When Do Monarchs Normally Arrive in Your Home Town?
Calcluating the Range, Median and Mean Arrival Dates

 Try This! See Example from Arkansas

...but first some mathematical terms:

• 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.

Step 1) Organize the data
On the chart below, record the dates "first spring monarchs" were sighted. In the column to the right, determine which year monarchs were seen 1st, 2nd, 3rd, etc.

 First Spring Monarch in My Home Town Date of 1st Sighting Order (1st, 2nd, etc) . . . . . . . . . . . . . .

Step 2) Determine the Median
Of the years above, which is the median? The median is the date at which half of the dates are earlier and half of the dates are later.

• The median arrival date is ______.

Step 3) Determine the Range
Find the earliest and latest date monarchs were first seen. Then count the number of days between the earliest and latest sighting over the years to determine the range.

• The earliest date is ________.
• The latest date is ________.
• The range is ______ days.

Step 4) Calculate the Mean
It can be tricky to calculate the mean when the dates span across different months, as they do in this example. You need to assign each date a value. The number line below is a helpful tool for giving values to calendar dates.

• Get ready to put all of the arrival dates in order on the number line below. The earliest arrival date will have a value of 1. Put the earliest date beside the value of 1.
• In the middle column, fill in the calendar date associated with each value.
• Add the rest of the arrival dates to the number line.
• Now calculate the mean. Add all of the values for all the total number of dates, then divide by the total number of dates.
• Find the value on the number line and notice the associated date. This is the mean arrival date.

 Value Calendar Date Date of First Sighting 1 . . 2 . . 3 . . 4 . . 5 . 6 . . 7 . . 8 . . 9 . . 10 . . 11 . . 12 . . 13 . . 14 . 15 . . 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

National Science Education Standards

• Use math in all aspects of scientific inquiry.

National Math Standards

• Select and use appropriate statistical methods to analyze data.