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Introducing AP Biology. The New Curriculum Framework Supports and Furthers Conceptual Knowledge. 4 Big Ideas. Enduring Understandings. Science Practices: Science Inquiry & Reasoning. Essential Knowledge. Learning Objectives. AP Biology Curriculum Is Framed Around Four Big Ideas. 1.
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The New Curriculum Framework Supports and Furthers Conceptual Knowledge 4 Big Ideas Enduring Understandings Science Practices:Science Inquiry & Reasoning Essential Knowledge Learning Objectives
AP Biology Curriculum Is FramedAround Four Big Ideas 1 • The process of evolution drives the diversity and unity of life. • B I G I D E A 2 • Biological systems utilize energy and molecular building blocks to grow, reproduce, and maintain homeostasis. • B I G I D E A 3 • Living systems retrieve, transmit, and respond to information essential to life processes. • B I G I D E A 4 • Biological systems interact, and these interactions possess complex properties. • B I G I D E A
Emphasis on Science Practices The science practices enable students to establish lines of evidence and use them to develop and refine testable explanations and predictions of natural phenomena 1.0 The student can use representations and models to communicate scientific phenomena and solve scientific problems 2.0 The student can use mathematics appropriately 3.0 The student can engage in scientific questioning to extend thinking or to guide investigations within the context of the AP course 4.0 The student can plan and implement data collection strategies appropriate to a particular scientific question 5.0 The student can perform data analysis and evaluation of evidence 6.0 The student can work with scientific explanations and theories 7.0 The student is able to connect and relate knowledge across various scales, concepts, and representations in and across domains • SCIENCE PRACTICES
Analyzing Data • Mean : The "Mean" is computed by adding all of the numbers in the data together and dividing by the number elements contained in the data set. • Example : Data Set = 2, 5, 9, 3, 5, 4, 7 Number of Elements in Data Set = 7 Mean = ( 2 + 5 + 9 + 7 + 5 + 4 + 3 ) / 7 = 5
Analyzing Data • Median : The "Median" of a data set is dependent on whether the number of elements in the data set is odd or even. First reorder the data set from the smallest to the largest then if the number of elements are odd, then the Median is the element in the middle of the data set. If the number of elements are even, then the Median is the average of the two middle terms. • Examples : Odd Number of Elements Data Set = 2, 5, 9, 3, 5, 4, 7 Reordered = 2, 3, 4, 5, 5, 7, 9 ^ Median = 5 • Examples : Even Number of Elements Data Set = 2, 5, 9, 3, 5, 4 Reordered = 2, 3, 4, 5, 5, 9 ^ ^ Median = ( 4 + 5 ) / 2 = 4.5
Analyzing Data • Mode : The "Mode" for a data set is the element that occurs the most often. It is not uncommon for a data set to have more than one mode. This happens when two or more elements accur with equal frequency in the data set. A data set with two modes is called bimodal. A data set with three modes is called trimodal. • Examples : Single Mode Data Set = 2, 5, 9, 3, 5, 4, 7 Mode = 5 • Examples : Bimodal Data Set = 2, 5, 2, 3, 5, 4, 7 Modes = 2 and 5 • Examples : Trimodal Data Set = 2, 5, 2, 7, 5, 4, 7 Modes = 2, 5, and 7
Analyzing Data • Range : The "Range" for a data set is the difference between the largest value and smallest value contained in the data set. First reorder the data set from • smallest to largest then subtract the first element from the last element. • Examples : • Data Set = 2, 5, 9, 3, 5, 4, 7 • Reordered = 2, 3, 4, 5, 5, 7, 9 • Range = ( 9 - 2 ) = 7
The Data – Now What? First, what kind of data do you have? Qualitative or Quantitative? How can you tell?
The Data – Now What? Make a picture
Histograms Not good enough yet!
Histograms 6 4 2 0 Frequency (hz) 630 680 730 780 830 880 Time in seconds Excellent for large data sets. Label and scale both axes Bin widths should be the same. Comparative data should use the same scale.
