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CCSS.Math: , , , , An ecologist surveys the
age of about 100 trees in a local forest. He uses a box-and-whisker plot
to map his data shown below. What is the range of tree
ages that he surveyed? What is the median age
of a tree in the forest? So first of all, let's
make sure we understand what this box-and-whisker
plot is even about. This is really a way of
seeing the spread of all of the different data points,
which are the age of the trees, and to also give
other information like, what is the median? And where do most of the
ages of the trees sit? So this whisker part, so you
could see this black part is a whisker, this
is the box, and then this is another whisker
right over here. The whiskers tell us essentially
the spread of all of the data. So it says the lowest to
data point in this sample is an eight-year-old tree. I'm assuming that this axis
down here is in the years. And it says at the highest--
the oldest tree right over here is 50 years. So if we want the
range-- and when we think of range in a
statistics point of view we're thinking of
the highest data point minus the
lowest data point. So it's going to be 50 minus 8. So we have a range of 42. So that's what the
whiskers tell us. It tells us that everything
falls between 8 and 50 years, including 8 years and 50 years. Now what the box does,
the box starts at-- well, let me explain it
to you this way. This line right over
here, this is the median. And so half of
the ages are going to be less than this median. We see right over
here the median is 21. So this box-and-whiskers
plot tells us that half of the ages of
the trees are less than 21 and half are older than 21. And then these endpoints
right over here, these are the medians for
each of those sections. So this is the median
for all the trees that are less than
the real median or less than the main median. So this is in the middle
of all of the ages of trees that are less than 21. This is the middle
age for all the trees that are greater than
21 or older than 21. And so we're actually
splitting all of the data into four groups. This we would call
the first quartile. So I'll call it Q1 for
our first quartile. Maybe I'll do 1Q. This is the first quartile. Roughly a fourth of the
tree, because the way you calculate it,
sometimes a tree ends up in one point or another,
about a fourth of the trees end up here. A fourth of the trees
are between 14 and 21. A fourth are between 21
and it looks like 33. And then a fourth
are in this quartile. So we call this the first
quartile, the second quartile, the third quartile, and
the fourth quartile. So to answer the question,
we already did the range. There's a 42-year spread between
the oldest and the youngest tree. And then the median age of a
tree in the forest is at 21. So even though you might have
trees that are as old as 50, the median of the
forest is actually closer to the lower end of
our entire spectrum of all of the ages. So if you view median as your
central tendency measurement, it's only at 21 years. And you can even see it. It's closer to the
left of the box and closer to the end
of the left whisker than the end of
the right whisker.