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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

First, what kind of data do you have? Qualitative or Quantitative?

How can you tell?

Make a picture

Not good enough yet!

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.

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.

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.

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

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

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

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!

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