Statistics, Data Analysis, Probability

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CAHSEE PREP.
Session 2 Statistics, Data Analysis,
Probability And Mathematical Reasoning Chapters
2 and 7 OFL Prep Sessions
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Mean, Median, and Mode

• Mean the average of the data
• Total of the values
• Number of values
• Median the middle number in a set of data
• (if there is an even number of data points,
  find the mean of the middle two points)
• Mode the value that occurs most frequently
  in a set of data. (It is possible to have a
  data set with no mode.)

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Mean, Median, and Mode
The scores on the last science test are as
follows 85, 75, 53, 43, 62, 65, 100, 70, 73,
75, 43, 83, 82, 60, 90, 69 What is the mean
score? What is the mode of the data?

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Mean, Median, and Mode

• Find the mean, median, and mode of the following
  data 2, 11, 9, 0, 4, 12, 4

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Mean, Median, and Mode
In their last seven games, the West Oaks
basketball team scored 24, 66, 82, 54, 74, 68,
and 78 points. What is the median number of
points scored?

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Circle Graphs
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Bar Graphs
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Scatterplots
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Scatterplots

Several library patrons were surveyed. They were
asked how many miles they drove to reach a public
library on their last visit and the number of
minutes they waited in line to check out books.
Would you expect to find a positive correlation,
a negative correlation, or no correlation between
the number of miles driven and the number of
minutes spent in line?
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Scatterplots
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Validity
1) The mean salary for the last five people
hired for the J.J. Smith Company was 38,000?
2) The mean salary for the last five people
hired for the W.P. Johnson Company was 38,000.
3) When searching for a job, it would make no
difference which company you chose to work for
since the mean salary for both is 38,000.
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Probability

• Probability the chance that an event will
  happen
• Probability of an independent event
• Number of favorable outcomes
• Number of possible outcomes

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Probability
A number cube has faces labeled 1 through 6.
What is the probability of rolling a 5 on a
single roll? What is the probability of not
rolling a 5? Express each answer as a fraction,
a decimal, and as a percent.

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Probability
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Probability Compound Events
Two bags contain marbles. Each bag has 1 purple
and 2 yellow marbles. One marble is pulled from
each bag. What is the probability of choosing 2
yellow marbles?

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Probability Compound Events
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Independent and Dependent Events
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Independent and Dependent Events

• Michael and April are playing a game with seven
  cards. The cards are numbered 1 through 7.
  Michael randomly draws one card and keeps it.
  Then he randomly picks a second card. What is
  the probability that the first card is a 5? What
  is the probability the second card is a 3? Are
  the events independent or dependent?

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Mathematical Reasoning

• Now we will continue with a section of
  Mathematical Reasoning.
• Mathematical Reasoning is Chapter 7 in your
  workbook.

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Formulate and Justify Mathematical Conjectures

• Conjecture The product of two odd whole
  numbers and an even whole number is an even whole
  number. Is this conjecture correct or incorrect?

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Use Estimation to Verify Reasonableness of Results

According to the U.S. census, the population of
San Francisco was 58,802 in 1860. By 1870, the
population had grown to 149,873. About how many
more people lived in San Francisco in 1870 than
in 1860? What was the approximate yearly
increase in population over the 10-year period?
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Use Estimation to Verify Reasonableness of Results

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Using Patterns to Make Conjectures

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Using Patterns to Make Conjectures

• Use deductive reasoning to explain why the
  expression -3y 7 5y is equivalent to 2y 7.
  Give a reason to justify each step.

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Use a Similar Problem to Solve a New Problem

There were 6 people in a room. Each person said
Hello to every other person once. How many
Hello greetings were exchanged?
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HOMEWORK

• See Assignment Sheet Session 2
• Homework is due at the next class meeting or by
  the assigned date!