1. Statistics & Graphs Unit 1 Home 61 Mean, Medians, Modes and Ranges 60 Central Tendency, Find Data 59 Frequency distributions and line plots 58 Bar Graphs 57 Scatter plots 56 Histograms 55 Circle graphs 54 Stem-and-leaf plots 53 Misleading graphs

2. Statistics & Graphs Quote A man who is not somewhat of a poet can never be a mathematician. Karl Weierstrass (VEER strass)

3. Statistics & Graphs Puzzle – Are you really awake? A certain five letter word becomes shorter when you add two letters to it. What is the word? SHORT

4. Statistics & Graphs Example 1-1a 61 a Means, Medians, Modes and Ranges Mean =Average of the data. -Add them up and divide by the number of items you have Median =Middle value of data -Arrange data in order, choose the middle value -If there is no middle number, the Median is the average of the middle numbers Mode =Value that occurs the most -Data with no repeats has no mode -Several repeats occurring same number of times has several modes Range =High value minus the low value

5. Statistics & Graphs 61b Means, Medians, Modes and Ranges What is the Mean, Median, Mode and Range for the data? 8, 7, 20, 8, 22, 7, 7, 9, 4, 28 Mean =12 Median =4, 7, 7, 7, 8, 8, 9, 20, 22, 28 Since there are two middle numbers take the average of the two middle numbers which is 8, The median is 8 Mode =7Range =28-4 = 24  12, 8, 7, 24

6. Statistics & Graphs 61c Means, Medians, Modes and Ranges For the first three sets of numbers below, the value of x represents the same type of measurement for central tendency. Find the value of x for the fourth set of numbers 5 15 20 25 50 x=20 4 8 16 28 40 52 x=22 16 22 22 22 24 x=22 13 13 17 23 29 29 x =___ 20 What type of measurement does x represent?___________Median

7. Statistics & Graphs 61d Activity 1) Form a group of four or five people of the same gender 2) Measure each persons height and total arm length in cm -Record this information alongside their name 4) Calculate mean, median, mode & range for the class. (M & F) Do this for height and arm length separately for M & F. Have in your notebook the height and arm length of everyone in this class….. You will need this data later…! 3) Place your name, height, and arm length on the board -copy this information into your notebook

8. Statistics & Graphs 60 Quote The pursuit of an idea is as exciting as the pursuit of a whale. Henri Poincare (pain ca RAY)

9. Statistics & Graphs 60 Puzzle – Anyone want some coffee? If boiling water is poured into a thick drinking glass or into a very thin wine glass, of the two, which is more likely to crack? The thick glass is more likely to crack.

10. Statistics & Graphs 60a Central Tendency – Find data (ex2) Martha averaged 21 points per game last season and was the leading scorer on her basketball team. This year she has already scored 102 points in 5 games. Which equation can be used to find P, the number of points she must score in the 6th game to tie her last year’s average? (ex1) Catherine scored 152 and 165 for her first two bowling games. What score will she have to achieve on her third game to have an average of 170?

11. Statistics & Graphs 60b Central Tendency – Find data (ex3) A group of four items have a mean of 63. What would the value of the fifth item have to be in order to produce a mean of 57? (ex4) You are shipping items for a shipping company. The items weigh 32, 34, 23, 35, 45 pounds each. You are going to add one more item weighing 52 pounds. Which would increase more by adding the last package, then mean or the median?

