MATH 1A CHAPTER TWELVE POWERPOINT PRESENTATION

DATA, STATISTICS, AND PROBABILITY

LEARNING TARGETS

• AFTER YOU FINISH THIS CHAPTER, YOU WILL BE ABLE TO:• CONSTRUCT GRAPHS AND INTERPRET INFORMATION

ILLUSTRATED BY THEM.• RECORD AND UNDERSTAND MEASURES OF CENTRAL

TENDENCY.• RECORD AND UNDERSTAND DATA IN A FREQUENCY

TABLE.• CONSTRUCT BOX AND WHISKER PLOTS/SCATTER-PLOTS/

AND STEM AND LEAF PLOTS.• SOLVE PROBLEMS INVOLVING PROBABILITY.

BAR GRAPHS

• SATISTICS: NUMERICAL FACTS ABOUT PEOPLE, PLACES, OR THINGS.

• DATA: INFORMATION GIVEN IN NUMBERS.• BAR GRAPH: A WAY OF COMPARING

INFORMATION USING RECTANGULAR BARS.• INTERVAL: A SET OF ALL NUMBERS BETWEEN

TWO STATED NUMBERS.• BAR GRAPH: USUALLY SHOWN WITH AN X AND

Y AXIS. IT WILL HAVE A TITLE AND DATA.

EXAMPLE OF A BAR GRAPH

CIRCLE GRAPHS

• CIRCLE GRAPH: USED WHEN YOUR DATA IS RECORDED IN PERCENTAGES. THIS IS A WAY OF PRESENTING DATA IN A CIRCLE FORMAT:

FREQUENY TABLE AND HISTOGRAM

• FREQUENCY: THE NUMBER OF TIMES AN EVENT, VALUE, OR CHARACTERISTIC OCCURS.

• FREQUENCY TABLE: A CHART SHOWING THE NUMBER OF TIMES SOMETHING HAS HAPPENED.

• TALLY: A MARK OF EACH COUNT.• HISTOGRAM: A BAR GRAPH WHERE THE BARS

TOUCH, MADE AFTER YOU HAVE MADE A FREQUENCY TABLE.

EXAMPLE OF FREQUENCY TABLE AND HISTOGRAM

MEASURES OF CENTRAL TENDENCY

• CENTRAL TENDANCY: THE MEAN, MEDIAN, AND MODE OF A SET OF DATA.

• MEAN: THE AVERAGE• MEDIAN: THE NUMBER IN THE MIDDLE• MODE: MOST OFTEN LISTED NUMBER• OUTLIER: A NUMBER THAT SKEWS THE DATA

BY BEING TOO LARGE OR SMALL.• RANGE: THE DIFFERENCE IN THE LARGEST AND

SMALLEST PIECE OF DATA.

THE BELL SHAPED CURVE

• DATA TRENDS AROUND A BELL SHAPED CURVE.

BOX-AND-WHISKER PLOTS

• BOX-AND-WHISKER-PLOT: A WAY TO SHOW THE SPREAD OF DATA IN A SET OF NUMBERS.

• LOWER EXTREME: LOWEST VALUE• UPPER EXPTREME: HIGHEST VALUE• LOWER QUARTILE: MEDIAN OF SCORES

BELOW THE MEDIAN.• UPPER QUARTILE: MEDIAN OF VALUE ABOVE

THE MEDIAN.

BOX-AND-WHISKER-PLOTS

• QUICKLY SHOW THE MEDIAN AND QUARTILES, OF THE DATA.

SCATTER PLOT

• SCATTER PLOTS SHOW EACH PIECE OF DATA WITH A DOT. IT IS A GRAPH THAT WILL SHOW HOW TWO EVENTS CORRELATE (HAVE AN IMPACT ON EACH OTHER).

• THERE ARE THREE KINDS OF CORRELATION:• POSITVE, NEGATIVE, AND NO CORRELATION.

EXAMPLE OF A SCATTER PLOT WITH POSITIVE CORRELATION

EXAMPLE OF A SCATTER PLOT WITH NEGATIVE CORRELATION

EXAMPLE OF A SCATTER PLOT WITH NO CORRELATION

STEM AND LEAF PLOT

• A WAY OF DISPLAYING EVERY PIECE OF DATA IN A WAY THAT RELIES ON SECTIONS OF TEN.

PROBABILITY

• PROBABILITY: THE CHANCE OR LIKELIHOOD OF AN EVENT OCCURRING.

• OUTCOME: THE RESULT OF A PROBABILITY EXPERIMENT.

• THE PROBABILITY FRACTION DIVIDES THE NUMBER OF FAVORABLE OUTCOMES BY THE NUMBER OF ALL POSSIBLE OUTCOMES.

• USUALLY, PROBABILITY IS DEMONSTRATED WITH: SPINNERS, NUMBER CUBES, COLORED MARBLES IN A BAG.

EXAMPLES

FUNDAMENTAL PRINCIPLE OF COUNTING

• This means that if one event can be counted in (a) ways and another event can be counted in (b) ways, then the first task followed by the second can be counted in (ab) ways.

• For example: if I have four sweaters, 6 blouses, and 7 pairs of shoes, the total amount of outfits I can combine is: 4 times 6 times 7 or: 168 outfits

Example

FACTORAL NOTATION!

• I CAN ALSO COUNT ALL THE POSSIBLE COMBINATIONS USING FACTORAL NOTATION.

• IT IS A NUMBER FOLLOWED BY AN EXCLAMATION POINT.

• EXAMPLE: MY NAME IS CAROLE – IT HAS SIX LETTERS – HOW MANY DIFFERENT WAYS CAN I ARRANGE THOSE SIX LETTERS: 6! OR 720 WAYS.

DATA!

• WE USE IT EVERY DAY.