Session 2

Statistics, Data Analysis, Probability

And

Mathematical Reasoning

Chapters 2 and 7

OFL Prep Sessions

CAHSEE PREP.

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.)

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?

Mean, Median, and Mode

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

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?

Circle Graphs

Bar Graphs

Scatterplots

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?

Scatterplots

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.

Probability

Probability = the chance that an event will happen

Probability of an independent event =

Number of favorable outcomes

Number of possible outcomes

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.

Probability

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?

Probability – Compound Events

Independent and Dependent Events

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?

Mathematical Reasoning

Now we will continue with a section of Mathematical Reasoning.

Mathematical Reasoning is Chapter 7 in your workbook.

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?

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?

Use Estimation to Verify Reasonableness of Results

Using Patterns to Make Conjectures

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.

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?

HOMEWORK

See Assignment Sheet – Session 2

Homework is due at the next class meeting or by the assigned date!