12. Statistics & Graphs 59Quote Let no one ignorant of geometry enter here. Plato (PLAY toe)

13. Statistics & Graphs 59 Puzzle – How many words are there? There is a word in the English language that the first two letters signify a male, the first three letters signify a female, the first four signify a great male and the whole word signify a great female. What is the word? Heroin

14. Statistics & Graphs 59a – Frequency distributions and line plots Frequency distribution = a display of how FREQUENTLY something occurred. Line plots = a graphical display using a number line to show data. Ex1. The pulse rates of students before physical education class are recorded in the table. Pulse Rate 68 69 70 71 72 73 74 75 76 77 Number of Students 3 4 0 0 5 2 1 4 3 1 How many students had a pulse rate lower than 74? _______ 14

15. Statistics & Graphs 59b – Frequency distributions and line plots Ex2. The line plot below shows the number of books read in a year by Swain Elementary School students. Each X represents 5 students. How many students read 10 or fewer books? 50 students read 10 or fewer books

16. Statistics & Graphs 59c – Frequency distributions and line plots Ex3. The numbers below represent the ages of the players on a softball team. Make a line plot to show the data. 29, 26, 25, 32, 27, 25, 32, 26, 24, 25 What numbers do we need on the number line? _______24-32 23 24 25 26 27 28 29 30 31 32 33 x xxxxxx x xx x

17. Statistics & Graphs 59d – Activity Construct a line plot using the height of the people in your class. Be sure you are using the height and make it look orderly. This is to be turned in for grading. On you paper, include your names, date and class period Don’t forget to label your graph so we know what it means. Use a different color for plots of the Boys and Girls Do this again for the Arm Span measurements.

18. Statistics & Graphs Quote There are two dangerous extremes. One is to shut reason out, the other is to let nothing in. Blaise Pascal (pass CAL)

19. Statistics & Graphs 58 Puzzle – Fish anyone? Two mothers and two daughters were fishing. They managed to catch one 5 pound fish, one 3 pound fish, and one 2 pound fish. How is it that they were each able to take home a fish?

20. Statistics & Graphs 58a - Bar Graphs Bar Graph = A graphical display representing data in different categories or groups. The length of a rectangle or bar is used to represent the numerical amount. Labels

21. Statistics & Graphs 58b - Bar Graphs

22. Statistics & Graphs 58c - Bar Graphs The graph below shows the sales of various vehicles by one dealer for the month of April. Approximately what percent fewer coupes were sold than sedans? Cross Multiply1200x =90000 Divide by 12x=75  25% fewer coupes were sold than sedans

23. Statistics & Graphs 58d - Bar Graphs The graph below shows the sales of various vehicles by one dealer for the month of April. Approximately how many times more compacts were sold than sedans? Cross multiply 12x=18 Divide by 12x=1.5  About 1.5 times more compacts were sold than sedans

24. Statistics & Graphs Quote If I have seen further than [others], it is by standing upon the shoulders of Giants. Isaac Newton

25. Statistics & Graphs 57 Puzzle – Need some stamps How many three cent stamps are in a dozen?

26. Statistics & Graphs 57a Scatter Plots Scatter Plot =Graph showing dots for points of data Line of best fit =Approximate line showing relations of graph Strong + Relation Strong - Relation Moderate + relation No correlation A Weak Relationship implies a spread out points A Strong relationship implies close to line

27. Statistics & Graphs 57b Scatter Plots The table shows the relationship between the time a student spends typing each week and his percent improvement on speed assessments. On graph paper, make a scatter plot of percent improvement vs. practice hours and then draw the line of best fit. Using the line of best fit, estimate what percent gain would be expected if the number of practice hours is 4 hours.

28. Statistics & Graphs 57c Scatter Plots % Improvement 60 50 40 30 20 10 2 4 6 8 10 12 14 16 18 20 Practice Time Vs. Improvement Practice Hours 4 hours?  Approx 12% imp

29. Statistics & Graphs 57 Activity Construct a scatter plot for height VS. Arm length Draw a “line of best fit” Label your graph. Do you feel there is a connection between height and arm length? Why? Arm length (cm) Student height (cm)

30. Statistics & Graphs Quote There is no branch of mathematics which may not be applied to the real world. Nicolai Lobachevsky (L0 ba CHEFF ski)

31. Statistics & Graphs 56 Puzzle - Ships There are two ships of equal size and strength. One is made of wood and one is made of steel. Can you explain which is heavier?

