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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 vegetablesBread and other cereals and potatoesFood 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

• 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?

• Used for showing trends like increasing or decreasing, especially over time

• Helpful in making predictions

Relationships between the Variables

Direct Relationship: When one variable increases, the other variable increases

Indirect Relationship: When one variable increases, the other variable decreases

This graph is non-linear, or not a straight line. 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?