1. Distinguish between quantitative, qualitative Computing central value of set of data: mean, median and mode Ways to report the variation in a set of data: range, standard deviation/variance, frequency distribution;

2. A study of two classes – the best class is… Class of 2015Class of 2016 Average GPA for class= 3.42Average GPA for class= 4.0

3. A closer look Class of 2015Class of 2016 4.5 = 15 students4.5 = 1 student 3.7 = 56 students3.7 = none 3.5 = 20 students3.5 = 100 students 2.1 = 10 students2.1 = none Total students: 101

4. Descriptive Stats: measure of central tendency and variation Pre-req knowledge: Variables Independent Dependent Constants Control Quantitative Data vs. Qualitative Data

5. Quantitative Definition Quantitative = based on measurements made using a scale with equal intervals

6. Qualitative Definition: data collected using non-standard scales with unequal intervals or discrete categories. Examples: gender, color of eye Sub-levels Nominal data – discrete categories cannot be rank ordered, for example gender and color of hair Ordinal data- exists when objects are placed into categories that can be ranked, for example activity of an animal could be rated on scale of 1-5

7. Quantitative Data – multiple trials Use Rate of Photosynthesis: floating spinach leaf disks Dependent Variable Time (minutes) ET50 Trial 1 5.5 ET50 Trial 2 8.0 ET50 Trial 3 6.5

8. Describing Data: measure of central tendency and variation Definitions Central Tendency - the one number that is most TYPICAL of the entire data set Variation – spread within the data Type of InformationQuant. DataQual. Data: Nominal vs Ordinal What is most typical or central value? MeanMode Median What is the variation or spread? RangeFrequency distribution Standard deviation

9. Measures of Central tendency Mean – the arithmetic average, can ONLY be calculated for interval or ratio data Mode – value that occurs most often, two or more data pts can be reported. Median – middle value, after all of the cases have been ranked in order low to high. Half cases fall below median value and half above.

10. Practice Use the hypothetical data from leaf disk lab to practice calculating central tendencies

11. Which to use? Need to analyze data Mean is generally considered the most powerful measure of central tendency. Exceptions? Extreme values that would distort this value Mode is only appropriate measure for nominal data.

12. Variation - Range Range – computed by finding the difference between smallest (minimum) and largest (maximum) measures of the dependent variable Why is range important? Red ground coverNo ground cover Mean Height of plants15.0 cm14.9 cm Range in HeightMax-18.0 cmMax - 16.0 cm Min – 8.0 cmMin- 14.0 cm Number of plants25

13. Variation – variance and standard deviation Variance – just how varied is the data, used to determine if the mean is an accurate reflection of the data set or sample Standard deviation – measures the average variation of the data from the mean, it is the square root of variance

14. Variation-Frequency Distribution Definition – the number of cases falling into each category of the variable, for example color of tomatoes Red ground cover No ground cover ModePink tomatoesRed tomatoes Freq. distributionRed: 0Red: 20 Pink: 12Pink: 5 Yellow: 8Yellow: 0 Green: 5Green: 0 Number25

15. Practice! The AP Biology Equation Sheet

16. Calculate Standard Deviation and Standard Error for each set of data. Trial Number ET 50 (time in seconds) Disks immersed in water and CO2 ET 50 (time in seconds) Disks immersed in water only 1530952 28221005 3745940 46201200 58221005 68371102

17. Calculate Standard Deviation and Standard Error for each set of data. Trial Number ET 50 (time in seconds) Disks immersed in water and CO2 ET 50 (time in seconds) Disks immersed in water only 1530952 28221005 3745940 46201200 58221005 68371102

18. Graph with standard error bars What does this mean?

19. How can these statistics be applied to your Big Idea 2 project?

20. Summary of measures of central tendency and variation Dependent VariableMeasure of Central Tendency Measure of Variation Height of PlantsMeanRange or Standard Deviation Health of PlantsModeFrequency Distribution Leaf QualityMedianFrequency Distribution