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# Mean

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## Mean Length of a Celebrity Marriage

### Topic

Determining the Mean Length of a Celebrity Marriage

### Vocabulary

• Mean
• Median
• Mode
• Measure of Central Tendency

### Student Exploration

#### What is the mean length of a celebrity marriage?

The world was in an uproar when Kim Kardashian filed for divorce from Kris Humphries after only 72 days of marriage. The couple dated for six months before getting engaged and then had a publicized, dramatic two-day wedding special, “Kim’s Fairytale Wedding.” Shortly after Time.com published an article on the “Top 10 Short-Lived Celebrity Marriages.”

1. Examine the Time’s list of the Top 10 celebrity marriages and then find the mean length of a celebrity marriage. The mean length of a celebrity marriage according to the Time’s list is 114 days (be sure to change Brittany Spears marriage to Jason Alexandar to days from hours).
2. What is the mode length of a celebrity marriage according to Time’s list? There is not a mode in this set, as all the lengths are different.
3. What is the median length of a celebrity marriage according to Time’s list? The median length is 114.5 days, you must find the mean of 107 and 122 as there are an even number of numbers in the set.
4. What measure of central tendency do you think is the most useful for analyzing the length of a celebrity marriage? Explain. Either the mean or the median is the most useful. They are both 114 days and give a good sense of where the data lays. The mode is not helpful as there is not one and it doesn’t tell us anything about the data except that there are no numbers that appear more than once.
5. What about the set up of this problem causes our data to generate inaccurate measures of the mean, median, and mode length of a celebrity marriage? Explain. The Time’s article, from which you are getting your data, only provides ten of the popular celebrity marriages. This isn’t a database of ALL the celebrity marriages. So from the beginning our data is skewed because of the list of these ten marriages is very random.
6. Propose a more accurate method. One example of a more accurate method for determining the mean, median, and mode length of a celebrity marriage would be to track all of the celebrity marriages within a specific time period (such as a year) and then researching all lengths of all the marriages from that time period.

### Extension Investigation

Check out this model of mean that uses Legos! http://www.joshharness.com/2012/06/understand-arithmetic-mean-with-legos.html

1. Why does the Lego structure tip over when the bottom piece is put at 2? Explain. The Lego structure tips over because it is not balanced and there are too many Legos on one side (the weight is not balanced).
2. Why does the Lego structure stay balanced when the bottom piece is put at 3? Explain. The Lego structure stays balanced because 3 is the mean and it provides a center for all the blocks. There is an equal number of blocks on each side of the mean and the weight of the blocks is balanced.
3. Do you have your own Legos? Build a larger structure with only pieces of the same size (make an interesting or random design) and then test the structure. Place a block on the bottom of your structure at different points to test where the structure will be balanced. Does it stay balanced at the mean value? Take photos and upload it to the CK-12 website and share it with other users!

### Connections to other CK-12 Subject Areas

• Measures of Central Tendency and Dispersion
• Median
• Mode