There are 10,000 possible 4-digit combinations for a phone that dials 0 through 9 if repetition is allowed. Some of the combinations include {0,0,0,0}, {9,9,9,9} and all arrangements between. Since the order of digits matters ({0,0,0,1} is not equal to {0,0,1,0}) and repetition is allowed (each digit can be in any of the four positions), the arrangements are called "permutations with repetition."
Know MoreAccording to Math Is Fun, permutations with repetition are the easiest to calculate. The person needs to determine the number of dial pad numbers she can choose from (n) and the number of selections (r). In this case, to calculate a 4-digit number with numbers 0 through 9 available, there are 10 available dial pad numbers (n=10) for each digit with four digits selected (r=4). The number of permutations can be calculated with the formula n^r, in this case by multiplying 10 x 10 x 10 x 10.
When repetition is not allowed, the permutation formula is adjusted to the factorial function, which is noted by ?!? and is simply a multiplication of a series of descending natural numbers. The formula is useful in the cases when each number can be selected only once. For example, if there are 10 competitors in the race (n=10), and the first four get a reward (r=4), a person can calculate the number of possible reward distribution combinations by dividing n!, which is 10x9x8x7x6x5x4x3x2x1, with the factorial function of the difference between n and r (n-r)!.
When the order does not matter, such as in lottery drawings, the calculations are called combinations.
Learn MoreAdvanced Placement, or AP, Statistics is an accelerated high school course involving the collection, analysis and interpretation of mathematical data. This non-calculus-based course challenges students to develop theories and draw conclusions by identifying trends and divergences in data patterns. The curriculum typically requires students to design mock studies and surveys.
Full Answer >Coefficient of variation is defined as the ratio of standard deviation to the arithmetic mean. Coefficient of variation gives a sense of "relative variability," as reported by the GraphPad Statistical software website. It can be expressed either as a fraction or a percent.
Full Answer >Normal distribution is when 50 percent of a quantity appears to the right of the halfway mark and 50 percent falls to the left. Used for phenomena such as blood pressure readings and height, the data can be depicted on a horizontal line and the quantity of data depicted on the vertical line. This arrangement forms a bell-shaped pattern called a normal curve, according to Regents Exam Prep Center.
Full Answer >The box-and-whisker plot is a technique in statistics that graphically shows the distribution of a set of data involving the minimum and maximum values, as well as the first, second and third quartiles. The plot is typically drawn using a number line.
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