Math Tip: Means, Medians, Modes

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[edit section] Calculating Means

The mean of a set of numbers is the sum of the elements divided by the number of elements. For example:

Set A = {1, 2, 3, 4, 5}

Mean A = (1 + 2 + 3 + 4 + 5)/5 = 15/5 = 3

Sometimes, you will get problems in which you will need to use algebra to find either 1) an element of the set, 2) the number of elements, or 3) the mean. For example:

A class of ten students has the following test grades: 10, 9, 4, 7, 6, 8, 8, 9, 3, and X. The average score in the class is 7. What is the value of X?

Mean = Sum of scores divided by number of scorers = (64+X)/10 = 7.

64+X = 70; X = 6

[edit section] Median

The median of a set is the element in the very middle when arranged in increasing order. For example, the set below has a median of 5:

Set B = {1, 2, 3, 4, 5, 6, 7, 8, 9}

"5" is the 5th element of 9, meaning it is right in the middle when counted. If two numbers are in "the middle," meaning if there is an even number of elements, you take the midpoint between the two numbers (add both, divide by two).

If you are asked to find an element given a set and a median, you can do so by counting. Consider the following question:

Set C has elements {1, 9, 4, 3, X, 2). The median is 3.5. What is a possible value of X?

1. Arrange in order {1, 2, 3, 4, 9, X}

2. Count off the numbers that you do know: 1, 9... 2, 4... 3 and X.

3. Since 3 + X / 2 = 3.5, X = 4

There is another possible set of solutions for X... see if you can find them! (Hint: X = 144 is a possible answer)

[edit section] Mode

Mode is the most frequently-occuring element of a set. For example:

Set C: {1, 1, 1, 2}

The mode is 1.

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