Lesson 1 data analysis with graphs
- 2. In order to draw conclusions, information must be gathered, organized, and displayed clearly.When information is gathered from all people in a population it is called a census. For example, Statistics Canada takes a census of the population every 5 years.The most recent census was conducted on May 10, 2011 (previously May 16, 2006, May 15, 2001 and May 21, 1996).
- 3. A poll is a method of collecting data from a sample of a population by asking people to give their answers to a set of questions. Once collected, the data are then organized in a meaningful way so that conclusion can be made.
- 4. Ways to Organize Data A FREQUENCYTABLE shows the possible values of a variable and the frequency of each value. Example:The members of a grade 12 class were asked in which month they were born and the results are as follows: Organize the data into categories (i.e. months) then, tally each category to determine the frequency.
- 5. A STEM & LEAF PLOT is a data plot that uses part of a data value as the stem and part as the leaf to form groups or classes. Example: The table below gives the number of days that rain fell in a month, over 36 months: In this case, the stem represents the tens digit.The leaf will represent the ones digit. Note: There are two stems that begin with a 1. One is for the interval 10 to 15, and the second is for the interval 15 to under 20. Ways to Organize Data
- 6. BACK-to-BACK STEM & LEAF PLOT Example: The table below shows the examination marks in French and English for a class of 20 students. In this case, the stem is in the middle of the table so that each side can contain a leaf. Ways to Organize Data
- 7. Some conclusions that can be drawn from this data include: • English marks are in general higher than French marks. • No student received a mark in the 90’s, in either subject. • More students got a mark in the 80’s in English that in French. • Four students failed English.
- 8. A CASETABLE displays data comparing cased to different attributes. Example: The following are two case tables, which display a scoring summary for the London Knights, for the 2004-05 Memorial CupChampionTeam. Ways to Organize Data
- 9. Ways to organize Data This CASETABLE is sorted by points.
- 10. Ways to organize Data This CASETABLE is sorted by penalties.
- 11. A BAR GRAPH displays the relationship among a set of numerical values using bars. Example: The bar graph shown shows the birth months of when grade 12 students were born (see previous example for frequency chart). The numerical scale should start at 0 and accommodate the magnitude of the numbers involved. Bar graphs are used for comparing the values of several categories of a variable (i.e. months) Note: Vertical bars are generally used when time is the independent variable, while horizontal bars are used when time is not a factor. 0 1 2 3 4 5 6 7 Frequency Month BIRTH MONTH BAR GRAPH Ways to Display Data
- 12. A PICTOGRAPH uses symbols to represent the data for a single variable. Example: The pictograph shows the past & projected world population. Ways to Display Data
- 13. A CIRCLE GRAPH shows the relative sizes (proportions) of data. Example: Ways to Display Data
- 14. A HISTOGRAM is a vertical bar graph which contains continuous data, grouped into frequency intervals. Example: The pictograph shows the past & projected world population. Ways to Display Data
- 15. Histogram Construction • BinWidth:The width of each vertical bar. • Different bin widths produce different histograms. • Small bin width may result in histogram that does not accurately represent the data (i.e. too many small bars). • Bin widths should be set so they are equal. • There should be at least five bins to have a representative histogram. • If a bin width has a frequency of zero, no bar will appear. bin width too large bin width too small