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Understanding Volume, Statistics, and Data Representation in Mathematics

This resource covers key mathematical concepts such as volume calculations using a cylindrical container, basic statistical principles, and data representation techniques. The container's water volume is explored through an example, alongside the significance of using samples to infer population characteristics. It includes a vocabulary section defining terms such as population, sample, and survey, in addition to explanations on stem-and-leaf and dot plots. The guide highlights the importance of understanding mean, median, and measures of central tendency and illustrates how box plots are utilized in data interpretation.

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Understanding Volume, Statistics, and Data Representation in Mathematics

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  1. 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

  2. Finish Unit 3 Test 20 minutes Work on papers/any make up work?

  3. §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:

  4. Find the percentage of accidental deaths caused by each of the following methods. • Motor vehicle accidents • Falls • Poisoning • Fires • Drownings • Choking • firearms

  5. 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

  6. Population • 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

  7. 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

  8. 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.

  9. Reminder: • Extra Credit projects due Thursday • Send copy of projects to my email: cphippen@lanier.k12.ga.us

  10. Assignment Section 1.1 p.10-11 #5 – 20 Discuss/Do as a class

  11. §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

  12. 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

  13. “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

  14. Summary How are stem plots useful for organizing data?

  15. 1.2 Handout

  16. Assignment Section 1.2 p. 16 – 18 #5 – 16, 19

  17. 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”?

  18. Assignment Section 1.2 p. 16 – 18 #5 – 16, 19

  19. In – Class Activity p. 19 – 20 In books

  20. §1.3: Measures of Center LEQ: How do you compare measures of center? What does it mean? Mean Median Mode

  21. 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.

  22. 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”

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

  24. 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)

  25. Check homework (1.3 worksheet)

  26. 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

  27. QUIZ

  28. §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)

  29. 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

  30. 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

  31. 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

  32. Warm-up 2/19/08 • Suppose x1 = 2, x2 = 7, x3 = 4 • Evaluate each expression.

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

  34. 1.4 Assignment? Section 1.4 p. 34 – 36 # 6 – 15, 17 - 24

  35. Guided Practice Getting back into the groove: 1.4 Worksheet

  36. §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

  37. 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)

  38. 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

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

  40. 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?

  41. Homework? Section 1.5 P. 43 – 45 #1, 4 – 8, 13 – 18, 20 – 26

  42. 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?

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