How to Find a Weighted Mean

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It is very easy to find the mean for a single set of data. Calculate the sum of the values and divide by the number of values. A different approach is required when calculating the mean for a larger data set or the weighted mean. In these cases, the data will be organized in a frequency table. For the purposes of this article, the following survey question will be addressed: How many people live in your house?

Things You'll Need

  • Pencil or Pen
  • Paper
  • Calculator
  • Examine the frequency table for this data set. The first column contains values that indicate the possible number of people in a household. In this case, the numbers are, as follows: 2, 3, 4, 5, 6, 7. The numbers in the second column indicate the frequency of these values: 4, 6, 12, 17, 8, 3.

  • Create ordered pairs to better understand the situation: (2, 4), (3, 6), (4, 12), (5, 17), (6, 8), (7, 3). The ordered pair (4, 12) indicates that 12 surveyed individuals have 4 people in their household.

  • Find the number of people surveyed by adding the numbers in the second column: 4, 6, 12, 17, 8, 3. In this case, the sum is 50.

  • Multiply the first coordinate of each ordered pair by the second. The resulting products are, as follows: 8, 18, 48, 85, 48, 21. If you are using a frequency table, multiply the values in the first column by the values in the second column.

  • Add the resulting products to obtain a sum of 228.

  • Divide the sum of the resulting products (228) by the total number of people surveyed (50). The result is the weighted mean: 4.56.

References

  • "Statistics"; Alan Graham; 1994
  • Photo Credit RUNSTUDIO/Photodisc/Getty Images
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