1 / 43

Data & Graphs

Data & Graphs. Review. Frequency Tables. Statistics involves collecting, organizing, analyzing, and presenting data. Data are pieces of information that are often numerical. A frequency table shows the number of pieces of data that fall within given intervals. Make a Frequency Table.

alaire
Download Presentation

Data & Graphs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Data & Graphs Review CONFIDENTIAL

  2. Frequency Tables • Statistics involves collecting, organizing, analyzing, and presenting data. • Data are pieces of information that are often numerical. • A frequency table shows the number of pieces of data that fall within given intervals. CONFIDENTIAL

  3. Make a Frequency Table • Example: The number of points scored by major league soccer teams in a recent season is shown. CONFIDENTIAL

  4. Make a Frequency Table • Step 1: Choose an appropriate scale and interval for the data • Scale: 1 to 60 • Interval: 15 The scale includes all of the data, the least number and the greatest The interval separates the scale into equal parts. CONFIDENTIAL

  5. Make a Frequency Table • Step 2: Draw a table with three columns and label the columns Points, Tally, and Frequency • Step 3: In the first column, list the intervals. In the second column, tally the data. In the third column, add the tallies. Some frequency tables may not have scales and intervals CONFIDENTIAL

  6. Your Turn Make a Frequency Table • Make a frequency table of the data shown in the table. CONFIDENTIAL

  7. Line Graphs • A line graph is used to show how a set of data changes over a period of time. The scale and interval are also shown on the vertical axis. Each frequency is shown using a point. Number of Coasters A line graph also has titles and labels The categories are written on the horizontal axis. CONFIDENTIAL

  8. Make & Interpret a Line Graph • Example: Make a line graph of the data at the left. Then describe the change in the number of tornadoes from 2001 to 2003. • Step 1; Decide on the scale and the interval. The data includes numbers from 941 to 1,424. The scale is 900 to 1,500 and the interval is 100. CONFIDENTIAL

  9. Make & Interpret a Line Graph • Step 2: Label the horizontal and vertical axes. • Step 3: Draw and connect the points for each year. Each point shows the number of tornadoes in that year. • Step 4: Label the graph with a title. Tornadoes The number of tornadoes decreased from 2001 to 2002 and then increased from 2002 to 2003. CONFIDENTIAL

  10. Your Turn Make & Interpret a Line Graph • Make a line graph of the data. Then describe the change from 1960 to 1995. CONFIDENTIAL

  11. Bar Graphs • A bar graph is used to compare data. The title and label describe the data The scale is written on the vertical axis Sales of toys The height of each bar represents the frequency Revenue $ millions On this scale, the interval is 50 Time The categories are written on the horizontal axis. CONFIDENTIAL

  12. Make & Interpret a Bar Graph • Example: Make a vertical bar graph of the data. Compare the number of students who scored a B to the number who scored a C. • Step 1: Decide on the scale and interval. The data includes numbers from 2 to 13. So, a scale from 0 to 14 and an interval of 2 is reasonable. CONFIDENTIAL

  13. Make & Interpret a Bar Graph • Step 2: Label the horizontal and vertical axes. • Step 3: Draw bars for each grade. The height of each bar shows the number of students earning that grade. • Step 4: Label the graph with a title. About twice as many students scored a B than a C. CONFIDENTIAL

  14. Your Turn Make & Interpret a Bar Graph • Make a vertical bar graph of the data. Compare the time it takes for a rabbit to be born to the time it takes for a camel to be born. CONFIDENTIAL

  15. Circle Graphs • A circle graph is used to compare parts of a whole. • Analyze data by comparing the size of the sections of the circle. • One can compare the percents to analyze the data as well. The interior of the circle represents a set of data. The pie-shaped sections show the groups. The percents add up to 100% CONFIDENTIAL

  16. Your Turn Circle Graphs • The circle graph shows which method of transportation students use to get to Martin Luther King, Jr. Middle School. • Which method of transportation do most students use? • How does the number of students who ride a moped to school compare to the number of students who take the bus? CONFIDENTIAL

  17. Stem & Leaf Plots • In a stem-and-leaf plot, the data is ordered from least to greatest and is organized by place value. • Step 1: Order the data from least to greatest 56 60 62 67 68 68 69 70 70 70 71 72 76 76 78 82 83 84 88 93 97 • Step 2: Draw a vertical line and write the tens digits from least to greatest to the left of the line. These digits form the stems. Since the least value is 56 and the greatest value is 97, the stems are 5, 6, 7, 8, and 9. CONFIDENTIAL

  18. Stem & Leaf Plots • Step 3: Write the units digits in order to the right of the line with the corresponding stem. The units digits form the leaves. Leaf Stem 5 6 The ones digit of the data form the leaves. In this data, the tens digit forms the stem. 6 0 2 7 8 8 9 7 0 0 0 1 2 6 6 8 Always write each leaf even if it repeats. 8 2 3 4 8 9 3 7 7 6 points key CONFIDENTIAL

