Calculating the Mean, Median, and Mode

Calculating the Mean, Median, and Mode Before you can begin to understand statistics, you need to understand mean, median, and mode. Without these three methods of calculation, it would be impossible to interpret much of the data we use in daily life. Each is used to find the statistical midpoint in a group of numbers, but they all do so differently.   The Mean When people talk about statistical averages, they are referring to the mean. To calculate the mean, simply add all of your numbers together. Next, divide the sum by however many numbers you added. The result is your mean or average score. For example, lets say you have four test scores: 15, 18, 22, and 20. To find the average, you would first add all four scores together, then divide the sum by four. The resulting mean is 18.75. Written out, it looks something like this: (15 18 22 20) / 4 75 / 4 18.75 If you were to round up to the nearest whole number, the average would be 19. The Median The median is the middle value in a data set. To calculate it, place all of your numbers in increasing order. If you have an odd number of integers, the next step is to find the middle number on your list. In this example, the middle or median number is 15: 3, 9, 15, 17, 44 If you have an even number of data points, calculating the median requires another step or two. First, find the two middle integers in your list. Add them together, then divide by two. The result is the median number. In this example, the two middle numbers are 8 and 12: 3, 6, 8, 12, 17, 44 Written out, the calculation would look like this: (8 12) /  2   20 / 2 10 In this instance, the median is 10. The Mode In statistics, the mode in a list of numbers refers to the integers that occur most frequently. Unlike the median and mean, the mode is about the frequency of occurrence. There can be more than one mode or no mode at all; it all depends on the data set itself. For example, lets say you have the following list of numbers: 3, 3, 8, 9, 15, 15, 15, 17, 17, 27, 40, 44, 44 In this case, the mode is 15 because it is the integer that appears most often. However, if there were one fewer 15 in your list, then you would have four modes: 3, 15, 17, and 44. Other Statistical Elements Occasionally in statistics, youll also be asked for the range in a set of numbers. The range is simply the smallest number subtracted from the largest number in your set. For example, lets use the following numbers: 3, 6, 9, 15, 44 To calculate the range, you would subtract 3 from 44, giving you a range of 41. Written out, the equation looks like this:   44 – 3 41 Once youve mastered the basics of mean, median, and mode, you can begin to learn about more statistical concepts. A good next step is studying  probability, the chance of an event happening.

Overview of United States v. Susan B. Anthony

Overview of United States v. Susan B. Anthony The United States v. Susan B. Anthony is a milestone in womens history, a court case in 1873. Susan B. Anthony was tried in court for illegally voting. Her attorneys unsuccessfully claimed that citizenship of women gave to women the constitutional right to vote. Dates of Trial June 17-18, 1873 Background When women were not included in the constitutional amendment, the 15th, to extend suffrage to black men, some of those in the suffrage movement formed the National Woman Suffrage Association (the rival American Woman Suffrage Association supported the Fifteenth Amendment).  These included Susan B. Anthony and Elizabeth Cady Stanton. Some years after the 15th Amendment passed, Stanton, Anthony, and others developed a strategy of attempting to use the Fourteenth Amendments equal protection clause to claim that voting was a fundamental right and thus could not be denied to women.  Their plan: to challenge limits on women voting by registering to vote and attempting to vote, sometimes with the support of the local poll officials. Susan B. Anthony and Other Women Register and Vote Women in 10 states voted in 1871 and 1872, in defiance of state laws prohibiting women from voting. Most were prevented from voting. Some did cast ballots. In Rochester, New York, almost 50 women  attempted to register to vote in 1872. Susan B. Anthony and fourteen  other women were able, with the support of election inspectors, to register, but the others were turned back at that step.  These fifteen women then cast ballots in the presidential election on November 5, 1872, with the support of the local election officials in Rochester. Arrested and Charged With Illegal Voting On November 28, the registrars and the fifteen  women were arrested and charged with illegal voting. Only Anthony refused to pay bail; a judge released her anyway, and when another judge set new bail, the first judge paid the bail so that Anthony would not have to be jailed. While she was awaiting trial, Anthony used the incident to speak around Monroe County in New York, advocating for the position that the Fourteenth Amendment gave women the right to vote.  She said,  We no longer petition legislature or Congress to give us the right to vote, but appeal to women everywhere to exercise their too long neglected citizens right. Outcome The trial was held in U.S. District Court.  The jury found Anthony guilty, and the court fined Anthony $100. She refused to pay the fine and the judge did not require her to be jailed. A similar case made its way to the U.S. Supreme Court in 1875. In Minor v. Happersett,  On October 15, 1872,  Virginia Minor  applied to register to vote in Missouri.  She was turned down by the registrar and sued.  In this case, appeals took it to the Supreme Court, which ruled that the right of suffrage- the right to vote- is not a necessary privilege and immunity to which all citizens are entitled and that the Fourteenth Amendment did not add voting to basic citizenship rights. After this strategy failed, the National Woman Suffrage Association turned to promoting a national constitutional amendment to give women the vote.  This amendment did not pass until 1920, 14 years after Anthonys death and 18 years after Stantons death.