1. HRSB, 2009 TI-83, TI-83 + Technology Integration DAY 1 Data Management

2. HRSB, 2009

3. Basic TI-83 Keys On – Play Time! (5 min) On – Play Time! (5 min) Multifunction keys Multifunction keys Screen brightness Screen brightness y ^ Negative vs. subtract Negative vs. subtract (-) - Arithmetic operations Arithmetic operations     Clear vs. Quit Clear vs. Quit

4. HRSB, 2009 The Home Screen and BEDMAS It’s a calculator! It’s a calculator! 6 + 3 * 4 = 18 6 + 3 * 4 = 18 It remembers stuff! It remembers stuff! ENTRY (2 nd ENTER) ANS (2 nd (-)) STO  2 nd, entry, STO, X, ENTER – x 2 +2x+1, ENTER It changes stuff! (123456) It changes stuff! (123456) DEL – highlight and DEL INS (2 nd DEL) CLEAR – line, homesreen

5. HRSB, 2009 The Home Screen and BEDMAS BEDMAS rules! BEDMAS rules! Brackets Exponents Division (in order they occur) Multiplication Addition Subtraction Brackets are extremely important!

6. HRSB, 2009 Key Considerations Memory – Resetting; Clearing Lists/entries Memory – Resetting; Clearing Lists/entries ‘The Big Five’ – ‘The Big Five’ – Mode: Mode: Normal SCI (power 10) ENG Digits both left and right of decimal1 Digit left of decimal up to 3 digits Catalog, Math Catalog, Math TI-83/83+ KEY List (handout) TI-83/83+ KEY List (handout) qr o p s

7. HRSB, 2009 DATA MANAGEMENT

8. HRSB, 2009 The Central Measures of Tendency (p.14 Booklet) Describing the Data Average : a number that is typical of a set of numbers. There are three ways of measuring the average: (1) Mean ( ) (2) Median (3) Mode

9. HRSB, 2009 The Mean ( ) Also commonly known as the ‘average’ Also commonly known as the ‘average’ Calculated by dividing the sum of the data set by the number of data values in the set. Calculated by dividing the sum of the data set by the number of data values in the set. EX: What is the class average (to the nearest whole number), given the following test scores? 161820202224242828 = = = = = 22 = 22

10. The Median The middle value in a data set, when arranged in order from least to greatest. The middle value in a data set, when arranged in order from least to greatest. (a) Odd number of data scores 3 8 12 15 15 15 17 18 23 Least ↑ Greatest Least ↑ Greatest middle middle (b) Even number of data scores 3 8 12 14 15 17 18 20 21 23 Least ↑ ↑ Greatest middles

11. HRSB, 2009 The Mode The measurement that occurs the most often in a set of data scores. The measurement that occurs the most often in a set of data scores. You can have more than one mode for a data set. You can have more than one mode for a data set. It is possible to have NO mode for a set of data scores. It is possible to have NO mode for a set of data scores.

12. HRSB, 2009 The Range The difference between the largest data value and the smallest data value within a particular data set. The difference between the largest data value and the smallest data value within a particular data set. EX: EX: 244881521 Range: 21 – 2 = 19 Activity Time – Yellow Page 1

13. HRSB, 2009 Measures of Central Tendency: Using the Calculator 1] For each set of data determine the mean, median, mode and range. Express your answers to two decimal places. (see Yellow Page 2 for calc. instructions) (a) 20, 24, 28, 18, 26, 24, 12, 16, 20 (b) 5, 9, 13, 12, 2, 4, 0, 1, 7, 15, 11 2] Calculate the mean, median, mode and range for the following data set: 12.5, 12.4, 12.2, 12.7, 12.9, 12.2, 12.3, 12.2, 12.6, 12.8

14. HRSB, 2009 Answers: [1] (a) mean: 20.89, median: 20.00, mode: 20 & 24 (b) mean: 7.18, median: 7.00, mode: no mode [2] mean: 12.48, median: 12.45, mode: 12.2 “The Central Measures of Tendency (A)” yellow worksheet Now try: “The Central Measures of Tendency (A)” – yellow worksheet

15. HRSB, 2009 The Central Measures of Tendency (A) StudentMeanMedianMode Alysia84.88%85.50%None Laurie79.13%83.00%90.00% Ahmed78.83%84.50%None (b) Alysia (c) Graduation Average: Alysia – 86.33%; Laurie – 85.17%; Ahmed – 78.83% (d) Both Alysia and Laurie (e) Laurie; Both other students…Fate is sealed!

