Chapter 15: Graphs, Charts, and Numbers Math 107

Transcription

1 Chapter 15: Graphs, Charts, and Numbers Math 107 Data Set & Data Point: Discrete v. Continuous: Frequency Table: Ex 1) Exam Scores

2 Pictogram: Misleading Graphs: In reality, the data looks like this 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% If Bush Tax Cuts Expire 39.60% 35% Now Jan 12013

3 CNN showed this graph of people who agreed with the court s decision to turn off Terri Schiavo s Life Support People who disagreed with the Court 70% 60% 50% 40% 30% 20% 10% 0% 62% Democrats 54% 54% Republicans Independents The Dow Jones Industrial Average for the last year. It looks as though the drop from the middle of July to the middle of August went down by 3/4ths! (75%!) Using the rounded values of 18,000 and 15,600, what percentage did it actually drop?

4 Let s investigate this a little, at this time the number of people who owned the following systems was: Wii: 50 million 360: 30 million PS3: 20 million Quantitative vs. Qualitative:

5 Pie Charts work well when you re looking at portions of a whole. How many hours a day spent doing X, or how much of your money is spent on different categories, or (as below) a poll where everyone gets one choice. When creating a pie chart, we need to think about the percentage of the whole that each category represents, and then each category gets that percentage of the total 360. Ex 2 (LC) The following pie chart represents the favorites sports of students who were polled. a) How many students were polled? b) Complete the chart to calculate the the percentage and degrees that each category receives in the pie chart. Sport Total: 146. % (out of 146 ) Number of Baseball = % 360 Basketball = % 360 Tennis = % 360 Swimming = % 360 Soccer = % 360 (LC) Football = % 360 (LC)

6 Class Intervals are when the data is put into groups or Ranges. The following SAT scores from 2011 are all scored in increments of 10. Histograms are more effective with continuous data. In other words, whether you make $44,999 a year or $45,001 isn t really that different, so the bars are connected to represent closeness of the endpoints of the regions of data.

7 Histograms in the News Response interval histograms for EMS calls (Dec 2010) 60-second intervals 240-second Intervals (4 minutes) 480-second intervals (8 minutes)

8 Average (Mean): So the average of the data set d1, d2, d3,... d N is Ex 3 (LC) d + d + d + + d A= N 1 2 3,... N a) How many firefighters are there? b) To calculate the Mean, what is the total sum of the ages of just the first row? Ex 4)

9 Percentiles: The p th percentile of a data set is a number XP such that p% of the data is smaller or equal to XP and (100-p)% of the data is bigger or equal to XP. In order to calculate this, our data must be arranged from smallest to largest and we need to find the locator which separates the data into p% and (100-p)%. Ex 5) (LC)

10 Median: Quartiles: Ex 6) (LC) (LC) Warning: Not everyone agrees on the procedure for finding percentiles and quartiles, so your calculator or other program might do it slightly differently than the procedure described in this book.

11 Five-number Summary: Box Plots: Ex 7) (LC)

12 Range: Interquartile Range: Ex 8) (LC) Looking at the Engineering Salaries from the previous example, find a) Range b) Interquartile Range Standard Deviation is basically a measure of how far away (deviation) the data of a set is from the average of the data. Ex 9) Find the standard deviation of {0,6,6,8}. Ex 10) (LC)