Analyzing Experimental Data

•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;

A study of two classes – the best class is…

Class of 2015 Class of 2016

Average GPA for class= 3.42 Average GPA for class= 4.0

A closer lookClass of 2015 Class of 2016

4.5 = 15 students 4.5 = 1 student

3.7 = 56 students 3.7 = none

3.5 = 20 students 3.5 = 100 students

2.1 = 10 students 2.1 = none

Total students: 101 Total students: 101

Descriptive Stats: measure of central tendency and variationPre-req knowledge:

Variables Independent Dependent Constants Control

Quantitative Data vs. Qualitative Data

QuantitativeDefinitionQuantitative = based on measurements made

using a scale with equal intervals

QualitativeDefinition: 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

Quantitative Data – multiple trialsUse Rate of Photosynthesis: floating spinach

leaf disks

Dependent Variable

Time(minutes)

ET50Trial 1

5.5

ET50Trial 2

8.0

ET50Trial 3

6.5

Describing Data: measure of central tendency and variationDefinitions

Central Tendency - the one number that is most TYPICAL of the entire data set

Variation – spread within the data

Type of Information

Quant. Data Qual. Data:Nominal vs Ordinal

What is most typical or central value?

Mean Mode Median

What is the variation or spread?

Range Frequency distributionStandard deviation

Measures of Central tendencyMean – 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.

PracticeUse the hypothetical data from leaf disk lab

to practice calculating central tendencies

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.

Variation - RangeRange – computed by finding the difference

between smallest (minimum) and largest (maximum) measures of the dependent variable

Why is range important?Red ground cover No ground cover

Mean Height of plants

15.0 cm 14.9 cm

Range in Height Max-18.0 cm Max - 16.0 cm

Min – 8.0 cm Min- 14.0 cm

Number of plants 25 25

Variation – variance and standard deviationVariance – 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

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

Mode Pink tomatoes Red tomatoes

Freq. distribution

Red: 0 Red: 20

Pink: 12 Pink: 5

Yellow: 8 Yellow: 0

Green: 5 Green: 0

Number 25 25

Practice! The AP Biology Equation Sheet

Calculate Standard Deviation and Standard Error for each set of data.

Trial Number

ET50 (time in

seconds)Disks immersed in water and CO2

ET50 (time in

seconds)Disks immersed in water only

1 530 9522 822 10053 745 9404 620 12005 822 10056 837 1102

Calculate Standard Deviation and Standard Error for each set of data.

Trial Number

ET50 (time in

seconds)Disks immersed in water and CO2

ET50 (time in

seconds)Disks immersed in water only

1 530 9522 822 10053 745 9404 620 12005 822 10056 837 1102

Graph with standard error barsWhat doesthis mean?

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

Summary of measures of central tendency and variation

Dependent Variable Measure of Central Tendency

Measure of Variation

Height of Plants Mean Range or Standard Deviation

Health of Plants Mode Frequency Distribution

Leaf Quality Median Frequency Distribution