO AHEAD AND TAKE A LOOK AT AN ANIMATION.
HERE WE HAVE A SET OF DATA,
AND YOU CAN SEE HERE WHAT THE MEAN, MEDIAN AND MODE ARE,
AND WHAT YOU'RE GOING TO SEE HERE
IS THE EFFECT ON THE MEAN, MEDIAN AND MODE
IF WE CHANGE JUST ONE VALUE IN THIS SET OF DATA.
WE'RE GOING TO START TO INCREASE THIS VALUE HERE OF -10.
NOTICE AS IT INCREASES, THE MEDIAN DOES NOT CHANGE,
BUT THE MEAN IS INCREASING DRAMATICALLY.
AND THIS JUST DEMONSTRATES WHY IT'S SO IMPORTANT TO HAVE
MORE THAN ONE STATISTICAL MEASURE
TO DESCRIBE A SET OF DATA.
OKAY. THAT'S GOING TO DO IT FOR THIS VIDEO.
I HOPE YOU FOUND THIS HELPFUL.