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Mean, Median, and Mode Study Guide (page 3)

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Updated on Oct 4, 2011

Weighted Average

In a weighted average, some or all of the numbers to be averaged have a weight associated with them.

Example: Don averaged 50 miles per hour for the first three hours of his drive to Seattle. When it started raining, his average fell to 40 miles per hour for the next two hours. What was his average speed?

You cannot simply compute the average of the two speeds as , because Don spent more time driving 50 mph than he did driving 40 mph. In fact, Don's average speed is closer to 50 mph than it is to 40 mph precisely because he spent more time driving 50 mph. To correctly calculate Don's average speed, we have to take into consideration the number of hours at each speed: 3 hours at an average of 50 mph and 2 hours at an average of 40 mph, for a total of 5 hours.

Average =

Or, take advantage of the weights, 3 hours at 50 mph and 2 hours at 40 mph:

Average =

Tip

Write down your age on a piece of paper. Next to that number, write down the ages of five of your friends or family members. Find the mean, median, and mode of the ages you've written down. Remember that some groups of numbers do not have a mode. Does your group have a mode?

Sample Questions

  1. This term, Barbara's test scores are 88, 96, 92, 98, 94, 100, and 90. What is her average test score?
  2. Find the average test score, the median test score, and the mode of the test scores for the 30 students represented in the following table.

    Number of Students Test Score
    1 100
    3 95
    6 90
    8 85
    5 80
    4 75
    2 70
    1 0

Solutions to Sample Questions

Question 1

Calculate the average by adding the grades together and dividing by 7, the number of tests:

Average = 94

Question 2

Average (Mean)

Use the number of students achieving each score as a weight:

Even though one of the scores is 0, it must still be accounted for in the calculation of the average.

Median

Since the table is already arranged from high to low, we can determine the median merely by locating the middle score. Since there are 30 scores represented in the table, the median is the average of the 15th and 16th scores, which are both 85. Thus, the median is 85. Even if the bottom score, 0, were significantly higher, say 80, the median would still be 85. However, the mean would be increased to 84.1. The single, peculiar score, 0, makes the median a better measure of central tendency than the mean.

Mode

Just by scanning the table, we can see that more students scored an 85 than any other score. Thus, 85 is the mode. It is purely coincidental that the median and mode are the same.

Find practice problems and solutions for these concepts at Mean, Median, and Mode Practice Questions.

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