16. HRSB, 2009 The Central Measures of Tendency (B) (A) Mean: 9.33 Median: size 10 Mode: 10 (b) Discussion (c) Discussion

17. HRSB, 2009 Extension: pg.212 Grade 8 Text Mathematics 8 – Focus & Understanding Yellow Page 5 – Table Groups (Check on Overhead) Yellow Page 5 – Table Groups (Check on Overhead) Last week Mr. Brighton measured the heights of his seven prized oak seedlings. He noted that the range of the heights was 6.20 cm and that his tallest seedling measured 10.80 cm. The mean height was 7.40 cm, the median height was 7.60 cm, and the mode was 8.00 cm. What could be the heights of all seven seedlings? Last week Mr. Brighton measured the heights of his seven prized oak seedlings. He noted that the range of the heights was 6.20 cm and that his tallest seedling measured 10.80 cm. The mean height was 7.40 cm, the median height was 7.60 cm, and the mode was 8.00 cm. What could be the heights of all seven seedlings?

18. HRSB, 2009 Extension Answer (s) (Many solutions) IE: 4.6 5.8 7 7.6 8 8 10.8 ____ ____ ____ ____ ____ ____ ____ Must Have: 4.6 ____ ____ 7.6 ____ ____ 10.8

19. HRSB, 2009 Box and Whisker Plots (pg.15-16 Booklet) Box and Whisker Plots (pg.15-16 Booklet) Orange Sheet 1 Orange Sheet 1 A type of graph used to display data; shows how the data is dispersed around the median but does not show specific scores in the data. A type of graph used to display data; shows how the data is dispersed around the median but does not show specific scores in the data. Key terms: Key terms: - Lower and Upper Extremes – Max & Min Value - Lower Quartile – The median of the lower half of the data - Upper Quartile – The median of the upper half of the data

20. How to Construct a Box and Whisker Plot 1] Construct a # line and mark the upper and lower extremes. The difference between extremes represents the range. 1] Construct a # line and mark the upper and lower extremes. The difference between extremes represents the range. 2] Find the median of the data. Mark this value on # line. 2] Find the median of the data. Mark this value on # line. 3] Find the lower quartile. Mark this value on the # line. 3] Find the lower quartile. Mark this value on the # line. 4] Find the upper quartile. Mark this value on the # line. 4] Find the upper quartile. Mark this value on the # line. 5] Construct a box to show where the middle 50% of the data are located. (Now try Orange Sheet 2) 5] Construct a box to show where the middle 50% of the data are located. (Now try Orange Sheet 2)

21. English Assignment Results… Now let’s display the same data using the TI-83+… 50, 50, 50, 50, 50, 50, 50 60, 60, 60, 60, 60, 60, 60 70, 70, 70,. 70, 70, 70, 70

22. HRSB, 2009 Activity: “Who do we want on our Team?” Orange Page 3 Orange Page 3 Complete in Table groups and discuss your results Complete in Table groups and discuss your results Debrief (next slide) Debrief (next slide)

23. HRSB, 2009 “Who do we want on our Team?” Anne Susan Sonya Discussion : - Middle 50% of the data (the spread) - Consistency - Outliers

24. HRSB, 2009 Box and Whisker Plots – Exercise (A) In table groups complete the “Raisin Activity” using the TI-83+ In table groups complete the “Raisin Activity” using the TI-83+ Discuss your results with table members Discuss your results with table members Debrief – next slide Debrief – next slide

25. HRSB, 2009 Box & Whisker plots: Using the Calculator Exercise A: Exercise A: Brand A Brand B b) Discussion c) Discussion

26. HRSB, 2009 Box & Whisker plots: Using the Calculator Exercise B: [1]Light Bulbs Exercise B: [1]Light Bulbs Brand A Brand B Exercise B: [2]Television (a)Median- 8 (b)Range – Between 6 – 11 hours (c)Discussion

27. HRSB, 2009 Histograms (pg. 17-18 booklet) Another way to display data; used when there are many pieces of continuous data Another way to display data; used when there are many pieces of continuous data Comprised of a graph in which the horizontal axis is a #line with values grouped in Bins (classes), and vertical axis shows the frequency of the data within each bin. Comprised of a graph in which the horizontal axis is a #line with values grouped in Bins (classes), and vertical axis shows the frequency of the data within each bin. Bin: a grouping of the data values (i.e. 0 – 5) Bin: a grouping of the data values (i.e. 0 – 5) Frequency Table: shows how often each data value, or group of values, occurs. Frequency Table: shows how often each data value, or group of values, occurs.

