Yesterday in class we started discussing Histograms and Stemplots.
Histograms
Histograms display the frequency of a variable.
The x-axis of a histogram displays the amount of variables. Histograms use bins to group data on an x-axis.
In this case, our individuals (or objects that are being described in a data set) are the black cherry trees. This histogram is looking at the height of the cherry trees, otherwise known as a variable, or
a characteristic of an individual.
Instead of having a bar graph, where each individual gets a bar like the graph below, histograms
group the individuals into categories. For example, black cherry trees with heights of 61ft, 62ft and 64ft would be grouped in the "60-64.9ft" bin on the graph.
EXAMPLE OF A BAR GRAPH:
We use bins because we can fit more data onto a histogram that way. If we created a bar graph of the heights of cherry trees it would need an enormous x-axis to fit all of our data.
The y-axis of a histogram represents the frequency of the variables.
So back to our cherry tree example, if you look at the graph, there were 10 cherry trees that were between 75-79.9 feet tall. It's pretty straightforward.
We then looked at the shape of a histogram.
If the histogram has a symmetric "hill" (5th period whaddup) the data is awesome, and nothing
seems to be wrong with it.
If the histogram has a
longer tail of information to the right, then the data is skewed to the right.
If the histogram has a longer tail of information to the left, the data is skewed to the left.
and finally...Outliers are distinct measurements that are separated from the rest of the data.
I found a website that lets you practice creating a histogram, for those of you still confused. Enjoy!
Stemplots
- make data easily presentable
- make plotting decimals easier
- you can display the exact measurement of each individual
A stemplot has two sections called the stem and leaves instead of a y-axis and x-axis.
To read this graph you would read 3|9 as 39 points were scored in a game.
4|0 1 5 7 7 7 9 reads as 40, 41 45... etc.
When making a stemplot the stems must be arranged vertically by numerical order from smallest to largest and the leaves must be arranged horizontally in order from smallest to largest in each stem category.
Leaves can ONLY BE ONE DIGIT. So if you wanted to represent a number like 356 you would make you stem 35 and your leaf 6. It would end up looking like this: 35|6
We also discussed finding the mean and median for the stemplots.
To find the mean (or average) all all of the individuals up and divide by the # of individuals.
We used the symbol of x̄ to represent the mean. The Σ (sigma) means "the sum of"
x̄ =(1/n)Σ
or basically: mean= (x1+x2+x3...)/(n)
The median is represented as m=(n+1)/(2) or the total number of individuals plus one, divide by two.
When you're finding the median on a stemplot you take the total number of individuals on a stemplot (if we're using the above stemplot that's 12) and apply it to the formula getting us the number 6.5. That is not our median. To find our actual median, we have to find individuals 6 and 7 on our stemplot. So on our graph above individual six has a value of 47, and individual seven also has a value of 47. Now we take the average of those two numbers, which ends up also being 47, and now you have the actual median.
It's a bit confusing, I know. But here's a link for extra clarification!
That's the gist of what we learned yesterday. It's a bit long, but hopefully it helps. Can't wait for Kenan's amazing scribe post....
Madison
P.s. I don't know why some of my words hilighted....sorry...!
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