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# Children's Defense Fund

## A strong effective, independent voice for all the children of America

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CDF has a long tradition of using data to support its work to create a level playing field for all children and takes great care to ensure the accuracy of any data used or provided to others.

CDF is affiliated with the U.S. Bureau of the Census as a Census Information Center for data on children and families. In this role, CDF analyzes and disseminates Census data in a variety of formats to concerned citizens, advocates, policy makers and the media.

CDF uses data from a wide range of sources, primarily federal data systems. Among the agencies whose published and unpublished data we use are: the Bureau of the Census, National Center for Health Statistics, Bureau of Labor Statistics, National Center for Education Statistics, Congressional Budget Office, Office of Management and Budget, Administration for Children and Families, Food and Nutrition Service, U.S. Department of Housing and Urban Development, and U.S. Department of Defense.

CDF also uses data from nonprofit and educational entities, including but not limited to the following: Center on Budget and Policy Priorities, Kaiser Family Foundation, Urban Institute, Food Research and Action Center, National Women's Law Center, College Board, National Association of Child Care Resource and Referral Agencies, and the Joint Center for Housing Studies of Harvard University.

(Download a printable version of this information.)

How to:

- calculate a percentage
- calculate a rate
- calculate a ratio
- calculate change over time
- rank numbers
- convert proportions and percentages

"Percent" means per 100; 25 percent means 25 out of 100. One hundred percent means everybody or everything; 0 percent means nobody or nothing.

To calculate a percentage you need just two pieces of information:

- the number in the entire (or total) group
- the number in the part of the group you are interested in (the "subgroup").

Divide the number in the subgroup by the number in the total group and then multiply by 100. (Number in subgroup ÷ Number in total group) x 100.

There are 1,257 children in a high school. Of them, 137 are in advanced science classes. You determine what percentage are in the advanced classes this way: 137 ÷ 1,257 = .109 (rounded) x 100 = 10.9%.

Use the same approach when dealing with budget figures rather than people.

If a social services agency with a budget of $2,500,000 for the year plans to spend $64,598 on child care, what percentage of the budget will be spent on child care?

64,598 ÷ 2,500,000 = .026 (rounded) x 100 = 2.6%

"Rate" simply means the number of things per some other number, usually 100 or 1,000 or some other multiple of 10. A percentage is a rate per 100. Infant mortality rates are calculated per 1,000.

To calculate a rate, you need three pieces of information:

- the number in the total group (for example,
- the total number of babies born in a given year)
- the number in the subgroup you are interested in (such as the number of infants that died that year) the "per" number - per 100, or 1,000, or 100,000. The "per" number is called a multiplier.

The formula for calculating a rate is:

(Number in subgroup ÷ Number in total group) x multiplier.

In 2005, 142,200 babies were born in Georgia. In that same year, 1,159 infants died in the state. The infant mortality rate is the number of infant deaths per 1,000 births. You calculate Georgia's 2005 infant mortality rate this way:

(1,156 ÷ 142,200) × 1,000 = 0.00815 (rounded) × 1,000 = 8.15

To calculate the rate you must work with numbers that are large enough to be meaningful. People who regularly work with numbers use this general rule: if the number of people or events or things is less than 30, do not calculate a rate. This is because rates based on such small numbers can vary tremendously from year to year and are not considered reliable. For example, if there were 17 infant deaths in your county last year, do not calculate an infant mortality rate.

A ratio is one number divided by another. A ratio tells you how much bigger or smaller one number is compared with the other.

For example, in 2005 the infant mortality rate among Blacks was 13.73; the rate among Whites was 5.73. The ratio of the Black rate to the White rate is: 13.73 ÷ 5.73 = 2.396 (or 2.40 rounded). The Black infant mortality rate in 2005 was more than twice the White rate.

You can compare any two numbers this way, provided you have the same measure for two groups for the same year (as in the infant mortality example above) or for one group in two different years (such as the unemployment rate in your state in 2008 compared with the 2000 rate).

The 2008 unemployment rate in Michigan was 8.3%; the 2000 rate was 3.6%. The ratio is: 8.3 ÷ 3.6 = 2.306 (or 2.3 rounded). In other words, the unemployment rate in Michigan in 2008 was more than twice the rate in 2000.

