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Warm-up 2/11/08

A cylindrical container with an inside height of 6 feet has an inside radius of 2 feet. If the container is 2/3 full of water, what is the volume, in cubic feet, of the water in the container?

≈50.3 cubic feet

§1.1: Tables and Graphs

LEQ: How do you use samples to make inferences about populations?

Refer to the chapter opener on p. 5.

Use the information to find the following:

Find the percentage of accidental deaths caused by each of the following methods.

- Motor vehicle accidents
- Falls
- Poisoning
- Fires
- Drownings
- Choking
- firearms

Vocabulary

- Statistics
- Branch of math dealing with collection, organization, analysis, and interpretation of information (data)
- Data
- Information that is collected
- Variable
- A characteristic that can be counted, measured, classified, or ordered
- Ex) religion, height, weight, race, # siblings

- The set of all things you want to study
- Sample
- A portion of a population that is being studied
- A subset of the population
- Survey
- Process of gathering information through interview or questions
- Census
- Survey of an entire population
- Random
- Every member of a population has an equal chance of being selected

Graphs

- Bar graphs
- Most appropriate when one variable is categorical and another numerical
- Circle graphs
- Most appropriate when data consists of a sum and its component parts
- Remember x/360 = part/whole population

Warm-up 2/12/08

Here are the approximate areas and populations (1995) of the continents of the world. Construct a circle graph of the areas.

§1.2: Stem plots and Dot plots

LEQ: How do you use stem plots to describe data sets and to compare/ contrast data sets?

Read p. 13 – 16 (10 minutes)

Answer p. 16 #1 – 3 in notes

NOTES…

- Stem plots can show data in the order they were recorded or in numerical order (both are ok)
- Dots can be used to split large leaves into more manageable groups
- Outliers are not just at extremes, but must also be away from the cluster of other values

“Coding”

- Data involving decimals or negative numbers can be changed to positive whole numbers by “coding” the data
- 1.001, 0.079, 0.167
- Multiply all by 1000
- Negative numbers can be coded by adding a large number to all data values to make them positive

Summary

How are stem plots useful for organizing data?

Warm-up 2/13/08

Find the mean and median salary.

Why do you suppose workers may be upset that the company reports the “Average Worker Earns $51,000”?

Summation Notation

- Sigma
- “summation notation”
- “sigma-notation”
- “Σ-notation”
- “the sum of the x-sub-i’s as i goes from a to b”
- “I” is the index because it indicates the position of a number.

Measures of Central Tendency

- “measures of center”
- Usually refers to all three (mean, median, mode); in some cases, may only refer to mean and median
- Very low or very high scores may pull a mean up or down, while the median may not change
- When finding mean, if there are multiple frequencies, don’t forget to multiply f# of x.
- “x-bar”

Calculator operations

- Stat utilities
- Sort
- 1 & 2 – var stats
- List utilities
- Retrieving lists
- “ops”
- “math”
- Min, max, mean, median, sum, std dev, variance
- Residuals

Warm-up 2/14/08

- Find the median of the #’s above the median.
- Find the median of the #’s below the median. (same chart from yesterday)

(1.3 worksheet)

Assignment

1.3 Worksheet (Guided Practice)

Section 1.3

p. 25 – 28

#1, 3, 9 – 15, 18 – 21

Read

Section 1.4

p. 29 – 33 in textbook

Answer p. 34 # 1 – 5

§1.4: Quartiles, Percentiles, Box Plots

LEQ: How do you read and interpret box plots?

Spread (range)

Quartiles

Four subsets of the data

First quartile (middle of lower #’s)

Second quartile (middle – Median)

Third Quartile (middle of upper #’s)

More Vocabulary

- Interquartile range
- Q3 – Q1 (the difference between the largest and smallest quartile)
- “five number summary”
- Min x, Q1, Med, Q3, Max x
- Percentiles
- “p” percent of the numbers are less than that value
- Ex. Maximum is the 100th percentile

Box Plots

- Enter data into stat
- 2nd Y=
- stat plot on
- Select box plot
- Lower “whisker” is minimum
- Lower box corner is lower quartile
- Middle is median
- Upper box corner is upper quartile
- Upper “whisker” is maximum

Finding outliers

- Technical definition of an outlier
- Find “interquartile range” (Q3 – Q1)
- Q3 + 1.5(IQR) is an upper outlier
- Q1 – 1.5(IQR) is a lower outlier
- Some statistics utilities will show any outliers as dots beyond the whiskers

Warm-up 2/19/08

- Suppose x1 = 2, x2 = 7, x3 = 4
- Evaluate each expression.

Reminders

- Take Home quiz
- Retests today and tomorrow after school
- Extra credit test this Friday (1st block) over Greek alphabet

§1.5: Histograms

LEQ: How do you read and interpret histograms?

What is a histogram?