28. BINFREQUENCY 0 – 5 # of times a value between 0 & 5 occurs, not including 5 5 – 10 # of times a value between 5 & 10 occurs, not including 10 10 - 15 # of times a value between 10 & 15 occurs, not including 15 Frequency Table (i.e.) How to Make a Histogram 1. Choose a bin size based on your range of data values. (keep # of bins to ≤10) – Discuss 2. Create a Frequency Table showing group frequencies. 3. Graph the frequency table; connect the bins together in a ‘Bar- graph’ fashion. (let’s try exercise A, Blue Sheet 1)

29. Histograms ex. A 2 6 17 12 24 22 9 10 3 24 5 13 8 14 21 20 11 8 19 7 Bin Sizes: 0 – 5, 5 – 10, 10 – 15, 15 – 20, 20 – 25 Frequency Table: BinsFrequency 0 – 5 2 5 – 10 6 10 – 15 5 15 – 20 2 20 – 25 5

30. HRSB, 2009 Histogram (A) Frequency 0 5 10 15 20 25 Bins Bins

31. Histograms (B) Possibilities: What do we see in each case? #1 - #2 - BinsFreq. 30-402 40-507 50-607 60-708 BinsFreq.30-352 35-400 40-455 45-502 50-552 55-605 60-657 65-701 Let’s use the technology to create a histogram for “Nancy’s Basketball scores” on Blue Sheet 3…(sketch)

32. Calculator Applications (pg 17-18 Booklet): Nancy JohnSam 1] Describe each of the Histograms. 2] Describe each person as a basketball player. 3] Compare these players with Janie’s Data distribution: Janie

33. HRSB, 2009 Histogram Extension Problem Blue Sheet 4 Blue Sheet 4 In table groups, complete the ‘Black Spruce Tree’ activity In table groups, complete the ‘Black Spruce Tree’ activity Discuss results Discuss results Refer to solution on next slide Refer to solution on next slide

34. Extension Problem (Discussion) Forest Environment VS. Nursery Environment Forest:Nursery:

35. Scatter plots – Line of Best Fit Regression!  A graph of ordered pairs of numeric data  Used to see relationships between two variables or quantities  Helps determine the correlation between the Independent & dependent variables  Correlation: a measure of how closely the points on a scatter plot fit a line  The relationship can be strong, weak, positive or negative  + Correlation – As indep.Var ↑, Dep. Var ↑  - Correlation – As indep. Var ↑, Dep. Var ↓

36. HRSB, 2009 Line of Best Fit  Drawn through as many data points as possible  Aim to have an equal amount of data points above and below the line  Does NOT have to go through the origin  Allows us to generate an equation that describes the relationship using an equation form (ie: y = mx+b) Example 1, Pink Sheet 1 – Discuss (draw LOBF for each) Example 2, Pink Sheet 1, Let’s do together using the TI-83+ TI-83+

37. Calculator Applications: 10. (pg. 38-42 Booklet)  Example 2: Line of Best Fit 1. 2. 3. 4. 5. 6. 7. 8. 9.

38. HRSB, 2009 Linear Regression & Correlation Coefficient (r)  Determining the Equation for the Line of best fit can be referred to as: Regression Analysis  We create a model that can be used to predict values of the Dep. Var. based on values of the Indep. Var.  The ‘r’ value – Correlation Coefficient - measures the strength of the association of the 2 variables; (-1 → +1) – the closer to either, the stronger the relationship (-1 → +1) – the closer to either, the stronger the relationship Pink Sheet 3 – complete in table groups – (steps on page 4, 5 pink sheets) (steps on page 4, 5 pink sheets)

39. HRSB, 2009 Regression Analysis Pg.383, Gr. 9 Text, #13 Window Scatter plotCorrelation  EquationGraph

40. HRSB, 2009 Extrapolating data:  Determining # injured in 2010: Change ‘window’ to include this x parameter (Xmax – 2050) The new graph: Next Key Strokes: 2 nd CALC 1:value Type in 2010 Y value when x = 2010, is

41. HRSB, 2009 Regression Analysis Cont.  Example 3, 4: Pink Sheet 3 - EXTENSION - Looking at Parabolic & Exponential Relationships - Complete these problems together

42. HRSB, 2009 THE END  Q & A  Possibilities for further extension on TI-83+  Suggestions for future PD sessions  Wrap-up; Sub Claim Forms Contact Information: Sohael Abidi Leader, Mathematics Halifax Regional School Board Ph: 464-2000 ext. 4456 sabidi@hrsb.ns.ca