If most of the data is on the left or right of the histogram, we say that the distribution is skewed. If the data is distributed evenly, then we say that it is symmetric.
B
b
Which numbers are better to describe skewed data sets?
A
a
See solution.
B
b
See solution.
Practice makes perfect
a
We are asked to create a histogram for each data set using a graphing calculator. Let's start with the Peter's Articles data set. We first have to enter the values into a list. Push STAT, choose Edit, and then enter the values in the first column.
Having entered the values, we have to instruct the calculator that we want to graph a histogram. Push 2nd and Y=, and choose one of the plots in the list. Make sure you turn the plot ON, set the Type to histogram, and assign L1 as XList.
To graph the histogram, push GRAPH. Note that you may need to change the window size so that it spans the length of the histogram. To do so, push WINDOW.
Looking at the histogram, we can see that the majority of data are on the left. Because of this, we can say that Peter's Articles data set has a positively skeweddistribution. Now, to graph the Paul's Articles data let's push STAT again and choose Edit, and then enter the values in the second column.
Having entered the values, let's push 2nd and Y=, and choose the same plot as we did last time. This time however, make sure that you assign L2 as XList.
You may need to change the window size. To do so, push WINDOW. Then, press GRAPH to graph the histogram.
Paul's Article data looks evenly distributed. Thus, we can say that this is a symmetric distribution.
b
In Part A we found that the distribution of the Peter's data set is positively skewed. Therefore, the mean and the standard deviation will not represent the data very well. Instead, to compare the data sets we will use the five-number summaries. To do this, push STAT and scroll right until you reach CALC.
Choose the first option, 1-Var Stats. Select L1, press Calculate, and scroll down to find Peter's data five-number summary by using 1-Var Stats.
Now we can do the same, but selecting L2 to find Paul's five-number summary.
Let's summarize our results in a table. We will add the range of the data, which is the difference between the maximum and the minimum of the data.
Peter
Paul
Minimum
3
19
Quartile 1
18
34
Median
22
42.5
Quartile 3
33
51
Maximum
67
72
Range
67-3=64
72-19=53
Paul's minimum is 19 and Peter's lower quartile is 18. This means that Paul's least liked article is more popular than 25 % of Peter's articles. Also, Paul's lower quartile is 34 and Peter's higher quartile is 33. This means that 75 % Paul's articles have more likes than 75 % of Peter's articles. Paul's articles are more popular.