32. Statistics & Graphs 56a Histograms Histogram =histogram is a graphical display of frequencies. A histogram shows what proportion of cases fall into each of several or many specified categories. The categories are usually specified as non- overlapping intervals of some variable. The categories (bars) must be adjacent Relative frequency= The frequency that something occurred divided by how many samples were taken.

33. Statistics & Graphs 56b Histograms The golf scores for the basketball team are listed below. Make a histogram using ten-point intervals to show the distribution of scores. 88, 105, 71, 84, 107, 99, 115, 78, 86, 93, 102, 74, 119, 98, 102, 86, 81, 95, 83, 97, 95, 99, 94, 96, 92 ScoreFre.R.F. 70-79 80-89 90-99 100-109 110-119 70 80 90 100 110 120 Golf Scores FrequencyFrequency 2 4 6 8 10 12 Current Golf Scores 3 6 10 4 2.12.24.4.16.08

34. Statistics & Graphs 56c Histograms Use the histogram below to find the total frequency for the interval from 1.5 to 3.5. The frequency from 1.5 to 3.5 is 35 times

35. Statistics & Graphs 56d Activity Construct a graph (Histogram) showing the heights of students from activity 65 (Total Class) Construct a graph (Histogram) showing the Total arm length of students from activity 65 (Total Class) Number of students Height / Length 654321654321 121-135 136-140 141-145 146-150

36. Statistics & Graphs Quote It is unworthy of excellent men to lose hours like slaves in the labor of calculation which could safely be relegated to anyone else if machines were used. Gottfried Wilhelm Leibniz (LIPEnitz)

37. Statistics & Graphs 55 Puzzle – Can you say this correctly? What word in the English language does every Harvard graduate pronounce wrong? Clue: You pronounce it wrong as well!

38. Statistics & Graphs 55a Circle graphs Circle graph  Pie graph (3- dimensional) How many degrees are in a circle? _____360° A full circle represents what percent? _____100% To work with circle graphs, use proportions to solve for additional information.

39. Statistics & Graphs 55b Circle graphs The circle graph below represents a family’s monthly budget. If the total monthly income is $2100, how much money is spent on food? CircleIncome Cross multiply100x = 52500 Divide by 100 x=525 $525 are spent on food.

40. Statistics & Graphs 55c Circle graphs Grade 7 students were surveyed to determine how many hours a day they spent on various activities. The results are shown in the circle graph below. About how much time altogether was spent on homework and sleeping? 100x=984 x=9.84 hours or about 10 hours

41. Statistics & Graphs 55d Circle graphs The circle graph below represents a student’s spending. Estimate the fraction of the budget that was spent on food. Music Other Food Convert each fraction to a % (Divide).2.6.15.33 Your answer should be just less that ¼. Which answer should we choose?

42. Statistics & Graphs 55e Circle graphs A survey about a music program found that 300 students wanted after-school music programs, 180 students wanted music programs during the day, and 120 students did not want a music program at all. If a circle graph were made using this data, what would the measure of the central angle be for the “in-school” group? 600 is the total of the students 600x=64800 x=108  The angle is 108°

43. Statistics & Graphs Quote The theory of probability is at bottom only common sense. Pierre Simon de Laplace

44. Statistics & Graphs 54 Puzzle – Got $$$ If nine thousand, nine hundred, nine dollars is written as: $9,909 How should twelve thousand, twelve hundred, twelve dollars be written?

45. Statistics & Graphs 54a Stem-and-leaf plots Original data set 22, 25, 25,31, 31, 31, 32, 35, 40, 40, 43, 44, 46, 47, 53, 53, 55, 58, 59, 59, 62, 62, 63 Find the mean, median, mode and the range. Mean  44.17 Median =44 Mode =31 Range =41

46. Statistics & Graphs 54b Stem-and-leaf plots What data is represented by the stem-and-leaf plot below? 9 10 11 12 3 6 8 0 3 6 1 3 9

47. Statistics & Graphs Quote The most important questions of life are... really only problems of probability. Pierre Simon de Laplace