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
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
10 and 17
(10 / 17) = .5882
.5582 – 1 = -.4117
-.4117 * 100 = -41.17
10 is 41% less than 17
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
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
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
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.
25 / 150,000 = .00016667
.00016667 * 10,000 = 1.6 murders per 10,000 residents
20 / 75,000 = .00026667
.00026667 * 10,000 = 2.6 murders per 10,000 residents
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
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:
Jo Jo $40
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.
-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.
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.”