(7.11) Probability and statistics. The student understands that the way a set of data is displayed influences its interpretation. The student is expected to: (A) select and use an appropriate representation for presenting and displaying relationships among collected data, including line plot, line graph, bar graph, stem and leaf plot, circle graph, and Venn diagrams, and justify the selection and (B) make inferences and convincing arguments based on an analysis of given or collected data. Circle Graphs

7.11A/7.11B INSTRUCTIONAL ACTIVITY #1 Data can be represented in a variety of ways, including tables, line graphs, bar graphs, and circle graphs. When data are organized and displayed in a graph or diagram, it is easier to see relationships between the pieces of data. The type of graph you use depends on the data you are representing and the relationships you want to analyze. A circle graph compares the numbers in a set of data by showing the relative sizes of the parts that make up a whole. The circle represents the whole, which is made up of all the data elements. Each section of the circle represents part of the whole.

7.11A/7.11B INSTRUCTIONAL ACTIVITY #1 If you draw radii out from the center of a circle, you are forming central angles in that circle. The central angles of a circle total 360˚. The fractional part of the circle contained in each sector of a circle graph is related to the fractional part of the 360˚ total of the central angles. 360° = 1 = 1.0 = 100% 45 ° = = = 12.5% ° = = 0.25 = 25% ° = = 0.5 = 50% 1414

7.11A/7.11B INSTRUCTIONAL ACTIVITY #2 Sometimes conclusions need to be drawn or convincing arguments need to be made about data. To do this, careful review of the data and finding evidence that supports conclusions or arguments is required. Here are some guidelines to follow to ensure that the conclusions drawn from graphs and data are valid: Be certain that any pattern found in the data is truly reflected by the data. Compare information presented in a table or graph accurately. Make sure the units used in a table or graph are consistent with the conclusions drawn. Be logical. Do not draw conclusions beyond those represented by the data.

The following graphs represent the seventh grade votes for class president. Odell M. 10% Cody T. 40% Barry S. 20% Richard B 30% Odell M. 30% Cody T. 45% Barry S. 5% Richard B 20% The editor of the student newspaper drew the following conclusions for an article he wrote: Cody T. received the _______ votes from both the _______ and the _______ This statement is supported by the fact that __________ received the _______ percentage of the votes from the girls and from the boys. Boys’ VotesGirls’ Votes most BoysGirls Cody T.largest

The following graphs represent the seventh grade votes for class president. Odell M. 10% Cody T. 40% Barry S. 20% Richard B 30% Odell M. 30% Cody T. 45% Barry S. 5% Richard B 20% Barry S. received a lower number of votes from the girls than the boys. This statement is supported by the fact that __________ received ____ percent of the votes from the boys and ____ percent of the votes from the girls. Boys’ VotesGirls’ Votes Barry S. 20 5

The following graphs represent the seventh grade votes for class president. Odell M. 10% Cody T. 40% Barry S. 20% Richard B 30% Odell M. 30% Cody T. 45% Barry S. 5% Richard B 20% Richard B. received half of the votes from the girls and boys. This is an incorrect conclusion supported by the fact that Richard B. only received ____ percent of the votes from the boys, which is not half of the boys’ votes, and he received ____ percent of the votes from the girls, which is not half of the girls’ votes. Boys’ VotesGirls’ Votes 40 45

The following graphs represent the seventh grade votes for class president. Odell M. 10% Cody T. 40% Barry S. 20% Richard B 30% Odell M. 30% Cody T. 45% Barry S. 5% Richard B 20% Half of the boys voted for either Odell M. or Cody T. This statement is supported by the fact that __________ received _____ percent of the boys’ votes and __________ received ____ percent of the boys’ votes. The total percent of votes for Odell and Cody was ______ percent, which is equal to ____ of the boys’ votes. Boys’ VotesGirls’ Votes Odell M. 10 Cody T half