Emergence Early or Late? What's the Range, Median and Mean?

Are tulip gardens emerging and blooming early or late this year? Let's take a look at gardens in one of our coldest regions: Anchorage, AK. Data from several years may give us new insights for making accurate predictions.

• Range: The difference between the earliest and latest dates in a set of data.
• Median: The median is the 50th percentile. The date in an ordered set of data such that half of the dates are earlier and half of the dates are later. Half the values are larger than the median, and half are lower. If there are an even number of values, the median is defined as the average of the two middle values.
• Mean: The mean is the average of all the values. It's the most common measure of center. To determine the mean, find the sum of the values in the set, then divide by the number of values.

Try This!
Here are emerging dates for tulips in Anchorage: 3/20/00, 5/07/99, 4/13/98, and 5/05/97. Take a close look at the data:

1. Arrange the data in order from earliest to latest date of sighting.
2. Count the number of days between the earliest and latest arrival dates. This difference is the range of emerging dates for Anchorage.
3. Next figure the median emerging date. Your data are already in order, so you can see on which date half of the records are earlier and half of the records are later. (Because there is an even number of records, you'll need to find the average of the two middle values.)
4. Finally, calculate the mean emerging date. (The mean is the concept most people think of as the "average.") When using calendar dates, this can be tricky. Before reading the example on the worksheet, challenge yourself to think this through!

Now, based on what you know to be the mean date of emergence, what do you think will happen in 2001?

Journaling Questions
1. After calculating the mean, or average date of tulip emergence in Anchorage, what do you predict this year's emergence date will be?
2. If you think it will be different than the mean, what factors this year might lead you to your prediction?"

National Science Education Standards

Science as Inquiry
Develop descriptions, explanations, predictions, and models using evidence. (5-8)

Use math in all aspects of scientific inquiry. (5-8)

National Math Standards

Data Analysis and Probability
Select and use appropriate statistical methods to analyze data.

Develop and evaluate inferences and predictions that are based on data.