Download 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 look
Class 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 variation
 Pre-req knowledge:
 Variables




Independent
Dependent
Constants
Control
 Quantitative Data vs. Qualitative Data
Quantitative
Definition
 Quantitative = based on measurements made using a
scale with equal intervals
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
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
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 Information
Quant. Data
Qual. Data:
Nominal vs Ordinal
What is most typical or
central value?
Mean
Mode
What is the variation or
spread?
Range
Frequency distribution
Standard deviation
Median
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.
Practice
 Use 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 - Range
 Range – 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
25
25
Number of plants
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
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
25
25
Number
Practice! The AP Biology Equation
Sheet
Calculate Standard Deviation and
Standard Error for each set of data.
Trial
Number
1
2
3
4
5
6
ET50 (time in
seconds)
Disks immersed in
water and CO2
530
822
745
620
822
837
ET50 (time in
seconds)
Disks immersed in
water only
952
1005
940
1200
1005
1102
Calculate Standard Deviation and
Standard Error for each set of data.
Trial
Number
1
2
3
4
5
6
ET50 (time in
seconds)
Disks immersed in
water and CO2
530
822
745
620
822
837
ET50 (time in
seconds)
Disks immersed in
water only
952
1005
940
1200
1005
1102
Graph with standard error bars
 What does
this 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