ID - Measures of Center (Lesson)

Measures of Center

Mean and Median

Two of the most common measures of center are the mean and median. Let, n be the number of data values in a data set.

meanandmedian.png

Example:

The April high temperatures (in degrees Fahrenheit) for five consecutive years in Rhode Island are listed below. Find the mean and median for the data set: 90, 86, 84, 92, 77

Find the mean:

Mean = LaTeX: \frac{90+86+84+92+77}{5}90+86+84+92+775= LaTeX: \frac{429}{5}4295 = 85.8

Find the median:

  • Write the data values from least to greatest: 77, 84, 86, 90, 92
  • The middle value is 86, so that is the median.

Watch this video to try a few more examples:

 

Finding Quartiles

The median divides the data set into two halves. The first quartile (Q1) of a data set is the median of the lower half. The third quartile (Q3) is the median of the upper half.

Example: 

Find the quartiles of the following data set: 1, 7, 8, 3, 4, 6, 8, 6, 3, 5

Put the data in order from least to greatest:

 1, 3, 3, 4, 5, 6, 6, 7, 8, 8

Find the median (the middle number):

 1, 3, 3, 4, 5, 6, 6, 7, 8, 8

The median would be between 5 and 6. We can take the average of those two values and the median will equal (5 + 6)/2 = 5.5

Find the quartiles:

Determine the median of the first half (Q1) and then determine the median of the second half (Q3).

mean median and mode image

 

 

 

 

 

Using Averages

Averages are often used to tell us how someone has done, or predict how they might do. There are also times when we want to ensure our average meets a certain standard. Watch this video to see a problem like that:

 

Measures of Center Practice

1. Leah's quiz scores are listed below. Find the mean and median of Leah's quiz scores: 88, 84, 85, 86, 90, 81.

2. Jerry recorded how many minutes of television he watched each week. Find the mean and median of Jerry's data: 35, 75, 25, 55, 60, 45, 70.

3. Find the first and third quartiles of the set of data: 3, 5, 1, 2, 8, 7, 9 10, 2, 4.

4. Find the first and third quartiles of the set of data: 11, 12, 8, 9, 15, 14, 8, 10, 10.

5. Corey is a basketball player and his goal is to average at least 15 points per game. Below are the scores for Corey's first 9 games. He has one game left, how many points should Corey try to score in this last game to meet his goal? 14, 16, 16, 13, 14, 15, 14, 14, 14.

6. Lauren has 6 quizzes in a semester and has made the following scores on the first 5 quizzes: 76, 84, 92, 91, 87. What does Lauren need to make on her last quiz so that her quiz average is above 85%?

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