hey it's Kaeleigh this lesson is about different things we can measure in
statistics it will be helpful if you've already completed the lesson called
statistical questions and dot plots alright let's get started
in the lesson statistical questions and dot plots we had asked the question how
tall are basketball players and we collected data and made a dot plot to
help us analyze our data by looking at the peaks and clusters on our dot plot
we were able to come up with a general answer to our question we said most
basketball players are about 80 inches but what if we want a more specific
answer a measure of center is a single number used to describe a set of data
for example let's say we have five bags of candy but the bags don't have the
same number of candy pieces in each bag we want to know how many pieces of candy
come in a bag if we count the pieces in each bag our data will look like 6 4 3 5
and 7 so now that we've collected our data we need to organize it remember we
do that by ordering our data from least to greatest now we can always make a dot
plot to help us visualize our data or we can use some math instead of coming up
with a general answer to our statistical question we can use a measure of center
calculation to find a single number that will describe our data measures of
center include the mean and the median let's start with the mean the mean also
called the average of a set of data is the sum of all the data values added
together and then divided by the total number of data values in the set so
let's find the mean of our data set this will answer our statistical question how
many pieces of candy on average are in a bag so first we write the sum of our
data in the numerator and we divide by the number of data values so on top we
have 3 plus 4 plus 5 plus 6 seven and on the bottom we have five
because we have five numbers in our data set so in the numerator our Sun comes
out to be 25 and 25 divided by five is five so we can say the mean or the
average is five a good way to check your work is to keep these facts about the
mean in mind since the mean represents an average value with a debt within a
data set the mean can never be larger than the largest value in the data set
this is because all the other numbers in the data set are smaller and they bring
the average down or lower than the greatest value and the opposite is also
true the mean can never be less than the
least number in the data set since all the other data values are greater they
bring the average up now let's talk about the median the median represents
the middle value of an ordered data set for the median it is super important
that you have ordered your data in numerical order like least to greatest
let's calculate the median of our data set I do this by systematically crossing
out the outside numbers and working my way into the center like this and the
middle value is the median so for our data we can say the median is five but
what if I had six data values in my set now when I work my way into the middle I
find two values so now to find the median value of my data set I have to
find the mean of these two middle values so I put the sum on the top five plus
six and two in the bottom since I'm only finding the average of these two data
values so I have eleven over two or five and a half so for this data set my
median would be five and a half anytime a dad is that has an even number of
values you will need to find the AB of those middle numbers to find the
median now there's another important thing to look at when we are analyzing
data the mode is the data value that occurs the most frequently in the data
set when we were looking at dot plots the peak would represent the mode for
this data set the mode is 81 because it appears four times in the data which is
more than any other data value appears if we look at our original data from the
five bags of candy we would say there is no mode since then of the diet of values
appear more than once but in this data set when I have six bags of candies we
do have a mode the data value six occurs twice which is more than any of the
other data values but a data set can have more than one mode if this was our
data we would have two modes both 4 & 6 occur more than the other data values a
data set can have multiple modes as long as they occur with the same frequency or
the same amount of times
now that we have looked at the measures of center let's talk about the measure
of variability the measure of variability is a single number to
describe the spread of a data set when we look at dot plots we think of the
spread of data as going from the smallest number to the largest number
but we can calculate a single number to tell us how much spread there really is
the range is a measure of spread it is the difference between the greatest data
value and the least data value if we look at our data from the candy bags we
find the range we take our largest data value seven and we subtract our smallest
data value three so we get seven minus three equals four the range of our data
is four so let's answer our question how many pieces of candy are in a bag and we
can say the average number of pieces per bag is five great work learning the
arithmetic of statistics practice what you've learned by playing the online
games and quizzes have fun and remember to always be clever