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Hello my name is Beth Dixon and this is part five of the video series on frequency distribution and
histograms and again thank you to Vicki Borlaug for allowing us to use her PowerPoint
and we're picking up right where we left off we're going to look in an example that will require us
to create our own classes from the directions given
first we need to find the highest and lowest links of parts from our data
we have of list of data that includes links of parts
and we need to find the lowest and the highest data values when creating our classes
we need to first find the lowest value in our data that will be 125.5
and the highest data value which will be 151.6 inches
when creating our classes the lowest class must begin at or below the 125.5 and the highest class must end
at or above 151.6 those are important things to remember
part B ask us to build classes using 125.0 for the first lower class limit
and 4.5 for the class width with those two pieces of information we can build a class-- a set of classes
we like numbers ending in five and zero because they're easier to count with but we
don't always use those numbers so we know that the first....
we know what the first lower limit is -- it told us so we'll use
125.0 for the lower class -- first lower class limit
now how can I use this number to build the rest of our classes
remember we also know our class width
with that information we can to find the lower last class limit
of class two
using the 4.5 for the class width
and adding it to the 125.0
that would give us 129.5 and that will be the next lower class limit
then we can proceed and add 4.5 to 129.5
to give us the next lower class limit of 134.0
adding 4.5 again to 134.0
we will get 138.5
to 138.5 we'll add 4.5
that gives us a lower class limit
of 143.0
to 143.0 we will add 4.5 the class width
and that will give us the next lower class limit of 147.5
that is not greater than 151.6 so we still need another class limit so we'll add 4.5 again
to 147.5 and that gives us 152.0
since 152 is greater than 151.6
we're finished
that is how we know when to stop our classes or when we have enough classes
we knew that 125 was a good place to start because it is lower than this first -- our lowest
class-- are lowest data item not our lowest class but our lowest data item and we know that
we need to go up for this class at 147.5 and 152 we don't need to start with this one because it's above the 151.6
so we can -----
since its higher
since the highest value is 151.6 we do not need a class that starts at 152 so
we can mark that out but notice we don't want to mark it out where we can't see it
we want to still be able to read it because it may be useful to us (hint hint) in the next slide
ok now the raw data has 1 decimal place
so we want a
upper class limit is 0.1 less than the next lower class limit so we want a 0.1
gap between the classes if you haven't watched the previous videos on this power point then we covered this in more detail their but
that's the gap that we need so that no data fall between two classes without making the gap smaller than it needs to be
now we can proceed to make
and create the upper class limits by taking one tenth from 129.5 and getting 129.4
and proceed to do that for every number along the list and I'm not going to read those numbers out to you
you can do so and see those for yourself
but as you get to the last one we take 147.5 and subtract one tenth and and we get 147.4 that will give us 152
and that's where we can use the 152 to create this last upper class limit even though it's not going to be our--- a class in itself we can use it
to create that upper class limit of our last class
and that's the way to create one way to create upper class limits
the raw data oops
now another way
to do this is to find the first upper class limit the same way as we did before
of 129.4 but instead of doing that 0.1 subtracting is to go back and use the class width of 4.5 and add 4.5
to each previous upper class limit to create those
upper class limits all the way down either way that we do that is fine and we still end up with the same answers
and we have our classes
now are ready to do part C which ask us to construct a frequency distribution
a relative frequency distribution a percent frequency distribution
and a histogram
we have done this in previous-- two previous examples so I'm going to cover this relatively quickly in this video
first we want to do the columns and label those
and since we have are classes we can do our tally
TADA the tally is done
we can turn the tally marks into frequency
5, 1, 5, 1 4, 2
then we can turn the frequency
into relative frequency
remember that relative frequency takes the frequency and compares by division to the total
number of the data set so for the first class we have five divided by eighteen which gives us
0.2788 we will want to take this out four decimal places
um I will explain more as we go on as to why we like to do that and we get to the percent distribution or the percent frequency
the next one will be 1/18 which equals 0.0556
5/18 gives us 0.2778
1/18 equals 0.0556
4/18 is equal to 0.2222
and 2/18 which is equal to 0.1111
and unlike previous examples these were repeating non ending decimal so we rounded to the 4 decimal places
now we're ready to complete that percent frequency distribution column to do this we want to change the relative frequency decimal to a
percent by moving our decimals two places to the right we want to have two places after the decimal for our percent accuracy
and so we need four decimals
four decimal places in our decimals which is why we rounded your rounding may vary from teacher
to teacher so please check with your teacher in our case that then gives us 27.78%
5.56%, 27.78%, 5.56%, 22.22%, and 11.11%
and that completes the percent frequency distribution
now let's draw our histogram place your axis and notice the labels the horizontal label axis-
excuse me - the horizontal axis is labeled with classes
remember that a teacher may do this differently so please check with him or her the vertical axis is labeled with the frequency our highest
frequency is five so we need something as large or larger than five
and because its a relatively small number we'll count by one's next draw the rectangles and bars for each class the first class has a
frequency of five so the height of the first bar will be five
and will look like this the second one has a height and frequency of one so that bar has a height
of one
then a height of five for the next bar then one then four then two
notice that each how each histogram in this series has a different shape
and we'll talk about that in part six I've already surpassed my 10 minute mark that I am supposed to be aiming for and as much as I
would like to continue and talk about shapes now we will stop here
and even though I said it was going to be a five part series it turns out that
this is going to be a six part series please watch the sixth part as well because are some interesting things about the shape of histograms
on part six
thank you for watching and I hope this
video was helpful in knowing how to create the classes
All spelling errors are mine...please no comments or laughter. Beth Dixon