Do Now

On Question #1 on the Math Studies Paper 1 Mock, students scored this many points out of 6 total possible:

6 6 6 5 6 3 3 33 6 3 5 2 5 3 34 4 3 1 6 5 2Find the mean, range, standard deviation and IQR.Mean = 4.04, Range = 6-1=5, Sx = 1.55, IQR = 3

Cornell Notes Set-Up

• Yes, we have a lot of objectives. Sorry.• 1.1.1 – Define Error Bars• 1.1.2 – Calculate mean and standard deviation• 1.1.3 – State what standard deviation is used for and state the

empirical rule• 1.1.4 – Explain how the standard deviation is useful• 1.1.6 – Explain difference between correlation and causation.

• Here is the Essential Question:• How do we represent quantitative information in biology lab

reports?

• Write in your notes column, not the cue column.

Error Bars

Error bars are a graphical representation of the variability of data.• That means they show “how variable the data is”

Error bars can show either the range or the standard deviation of data.• They show this by stretching up and down.

Error Bars Example

Let’s compare questions #1 and #2 on Math Studies. Here are the scores on Question #2, also out of 6 points:

6 3 6 2 2 2 3 25 6 4 5 2 0 2 62 3 2 2 6 5 2Calculate the mean, range, standard deviation and IQR.Mean = 3.39, Range = 6-0=6, Sx = 1.83, IQR = 3

Error Bars Example (cont.)

Comparing Range• Question 1 Mean = 4.04• Question 1 Range = 6-1=5• Question 2 Mean = 3.39• Question 2 Range = 6-0=6

Comparing Std. Dev.• Question 1 Mean = 4.04• Question 1 Sx= 1.55• Question 2 Mean = 3.39• Question 2 Sx= 1.83

Q1 Q20

2

4

6

Error Bars with Range

Q1 Q20246

Error Bars with Std. Dev.

Calculations Recap

• If you just have a list of data, then make sure FreqList is clear in 1-Var Stats!!!!!

• If you DO have a frequency list, then make sure FreqList says L2 in 1-Var Stats!!!!!

• X-Bar (x with a line over it) is the mean.

• “Baby sigma” x is the standard deviation for math.

• SX is the standard deviation for biology because S stands for Sample.

Standard Deviation

The term “standard deviation” is used to summarize the spread of values around the mean.

The bigger the standard deviation, the more spread out your data is.

If your data is close together, the standard deviation should be SMALL.

The Empirical Rule

• How big should your empire be?

• 68% - 95% - 99.7% is the empirical rule!• 68% of values fall within one standard deviation.• 95% of values fall within two standard deviations.• 99.7% of values fall within three standard deviations.

How is standard deviation useful?

A small standard deviation means the data is clustered closely around the mean.

A large standard deviation means the data is more spread out (but the mean is still in the middle!)

Correlation vs. Causation

The existence of a correlation does not establish a causal relationship between two variables.

Ex.: Ice cream and Rape… More on this in the Wednesday PowerPoint.

Correlation vs Causation

• Identify as correlation or causation:1. People who have high blood pressure are more likely to

suffer stroke.2. People who start taking aspirin are less likely to have a heart

attack than they were before.3. The plants in this room are all taller than the plants in that

room.4. The bean sprouts in the light grew taller than the bean

sprouts in the dark.5. Ms. Griffith never met anyone with gastritis until she moved

to the valley.

TO PROVE CAUSATION YOU NEED AN EXPERIMENT!!

Correlation or Causation?

Exit Slip: NO NOTES

1. Given SL scored an average of 3 and 4 points on questions #1 and #2 respectively, with a sample standard deviation of 1.2 and 0.7, plot this data with error bars.

2. What are error bars?3. What is standard deviation used for?4. ___% of values fall within one standard

deviation of the mean.5. What is the difference between correlation and

causation?