Statistics for Dummies

Read Statistics for Dummies for Free Online

Book: Read Statistics for Dummies for Free Online
Authors: Deborah Jean Rumsey
Tags: Reference, Non-Fiction
500 = 0.02 or 2%. To find percentage decrease, do the same steps. You'll just get a negative number, indicating a decrease.

    Table 2-2 shows the estimated population of the U.S. for 1987–1997, along with the estimated number of crimes and the estimated crime rates (crimes per 100,000 people).

Table 2-2: Number of Crimes, Estimated Population Size, and Crime Rates in the U.S. (1987–1997)
Year
Number of Crimes
Estimated Population Size
Crime Rate (Per 100,000 People)
----
1987
13,508,700
243,400,000
5,550.0
----
1988
13,923,100
245,807,000
5,664.2
----
1989
14,251,400
248,239,000
5,741.0
----
1990
14,475,600
248,710,000
5,820.3
----
1991
14,872,900
252,177,000
5,897.8
----
1992
14,438,200
255,082,000
5,660.2
----
1993
14,144,800
257,908,000
5,484.4
----
1994
13,989,500
260,341,000
5,373.5
----
1995
13,862,700
262,755,000
5,275.9
----
1996
13,493,900
265,284,000
5,086.6
----
1997
13,175,100
267,637,000
4,922.7

    Looking again at 1987 compared to 1993, you can see that the number of crimes increased from 13,508,700 in 1987 to 14,144,800 in 1993. (Note that this represents a 4.7% increase, because 14,144,800 − 13,508,700 equals 636,100, and if you divide this number by the original value, 13,508,700, you get 0.047, which is 4.7%.) So, looking at it this way, someone may report that crime went up 4.7% from 1987 to 1993. But this 4.7% represents an increase in the total number of crimes, not the number of crimes per person , or the number of crimes per 100,000 people. To find out how the number of crimes per 100,000 people changed over time, you need to calculate and compare the crime rates for 1987 and 1993. Here's how: (5,484.4 – 5,550.0) ÷ 5,550.0 = –65.6 ÷ 5,550.0 = –0.012 = –1.2%. The crimes per 100,000 people (crime rate) actually decreased by 1.2%
    Depending on how you spin the numbers, the results could be made to show opposite trends: that crime went up or down between 1987 and 1993. But now that you know the difference between the number of crimes and the crime rate, you know that some statistics should not simply be reported as the total number of events, but instead should be reported as rates (that is, the number of events divided by the number in the entire group).
REMEMBER 
Question the type of statistic that was used before you try to make sense of the results. Is it a fair and appropriate measurement? Is it an accurate way to portray the real story behind the data, or is there a better way?
Tip 
The scale tells you a lotto!
    Charts and graphs are good ways of showing clearly and quickly the point that you want to make, as long as the drawings are done correctly and fairly. And just to be clear, what's the difference between a chart and a graph? Not much: Statisticians use these terms quite interchangeably when talking about visual displays of statistical information. But a good rule is that if the picture shows bars or pies or other figures or shapes, you're looking at a chart. Otherwise, you are looking at a graph, which plots numbers as they change over time, or as they appear as pairs on the (x,y) plane. (More on that stuff in Chapter 18 .)
    Unfortunately, many times, the charts and graphs accompanying everyday statistics aren't done correctly and/or fairly, and you need to be on the look-out for problems. One of the most important elements to watch for is the way that the chart or graph is scaled. The scale of a graph is the quantity used to represent each tick mark on the axis of the graph. Do the tick marks increase by 10s, 20s, 100s, 1,000s, or what? The scale can make a big difference in terms of the way the graph or chart looks.
    For example, the Kansas Lottery routinely shows its recent results from the Pick 3 Lottery. One of the statistics reported is the number of times each number (0 through 9) is drawn among the three winning numbers. Table 2-3 shows a chart of the number of times each number was drawn through March 15, 1997 (during 1,613 total Pick 3 games, for a total of 4,839

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