Nathan VanHoudnos

10/17/2014

- Checkpoint results
- Homework comments
- Review

These are off by plus or minus `10/160 = .0625`

```
mean(hw4.grades/160)
```

```
[1] 0.7055556
```

```
median(hw4.grades/160)
```

```
[1] 0.84375
```

Your grades are likely off by 10 pts (Question #4 part E):

- I distributed an incorrect solution set to both the TA and BlackBoard, and
- did not catch the error until
**after**the the TA had graded your assignments (Thanks Stephanie!).

The correct solutions are now on BlackBoard, and in the hands of the TA.

Aaron will re-grade Question #4 part E on **Monday**.

My apologies!

Larry Summers President of Harvard (2001-06)

Gave a speech claiming that aptitude differences between men and women explained why men are over represented in science faculty positions.

The speech was met with intense criticism

- Resigned within a year
- Cost him the US Treasury Secretary position in Obama's administration

From Question #5:

Can all three of the following statements be true?

- The average woman is smarter than the average man.
- In fact, 97.5% of women are smarter than the average man.
- And yet, the top 2.5% of men are smarter than 99.85% of women.

Assume that the IQs of men and women are distributed normally.

- Let the IQs of women be distributed with a mean of 100 and a standard deviation of 10.

Assume that the IQs of men and women are distributed normally.

- Let the IQs of women be distributed with a mean of 100 and a standard deviation of 10.
- The 68-95-99.7 rule implies that .05/2 = 2.5% of women have an IQ below 80.

Assume that the IQs of men and women are distributed normally.

- Let the IQs of men be distributed with a mean of 80 and a standard deviation of 25.

Assume that the IQs of men and women are distributed normally.

- Let the IQs of men be distributed with a mean of 80 and a standard deviation of 20.
- The 68-95-99.7 rule implies that only .05/2 = 2.5% of men have an IQ above 130.

The 68-95-99.7 rule implies that

- 2.5% of men have an IQ over 130
- 0.003/2 = 0.15% of women have an IQ over 130

- The average woman is smarter than the average man.
- 97.5% of women are smarter than the average man.
- And yet, the top 2.5% of men are smarter than 99.85% of women.

“even small differences in the standard deviation [between genders] will translate into very large differences in the available pool substantially out [from the mean]”

If assume IQ is normally distributed and interpret

- “substantially out from the mean” as several standard deviations, and
- have evidence\( ^\text{[citation needed]} \) that the standard deviation of Men's and Women's IQ differs,

then Larry was was correct. (Question #6)

Political discussions are rarely settled by mathematics because the

**assumptions**of the two sides often differ.- The Pinker v. Spelke debate (2 hours!) barely touches upon the math, but focuses instead on Larry's assumptions.

Your

**assumptions**can be more important than your mathematics.If your assumptions are

**strongly contrary**to the intuitions of your audience, you must provide**strong evidence**to counteract those intuitions.