Newsroom Math Crib Sheet

By Prof. Steve Doig

Arizona State University

To convert a fraction into a decimal:

n        Divide the top number by the bottom number

n        Examples: 5/8 = 0.625     17/64 = 0.265…

To convert a decimal into a percentage:

n        Multiply by 100 (or simply move the decimal two places to the RIGHT)

n        Examples: 0.658 = 65.8%     1.255 = 125.5%

To turn a percentage into a decimal:

n        Divide by 100 (or simply move the decimal two places to the LEFT)

n        Examples:  43.7% = 0.437     148.2% = 1.482

To get X% of Y:

n        Turn X% into a decimal, then multiply it by Y

n        Example: 20% of 90 = 0.20 * 90 = 18        130.5% of 45 = 1.305 * 45 = 58.7…

To compare X and Y using percentages (X is what percent of Y?):

n        X is (X/Y * 100) percent of Y

n        Example: 5 and 8:  5/8 = .625 = 62.5%, so 5 is 62.5% of 8

n        Example: 8 and 5:  8/5 = 1.6 = 160%, so 8 is 160% of 5

To compare X and Y using percentage differences:

n        X is ((X/Y –1) * 100) MORE/LESS than Y

n        Use MORE THAN if the answer is positive, and LESS THAN if it’s negative

n        Example: 5 and 8:  5/8 –1  = .625 – 1 = -0.375 = -37.5%, so 5 is 37.5% less than 8

n        Example: 8 and 5:  8/5 –1  = 1.6 – 1 = .6 = 60%, so 8 is 60% more than 5

To compare a NEW number with an OLD number using percentage change:

n        NEW has increased/decreased ((NEW/OLD –1) * 100) percent since OLD

n        Use INCREASED if the answer is positive, and DECREASED if it’s negative

n        Example: This year’s \$8 million budget is a 60% increase over last year’s \$5 million budget.

n        Example: This year’s \$5 million budget is a 37.5% decrease from last year’s \$8 million budget.

To calculate rates (the number of events per some standard unit):

n        Do this to account for different size populations

n        RATE = (EVENTS / POPULATION ) * (“PER” Unit)

n        Example Problem: If there were 320 murders in a population of 1,937,086, what is the murder rate per 100,000?

n        First, divide the 320 murders by 1937086 = 0.0001652…

n        Now multiply 0.0001652… by 100,000 = 16.5 murders per 100,000 population

To calculate the effect of inflation using the Consumer Price Index (CPI):

Price Now   =   CPI Now

Price Then       CPI Then

n        With this formula, all you need is any three of the numbers to calculate the fourth.

n        Example: CPI now = 194.6; CPI in 1965 was 30.8; price of gas in 1965 was \$0.30 per gallon.

X / 0.30 =194.6 / 30.8

X = (194.6 / 30.8) * 0.30 = 6.32 * 0.30 = gas in 1965 cost the equivalent of \$1.90 per gallon

Newsroom statistics:

n        Mean (average): Add the numbers, then divide by how many numbers there are

n        Median: Sort the numbers in order, then find the middle value

n        Sampling error margin: 1/ÖN   (example: sample of 625:  1/Ö625 = 1/25 = 0.04 = +/- 4 points)

"Ratios, Percentages, Statistics! Oh My!"
News Division Program, SLA 2005 Annual Conference

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