Transcript Statistics, Data Analysis, and Probability

Statistics, Data
Analysis, and
Probability
PS 1.1- Mean, Median, Mode
Period 3, 5: 1/3/11
Period: 2, 4, 6: 1/4/11
Mode
• Mode is the most frequently
occurring number in a set.
Example:
For the set [3, 2, 8, 2, 4]
The number that appears most
often is 2, so 2 is the mode.
Mode
Big Note: If there’s more than one
number that appears most often,
that’s okay. Some sets will have
multiple modes.
Example:
For the set [3, 2, 8, 2, 4, 3]
The numbers that appear most often
are both 2 and 3, so the modes of
this set are 2 and 3.
continued…Mode
• For the set [3, 2, 8, 4]
Since no numbers appear more
than any other numbers, there
is no mode for this set.
White Board CFU
• The box below shows the number of
kilowatt-hours of electricity used last
month at each of the houses on Harris
street.
620, 570, 570, 590, 560, 640, 590, 590,
580
What is the mode of this data?
Mean
• Mean is often referred to as the
“average” of a set of numbers. To find the
mean, add up all the values, and divide
the sum by the number of values in the
set.
MEAN= (sum of a group of numbers)
(NUMBER of numbers in the group)
Example
In calculating mean…
• If the values are 15, 45, and
33
• The sum is 15+45+33=93
• The number of numbers in the
set is 3
• So 93÷3=31
Whiteboard CFU
Parisa’s four math test scores were 7, 8,
10, and 6. Hector’s test scores were 6, 7,
9, and 10. Charles’ test scores were 8,
10, 10, and 9.
What is Hector’s mean score?
Median
• Median is the middle number
in an ordered set.
• You must put the numbers in
order.
• In an even set of numbers, the
median is the mean of the two
middle terms.
Example
• For the set [3, 7, 8, 2, 4]
These numbers aren’t in order,
so place them in order:
2, 3, 4, 7, 8
The middle number is 4, so 4 is
the median.
Whiteboard CFU
• Find the median for the
following set
[3, 7, 8, 2, 4, 6]
ANSWER
• 4 and 6 are both in the middle
• The average of 4 and 6= 5, so
the median of this set is 5.
PS 1.2- Probability
• Probability refers to the likelihood that a
certain event will happen, such as
flipping heads or tails on a coin, or
pulling particular color of marble out of a
bag.
Probability
The probability of an event occurring
is always
the number of DESIRED outcomes
The TOTAL POSSIBLE outcomes
Example
For instance, if you’ve got a deck of cards and
you want to pull out a spade, the number of
desired outcomes (what you want to happen)
would be 13, since there are 13 spades in a deck
of cards.
The number of total possible outcomes would be 52,
since there are 52 total cards in the deck.
Therefore:
the number of DESIRED outcomes= 13 = 1
the TOTAL POSSIBLE outcomes
52 4
So the probability of picking a spade would be 1/4 or
25%.
BIG NOTE
• The CAHSEE will try to trick you on
probability problems. If the previous
example has told us that the ace of
spades had been removed from the
deck, and then we were to choose a
card, that would change how we
determine the probability.
Big Note continued…
• Since one of the spades had been
removed, there would only be 12 spades
(instead of 13), so 12 would have been
the number of desired outcomes.
• Also, removing that one card from the
deck means that there would only be 51
total cards.
BIG NOTE #2
• Another common trick involves understanding
what doesn’t affect probability. Let’s say you
flipped a coin ten times, and it came up heads
every single time.
• What would be the probability that it came up
heads on the eleventh flip?
* Getting heads ten times in a row may be unlikely,
but it doesn’t affect probability on the eleventh
flip.
WHITE BOARD CFU
• A bucket contains 3 bottles of apple
juice, 2 bottles of orange juice, 6 bottles
of tomato juice, and 8 bottles of water. If
Kira randomly selects a bottle, what is
the probability that she will select a drink
other than water?
ANSWER
• DESIRED outcomes= 11
• TOTAL POSSIBLE outcomes=
19
= 11
19
Independent Practice
Independent Practice PS 1.1
1) 18, 18, 15, 18, 18, 24, 21, 21,
24, 14
Independent Practice PS 1.2
• 1) Drawing a 6 from a deck of cards?
•
2) Drawing a black card from a deck of
cards?
3) 4, 18, 18, 23, 23, 19, 8, 8, 8, 8,
28
•
3) Rolling an odd number on a die?
4) 12, 15, 16, 17, 15, 17, 17, 17,
18, 17
•
4) Drawing a 3 from a deck of cards?
•
5) Drawing a club from a deck of
cards?
•
6) Rolling an even number on a die?
•
7) Rolling a 6 on a die?
2) 94, 69, 84, 69, 90, 75, 94, 90,
90, 9, 5
5) 16, 3, 3, 3, 8, 24, 16, 9, 11, 11
6) 22, 5, 22, 13, 12, 24, 24, 9, 24,
19
7) 23, 1, 1, 18, 1, 3, 18, 10, 7, 3
8) 23, 10, 2, 6, 10, 14, 1, 19, 8, 19