Frequency histogram –

Organizes data into groups by frequency

Relative Frequency histogram –

Organizes data into groups by percent values

Drawing a histogram

- Organize the data into non-overlapping intervals of EQUAL WIDTH
- Count number of observations per interval & record results in a frequency table
- Draw the histogram
- Mark endpoints of intervals on horizontal axis
- Mark frequencies on vertical axis
- No space should be between horizontal groups (because histograms often represent continuous variables)

What a histogram tells you

- Information about spread
- Shows clusters
- A skewed histogram has more data to the left or right
- Poor choice of intervals can make a histogram difficult to interpret
- Histograms can be distorted if intervals are not of equal width
- Too few intervals will lump data together

Practice

- 1.5 Worksheet
- Section 1.5
- P. 43 – 45
- #1, 4 – 8, 13 – 18, 20 - 26

Warm-up 2/20/08

- Mara knows she has an 88 average in her biology class. But she lost one of her papers. The three papers she could find have scores of 98%, 84%, and 90%. What is the score on her fourth paper?
- Gabriel earns 87 % on his first geography test. He wants to keep a 92% average. What does he need to get on his next two tests to bring his average up?

Reminders

- Retests today after school
- Sign-up for verbal tests over Greek alphabet on Friday
- Another Extra Credit?!
- Read 1-8 in book and answer questions 1 – 9
- Turn in date?

§1.7: Standard Deviation & Variance

LEQ: How do you describe relations between measures of central tendency and spread?

What does deviation mean?

What do you think it means in terms of statistics?

Standard Deviation

Four students had summer jobs at a camp last year. Four other students had jobs at a nursing home. Their weekly pay is listed.

Camp Nursing Home

$150 $140

$160 $190

$220 $210

$270 $260

Calculate the mean for the pay in each location.

What is the range of weekly pay for each location?

- Copy the table

Find the deviation from the mean by subtracting the mean from the salary value.

- Complete column 4 by squaring each value in column 3.
- Complete a table like the one above for the nursing home workers.
- Compare the deviations from the mean at the two locations.

At which location does the pay vary more?

Standard deviation shows how a set of data is spread out.

Small standard deviation means that everything is right around the mean.

Large standard deviation means that everything is more spread out.

Eight Steps for Standard Deviation

- Find the mean of the data. X
- Find the difference (deviation) of each data value from the mean
- Calculate the square of each deviation
- Find the sum of the squares of the deviations
- Divide the sum by the number of data values minus 1 (n – 1).
- This is the variance.
- Take the square root of the variance.
- This is the standard deviation.

Using the calculator

Of course, the standard deviation can be found using the calculator.

Input values into stat.

Stat, calc, 1 variable stats

Now you know what the rest of them mean!

Center vs. Spread

- Measures of Center
- Mean
- Median
- Mode
- Measures of spread
- Range
- Variance
- Standard deviation
- Interquartile range

Assignment

1 – 7 Handout

Section 1 – 7

p. 58 – 59

#1,2, 6, 8, 10 – 14, 16 – 18, 20, 24

HW: Read p. 46 – 50 in books

(for comprehension!)

Warm-up 2/21/08

- A single word with the same meaning as “average rate of change” is _________.

What types of graphs…

(list all that apply)

2) Show individual data points?

3) May be used for one-variable data sets?

- Display a relation between parts to whole?
- Show the five-number-summary?
- Display distribution of data?
- Show time-series data?

Reminders

- Final retests for Unit 3 Test must be done by Friday afternoon
- Test over Greek alphabet changed to next Wednesday
- Another Extra Credit
- Read Section1-8 in book and answer questions 1 – 9
- Turn in by Wednesday (2/27)

Assignment

1 – 7 Handout (HW)

HW: Read p. 46 – 50 in books

(for comprehension!)

Section 1 – 7

p. 58 – 59

#1,2, 6, 8, 10 – 13, 16 – 18, 24

Warm-up 2/22/08

In a botany experiment, Lana recorded the number of days it took for each of ten plants to flower. She obtained the following data:

13,15,12,10,17,18,8,10,13,14

- For these data, find the mean, variance, and standard deviation.
- In an earlier experiment, Lana found that when fertilizer was applied, the number of days before plants flowered had mean 11 and standard deviation 1.5. What seems to be the effect of the fertilizer?

Group Work

- Form 5 groups (desk groups?) of 4 – 5
- Collect data: (“project 6, p.69)
- Work as a class or as a group??
- Gender/grade in school/age
- Pulse rate
- Height
- Eye color
- # siblings

Process, Explanation, Questions?

Using the data collected from the class:

- Construct a table/spreadsheet for the data
- Summarize and display the data

For each variable, decide which type of display is most appropriate (box plot, stem plot, circle graph, bar graph, etc.)

Whenever appropriate, calculate statistics such as mean, median, standard deviation, percentiles, and range.

3) Display your information in a professional format.

After all the data is displayed:Write 2 paragraphs

- Write one paragraph describing a “typical” student in this class in terms of the variables analyzed. For numerical values, this will include both the center and spread of the distributions.
- Find a variable whose value differs quite a bit by gender (or age). Find a variable whose value doesn’t differ much by gender. Justify your conclusions with numerical measures or displays.

Reminders:

I’ll be out tomorrow.

I will have you starting a new unit on functions.

You’ll have to read as well as complete an assignment.

Remember, Wednesday morning will be the verbal Greek test and also section 1-8 E.C. will be due.

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