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When
Do Monarchs Normally Arrive in Your Home Town?
Calcluating the Range, Median and Mean Arrival Dates
...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
|
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| 2
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| 3
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| 4
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| 5
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| 6
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| 7
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| 8
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| 9
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| 10
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| 11
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| 12
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| 13
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| 14
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| 15
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| 16
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| 17
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| 18
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| 19
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| 20
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| 21
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| 22
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| 23
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| 24
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| 25
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| 26
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| 27
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| 28
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| 29
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| 30
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| 31
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| 32
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| 33
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| 34
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| 35
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National
Science Education Standards
- Use math
in all aspects of scientific inquiry.
National
Math Standards
- Select and use appropriate statistical methods to analyze
data.
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2004-2007 Journey North. All Rights Reserved.
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