Transcript When do we need to analyze data in science?

Copyright 2010. PEER.tamu.edu
Data Analysis
Definition: systematically identifying patterns in the
information gathered and deciding how to organize,
classify, interrelate, compare, and display that information.
Can you put that definition into your own words?
Can the class come up with a definition in common terms?
When do we need to analyze
data in science?
• After data are collected in an experiment
• Before a scientist moves to a different stage of an
experiment or clinical trial
• Before conclusions are made
• Whenever we need to see relationships in the data
• In science, some of the most useful ways to
analyze data are finding the mean (or average)
and the median.
• Standard deviation, quartiles, and deciles are
also useful.
• Graphing the data can show important
relationships and help in forming conclusions
and predicting trends.
Finding the Average or Mean
• This is a measure of central tendency of a data set.
• To calculate the average or mean, add all of the
items in the data set and divide by
the total number of items.
• Example:
Take the average of these numbers:
6, 9, 10, 12, 13, 19
1. First add the numbers:
6+9+10+12+13+19=69
2. Now divide by the number of items, which is 6:
69÷6=11.5
– The average is 11.5
What are some averages that might be
useful in describing these puppies?
• Average weight
• Average length
• Average height
Looking at Standard Deviation
• The standard deviation
shows how much
difference there is from
the average or mean.
• A low standard deviation
indicates that the data
points tend to be very
close to the mean.
• A high standard
deviation indicates that
the data are spread out
over a large range of
values.
The average height of these two dogs would be a medium
height. However, there is so much deviation from the
average because one dog is tiny and the other is huge!
Why the Average Might be
Misleading
• An experiment was done testing a drug to help people
lose weight. The maker of the drug claims that people
lost an average of 10 pounds while taking this drug.
• Look at this data. Why is the average misleading?
– Patient A lost 42 pounds
– Patient B gained 2 pounds
– Patient C lost 5 pounds
– Patient D gained 5 pounds
• Answer: The standard deviation was very large!
It pays to look at your data in various ways.
Finding the Median
• To get the median, rank the data
from lowest to highest and pick the
middle number.
• Example: Find the Median of the
following numbers.
30, 3, 5, 19, 23, 7, 1
1. Rank the numbers in order
from lowest to highest.
1, 2, 5, 7, 19, 23, 30
2. Pick the middle number
1,2,5,7,19,23,30
Answer: 7 is the median
• Half of the data is below the median,
half of the data is above the median.
Which one is the median for height?
Quartiles and Deciles
• Quartiles describe data that has been divided into
fourths. The lowest quartile is the lowest 25% of the
data. The highest quartile is the top 25% of the data.
• For even more precision, data can be broken into
deciles, or 10% increments.
Let’s Review:
• Find the average (mean) of these
numbers:
20, 25, 31, 34, 17
• What is the median of those same
numbers?
• Why is an average sometimes
misleading?
• What is a standard deviation?
Why do we Graph in Science?
• We graph in science so
we can analyze data
from our experiments
and research.
• Graphing helps us see
results very easily.
• Graphing helps us see
trends.
Common Types of Graphs
1. Pictograph
2. Bar Graph
3. Circle Graph or
Pie Chart
4. Line Graph
Pictograph
• Great for younger
audiences
• Very easy to read
• Numbers are
represented by
pictures
Which lunch was chosen by the
majority of students?
Examine this pictograph.
• What is the topic of this graph?
• What are some conclusions or predictions you
can make from this graph?
Circle Graph or Pie Chart
• Show parts of
a whole
• Shows
percentages
This Pie Chart shows Texas surface water use by different sectors.
What percent of Texas’ surface water is used by municipal sectors?
What percent is used by livestock?
• Examine this pie chart
– What is its topic?
– According to this chart, estimate what percentage of your
diet should be:
Fruits and vegetables
Bread and other cereals and potatoes
Food containing fat or food containing sugar
Bar Graph
• Used for comparing data
• Very easy to see comparisons
What is the topic of this graph? What is it comparing?
What type of event caused the most weather-related deaths in Texas?
What type of event caused the fewest weather-related deaths in Texas?
Line Graph
• Used for showing trends like increasing or
decreasing, especially over time
• Helpful in making predictions
• What is the topic of
this graph?
• What is the
general trend of
this graph?
• What happened to
the graph in 2001?
• What can you infer
about what
happened in 2001?
Relationships between the
Variables
Direct Relationship: When
one variable increases,
the other variable
increases
This graph is non-linear, or not a straight line.
Indirect Relationship: When
one variable increases,
the other variable
decreases
This graph is linear, or in a straight line.
Non-linear Graphs
Many times graphs are not linear (in a
straight line). Instead, they are non-linear.
Notice that this
graph does not
show two
straight lines. It
does, however,
show a
relationship
between the
wolves and the
moose.
This graph shows the peak number of monarch butterflies at their
winter habitats in Mexico.
• What information can you infer from this graph?
• Can you made any predictions from this graph?
• What other information might help you interpret the meaning of
this graph?
Conclude:
• What are four different types of graphs?
• What are two ways in which a line graph is
useful?
• Which type of graph is useful for younger
audiences?
• How do you decide which type of graph to
use when presenting data?