Manipulating Numbers
Mean
Example: You are writing about the World Wide Widget Co. and the salaries of its nine employees. You want to find out the average salary.
– The CEO makes $100,000 per year
– Two managers make $50,000 per year
– Four factory workers make $15,000 each
– Two trainees make $9,000 per year
To find the mean salary, or average salary, add each of the salaries and divide by the total number of employees.
Find the mean Salary:
$100,000 + $50,000 + $50,000 + $15,000 + $15,000 + $15,000 + $15,000 + $9,000 + $9,000 (all the values in the set of data).
= $278,000 / 9
That gives you the mean, which is $30,889.
But: Be Careful
Only 3 of the 9 workers make that much money. And the other 6 workers don’t even make half the average salary.
Median
If your story want to get at the salary of the average worker, the statistical average may not be very useful. Instead you may want to explore the median salary.
Find the Median Salary. Of the nine salaries, which one is in the middle?
$100,000
$50,000
$50,000
$15,000
[$15,000]
$15,000
$15,000
$9,000
$9,000
Percent Change
To find a percent change between 2 numbers:
Subtract the old value from the new value, then divide by the old value and Multiply the result by 100.
Example: You are doing a story comparing murder in Vancouver to Toronto.
Vancouver 2010: 50 murders. Toronto 2010: 50 murders.
Vancouver 2005: 29 murder. Toronto 2005: 42 murders.
What is the percent change in murders for each city?
Toronto: 50-42/42 x 100 = 19%
Vancouver: 50-29/29 x 100 = 72%
That will show you that, over a five year period, Toronto had a 19 percent increase in murders, while a Vancouver’s increase was more than 72 percent.
What is the lead?
Murder in Vancouver increases by 72 percent, compared to only 19 percent in Toronto.
Per Capita and Rates
But what if the population of one city grew much faster than the other? How would this change our trend?
Vancouver 2010: Pop 800,000. Toronto 2010: Pop 600,000
Vancouver 2005: Pop 450,000. Toronto 2005: 550,000
To calculate murders per capita: Divide the number of murders by the total population.
To calculate the rate, multiply this number by 100,000 to get the result as the number of murders per 100,000 people.
Do this for both the 2010 numbers and the 2005 numbers.
What is the change in murder rate for each city?
2010:
Vancouver: 50/800,000×100,000=6.25
In Vancouver’s case, 50 murders divided by 800,000 people equals a murder rate of 6.25 per 100,000 people.
Toronto: 50/600,000×100,000=8.33
Toronto’s 50 murders divided by 600,000 people equals a murder rate of 8.33 per 100,000 people.
2005:
Vancouver: 29/450,000×100,000=6.44
Vancouver’s 29 murders divided by 450,000 people equaled a murder rate of 6.44 per 100,000 people.
Toronto: 42/550,000/100,000=7.64
Toronto’s 42 murders divided by 550,000 equaled a murder rate of 7.64 per 100,000 people.
SO, Calculate the Murder Rates Percentage Change:
Subtract the old value from the new value, then divide by the old value and Multiply the result by 100.
Vancouver: 6.25-6.44/6.25×100= -3.04%
Toronto: 8.33-7.64/8.33×100= 8.2%
Now what is your lead?
Vancouver’s murder rate decreased by almost 3 percent, while Toronto’s per capita murder rate increased by more than 9 percent
That’s the story.