  19. Your Turn Stem & Leaf Plots • Make a stem-and-leaf plot for the data in the table. CONFIDENTIAL

  20. Making Predictions & Interpreting Graphs • Line graphs are often used to predict future events because they show trends over time. Example: You can predict the average temperature for Miami in February by the trend in the line graph. CONFIDENTIAL

  21. Your Turn Making Predictions & Interpreting Graphs • The graph shows the number of participants in bowling from 1975 to 2000. What does the graph tell you about the popularity of bowling? CONFIDENTIAL

  22. Mean • The mean of a set of data is the sum of the data divided by the number of pieces of data. • Example: data set : 8, 7, 9, 6, 10 • Mean = 8 + 7 + 9 + 6 + 10 = 40 = 8 5 5 CONFIDENTIAL

  23. Determine how Outliers affect Mean • A set of data may contain a value much higher or lower than the other values. This value is called outlier. • Outliers can significantly affect the mean. • Example: data set : 80, 81, 40, 77, 82 • Mean with outlier = 80 + 81 + 40 + 77 + 82 = 360 = 72 5 5 • Mean without outlier = 80 + 81 + 77 + 82 = 320 = 80 4 4 CONFIDENTIAL

  24. Median, Mode, and Range • The median of a set of data is the middle number of the ordered data, or the mean of the middle two numbers. • Examples: • data set: 3, 4, 8, 10, 12 -> median: 8 • data set: 2, 4, 6, 8, 11, 12 -> median: 6 + 8 = 7 2 CONFIDENTIAL

  25. Median, Mode, and Range • The mode of a set of data is the number or numbers that occur most often. • Examples: • data set: 12, 23, 28, 28, 32, 46, 46 -> modes: 28 and 46 CONFIDENTIAL

  26. Median, Mode, and Range • The range of a set of data is the difference between the greatest and the least values of the set. • Examples: • data set: 125, 45, 67, 150, 32, 12 • The greatest value is 150. • The least value is 12. • So, the range is 150 – 12 or 138. CONFIDENTIAL

  27. Median, Mode, and Range • Concept Summary CONFIDENTIAL

  28. Your Turn Median, Mode, and Range • What are the mean, median, mode, and range of the temperature data 640, 700, 560, 580, 600, and 700 . CONFIDENTIAL

  29. Let us take a break! CONFIDENTIAL

  30. Jig-saw puzzle • http://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw-puzzles/12-piece-jigsaw/05-04-06-kitten.html CONFIDENTIAL

  31. Box & Whisker Plots • A Box-and-whisker plot is a way to show how data are clustered or spread out. • Example: The monthly mean temperatures for Burlington, Vermont, are shown. CONFIDENTIAL

  32. Box & Whisker Plots • Step 1: Write the data from least to greatest. 16 18 23 31 37 44 48 56 59 65 68 71 • Step 2: Draw a number line that includes all of the data. 20 25 50 15 30 60 65 75 55 70 40 45 35 • Step 3: Mark the least and greatest as the lower extreme and upper extreme. Find and label the median. Lower Extreme Upper Extreme Median 20 25 50 15 30 60 65 75 55 70 40 45 35 CONFIDENTIAL

  33. Box & Whisker Plots • Step 4: The median of a data set separates the set in half. Find the medians of the lower and upper halves. 16 18 23 31 37 44 48 56 59 65 68 71 Median 59 + 65 = 62 2 23 + 31 = 27 2 • Label these values as lower quartile and upper quartile. Draw a box around the quartile values, and whiskers that extend from each quartile to the extreme data points. Upper Quartile Lower Quartile Median Upper Extreme Lower Extreme 20 25 50 15 30 60 65 75 55 70 40 45 35 CONFIDENTIAL

  34. Your Turn Box & Whisker Plots • Draw a Box-and-whisker plot for the set of data below. CONFIDENTIAL

  35. Assessment 1) Make a frequency table for the set of data. CONFIDENTIAL

  36. Assessment 2) Make a line graph for the set of data. CONFIDENTIAL

  37. Assessment 3) Name two muffins that together are preferred by half the people surveyed. CONFIDENTIAL

  38. Assessment 4) Describe the trend in the winning times. Predict the winning time in 2006. CONFIDENTIAL

  39. Assessment 5) Make a stem-and-leaf plot for the set of data. 83, 72, 95, 64, 90, 88, 78, 84, 61, 73 CONFIDENTIAL

  40. Assessment 6) Find the mean for the set of data. 23, 34, 29, 36, 18, 22, 27 CONFIDENTIAL

  41. Assessment 7) Find the median, mode, and range for the set of data. 21, 23, 27, 30 CONFIDENTIAL

  42. Assessment 8) Which graph would you show to a telephone customer? Explain. CONFIDENTIAL

  43. Great Job! Session! See you in the CONFIDENTIAL

More Related