You can compare any two numbers in this way, providing you have the same measure for two groups for the same year (as in the infant mortality example) or for one group in two different years (such as the unemployment rate in your state in 2009 compared with the 2000 rate).

When you have data for two or more points in time, you can calculate how much change there was between the first and second times. Sometimes all you need to know is whether the number went up or down or stayed the same. Usually you will want to know the size of the change - that is, the percent by which the number changed. It is very simple to calculate this "rate of change." You need to know only 2 numbers: the number from the earlier point in time and the number from the later point in time.

The rate of change is:

[(Number at later time ÷ Number at earlier time) - 1] x 100

The easiest way to do this is with a calculator. That way you'll automatically see if the resulting number is positive (meaning there was an increase over time) or negative (meaning there was a decrease).

The infant mortality rate in Mississippi was 10.5 in 1995 and 11.35 in 2005. Calculate the change this way:

11.35 ÷ 10.5 = 1.08095

1.08095 - 1 = 0.08095

0.08095 × 100 = 8.095% (or 8.1%, rounded)

This means that the infant mortality rate in Mississippi increased by 8.1 percent between 1995 and 2005.

In New Jersey, the infant mortality rate was 6.6 in 1995, 5.23 in 2005. The change in the rate was:

5.23 ÷ 6.6 = 0.79242

0.79242 – 1 = -0.20758

-0.20758 x 100 = -20.758% (or -20.8%, rounded)

The infant mortality rate in New Jersey decreased by 20.8 percent between 1995 and 2005.

Why is it useful to rank numbers? Ranking allows you to say whether one state's children are faring better than another state's or to say that there are 17 states with lower infant mortality than yours.

Ranking should be done only when you can compare the same measure of data for each of the geographic areas or groups you are studying.

Ranking involves two steps:

- putting the numbers in order
- assigning a rank to each based on its place in the order.

Numbers can be ordered from largest to smallest or from smallest to largest. The "best" number (the highest number for median income would be best; the lowest number would be best for an infant mortality rate) can be assigned a rank of 1, with number 2 going to the second best, and so forth down the list. The worst number would be assigned to the lowest rank.

When two or more numbers in the list are the same, it does not make sense to give them different ranks. Give them the same rank and skip the next rank. If three items have the same rank, give them the same rank and skip the next two ranks.

Data can be communicated in a number of ways. If you think your audience might have trouble understanding or feeling moved by percentages, for example, you can use less formal (but still accurate) terms. For example:

Proportion |
Percent |
Converts to: |

.10 | 10% | 1 in (or out of) 10 |

.111 | 11.1% | 1 in 9 |

.125 | 12.5% | 1 in 8 |

.143 | 14.3% | 1 in 7 |

.167 | 16.7% | 1 in 6 |

.20 | 20% | 2 in 10 or 1 in 5 |

.222 | 22.2% | 2 in 9 |

.25 | 25% | 1 in 4 |

.286 | 28.6% | 2 in 7 |

.30 | 30% | 3 in 10 |

.333 | 33.3% | 1 in 3 |

.375 | 37.5% | 3 in 8 |

.40 | 40% | 4 in 10 or 2 in 5 |

.429 | 42.9% | 3 in 7 |

.44 | 44% | 4 in 9 |

.50 | 50% | 5 in 10, or 1 in 2 |

.56 | 55% | 5 in 9 |

.571 | 57.1% | 4 in 7 |

.60 | 60% | 6 in 10 or 3 in 5 |

.625 | 62.5% | 5 in 8 |

.667 | 66.7% | 2 in 3 |

.70 | 70% | 7 in 10 |

.714 | 71.4% | 5 in 7 |

.75 | 75% | 3 in 4 |

.778 | 77.8% | 7 in 9 |

.80 | 80% | 8 in 10 or 4 in 5 |

.833 | 83.3% | 5 in 6 |

.857 | 85.7% | 6 in 7 |

.875 | 87.5% | 7 in 8 |

.889 | 88.9% | 8 in 9 |

.90 | 90% | 9 in 10 |