Think of math in the context of stories…

Math is useful for:

– Going beyond anecdotes.

– Ensuring accuracy and credibility of anecdotes.

– Finding the numbers that will lead to the best anecdotes.

**1. Fraction to decimal and percent –** Because percents are easier to understand than fractions.

*Formula:* Divide top number by bottom number

Then multiply result by 100

*Example: *

Five-eighths

5 / 8 =.625

.625 * 100 = 62.5%

**2. Compare two numbers using percent difference** – To see how much more/less one number is than another.

*Formula: * X is (X/Y) – 1 * 100 = MORE OR LESS THAN Y

*Example:*

10 and 17

(10 / 17) = .5882

.5582 – 1 = -.4117

-.4117 * 100 = -41.17

10 is 41% less than 17

*Your turn:*

Compare the pay of two employees by percent. Lisa makes $14 an hour. Joe makes $9 an hour. Lisa makes how much more than Joe (in percent)?

**3. Percentage change** – Comparing a new number to an old number.

*Formula:* (NEW minus OLD) divided by OLD

Then multiply the result by 100 and put % on it

*Example:*

50 murders in 2014

40 murders in 2013

50 – 40 = 10

10 / 40 = .25

.25 X 100 = 25

25% increase in murders

or the reverse

40 murders in 2014

50 murders in 2013

40 – 50 = -10

-10 / 50 = -.2

-.2 X 100 = -20

20% decrease in murders

*Your turn:*

In 2013, there were 342 homes sold in Thrillsville. In 2014, there were 432 homes sold. How much did home sales increase in the last year?

**4. Rates** – Allows you to compare places of different size.

*Formula:* EVENTS divided by POPULATION multiplied by PER UNIT

Common PER UNITS are 100,000, 10,000, 1,000, 100 or 10

The phrase Per capita = 1

*Example:*

Compare the murder rates of two cities:

City 1 of 150,000 people with 25 murders

City 2 of 75,000 people with 20 murders.

City 1:

25 / 150,000 = .00016667

.00016667 * 10,000 = 1.6 murders per 10,000 residents

City 2:

20 / 75,000 = .00026667

.00026667 * 10,000 = 2.6 murders per 10,000 residents

*Your turn:*

Find the arson rate (per 1,000 people) for each of the following:

- Maplewood – Population 23,867 Arsons 51
- Mount Holly – Population 9,536 Arsons 15
- North Brunswick – Population 40,742 Arsons 42

**5. Mean, median, mode and outliers** – Where is the center or middle of the data?

**Mean** or **Average**: Total of the values, divided by the number of those values.

**Median**: The middle value of an ordered list.

**Mode**: The most common value.

**Outliers**: Atypical values far from the average.

*Example: *2018 salaries for MLS players

See the story that ESPN did with these numbers

*Your turn:*

Find the mean, median, mode and outlier for the following. There are ten employees at a business. Pay ranges from $9 an hour to $40 an hour. The employees and their hourly wages are:

Joe $9

Mary $10

Bob $9

Marshall $15

Carrie $25

Alex $14

Jo Jo $40

Elizabeth $9

Bernard $14

Stephan $9

**6. Correlation **– The relationship between two or more variables in your data**.**

Positive r: if one variable goes up, the other goes up.

Negative r: if one variable goes up, the other goes down.

**Causation** – The act or process of causing; the act or agency which produces an effect.

*IMPORTANT: Correlation does not imply causation.*

**7. Normal distribution** – The probability that any real observation will fall between any two real limits or real numbers, as the curve approaches zero on either side.

Normal distribution (Mathisfun.com) -The peak is in the middle near the mean. The curve covers 100%.

**8. Variability** – How data can vary from the center.

Measures of variability:

**Maximum** and **minimum**: largest and smallest values.

**Range**: the distance between the maximum and minimum.

**Quartiles**: the medians of each half of the ordered list of values.

-Halfway down from the median is the first quartile.

-Halfway up from the median is the third quartile.

**Standard deviation**: the average distance from the mean.

**9. Standard deviation** – Defines whether a value is in fact a true outlier.

Values are reliably an outlier if found more than 3 StdDev from the mean.

Empirical rule:

-68% of values within 1 StdDev of mean

-95% of values within 2 StdDev of mean

-99.7% of values within 3 StdDev of mean

Variability is normal. Values within 3 StdDev are considered normal.

*Your turn:*

Is Messi an outlier? Why or why not?

Is Ronaldo an outlier? Why or why not?

**10. Margin of Error** – The likelihood (not a certainty) that the result from a sample is close to the number one would get if the whole population had been queried.

*The margin of error in a sample = 1 divided by the square root of the number of people in the sample*

Or as Robert Niles says, “If a poll has a margin of error of 2.5 percent, that means that if you ran that poll 100 times — asking a different sample of people each time — the overall percentage of people who responded the same way would remain within 2.5 percent of your original result in at least 95 of those 100 polls.”

*Your turn:*