Stemplot Data rounded to nearest 10 seconds 6 4 * 8 9 9 7 1 2 2 3 4 4 4 6 │4 = 640 seconds * 6 7 7 9 8 1 1 2 * 6 6 Use only for small data sets. Stem should be one digit only. Include a key/legend.
If you rotate a stemplot… 6 4 * 8 9 9 7 1 2 2 3 4 4 4 * 6 7 7 9 8 1 1 2 * 6 6 6 4 * 8 9 9 7 1 2 2 3 4 4 4 * 6 7 7 9 8 1 1 2 * 6 6 Then it has the same shape as a histogram but includes actual values.
Back to back Stemplots ExperimentalControl 3 6 4 * 8 9 9 4 7 1 2 2 3 4 4 4 9 8 6 5 * 6 7 7 9 3 3 3 1 0 8 1 1 2 9 8 8 7 5 * 6 6 3 1 9 * 1 0 10 6│4 = 640 seconds
Boxplots control experimental 630 740 780 830 880 1000
Making a boxplot We’ll use the experimental data 1. Put the numbers in order from smallest to largest. 2. Find the median. 3. Find the median of the upper and lower halves, Q1 & Q3. 4. Locate the minimum and maximum. 5. Now you have the 5-number summary. 630 , 784.5 , 832.5 , 882.5 , 1007 Q3 Q1 median maximum minimum 834 756 735 877 779 831 829 888 929 853 797 912 790 1004 805 872 1007 630 746 877 630 735 746 756 779 790 797 805 829 831 834 853 872 877 877 888 912 929 1004 1007
5-number summary: 630 , 784.5 , 832.5 , 882.5 , 1007 Sketch your number line with scale 600 650 700 750 800 850 900 950 1000
5-number summary: 630 , 784.5 , 832.5 , 882.5 , 1007 Make the box from Q1 to Q3. 600 650 700 750 800 850 900 950 1000
5-number summary: 630 , 784.5 , 832.5 , 882.5 , 1007 Place the median line in the box. 600 650 700 750 800 850 900 950 1000
5-number summary: 630 , 784.5 , 832.5 , 882.5 , 1007 Sketch the “whiskers” from the box to the minimum and the maximum 600 650 700 750 800 850 900 950 1000 Ta Da!
5-number summary: 630 , 784.5 , 832.5 , 882.5 , 1007 Outliers? A whisker cannot be longer than 1.5 X length of the box (IQR) 600 650 700 750 800 850 900 950 1000
5-number summary: 630 , 784.5 , 832.5 , 882.5 , 1007 A whisker cannot be longer than 1.5 X length of the box (IQR) IQR = 882.5 ̶ 784.5 = 98 600 650 700 750 800 850 900 950 1000 98(1.5) = 147
5-number summary: 630 , 784.5 , 832.5 , 882.5 , 1007 A whisker cannot be longer than 1.5 X length of the box (IQR) IQR = 882.5 ̶ 784.5 = 98 600 650 700 750 800 850 900 950 1000 98(1.5) = 147 Q3 + 147 = 882.5+147 = 1029.5
5-number summary: 630 , 784.5 , 832.5 , 882.5 , 1007 A whisker cannot be longer than 1.5 X length of the box (IQR) IQR = 882.5 ̶ 784.5 = 98 600 650 700 750 800 850 900 950 1000 98(1.5) = 147 Q1̶ 147 = 784.5 ̶ 147 = 637.5
5-number summary: 630 , 784.5 , 832.5 , 882.5 , 1007 * 600 650 700 750 800 850 900 950 1000 Appropriate for large data sets Label the data, especially if more than one boxplot used Include scale May show outliers Cannot be used to show normality – use the term symmetric
Summary Statistics When describing a distribution, CUSS and BS. C - center : mean or median U - unusual features : outliers or gaps S - shape : approximately normal, skewed, bimodal S - spread : range, IQR, standard deviation BS – and Be Specific
Wrap Up 1. Collect your data. 2. Make an appropriate graph. 3. Use summary statistics to describe your graphical display. 4. CUSS and BS to clarify your results. • Possibly run a statistical test to analyze any difference. • That’s another entire lesson!