Using the $\displaystyle Q1-1.5*IQR$ and $\displaystyle Q3+1.5*IQR$ formulas, we can determine that both the minimum and maximum values of the data set are outliers.

$\displaystyle Q1-1.5*IQR$

$\displaystyle 60-1.5*16=36$

$\displaystyle Q3+1.5*IQR$

$\displaystyle 76+1.5*16=100$

This allows us to determine that there is at least one outlier in the upper side of the data set and at least one outlier in the lower side of the data set. Without any more information, we are not able to determine the exact number of outliers in the entire data set.

Step 1: Recall the definition of an outlier as any value in a data set that is greater than $\displaystyle Q3+1.5*IQR$ or less than $\displaystyle Q1-1.5*IQR$.

Step 2: Calculate the IQR, which is the third quartile minus the first quartile, or $\displaystyle Q3-Q1$. To find $\displaystyle Q1$ and $\displaystyle Q3$, first write the data in ascending order.

$\displaystyle 75, 75, 79, 79, 85, 87, 87, 88, 89, 90, 105$. Then, find the median, which is  $\displaystyle 87$. Next, Find the median of data below $\displaystyle 87$, which is $\displaystyle Q1 = 79$ . Do the same for the data above $\displaystyle 87$ to get $\displaystyle Q3 = 89$. By finding the medians of the lower and upper halves of the data, you are able to find the value, $\displaystyle Q1$ that is greater than 25% of the data and $\displaystyle Q3$, the value greater than 75% of the data. 

Step 3: $\displaystyle Q1-1.5*IQR = 79 - 1.5*10 = 64$. No values less than 64.

$\displaystyle Q3+1.5*IQR= 89 + 1.5*10 = 104$. In the data set, 105 > 104, so it is an outlier.  

An outlier is any data point that falls $\displaystyle 1.5\ast IQR$ above the 3rd quartile and below the first quartile.  The inter-quartile range is $\displaystyle 16-8=8$ and $\displaystyle 1.5\ast8=12$.  The lower bound would be $\displaystyle 8-12=-4$ and the upper bound would be $\displaystyle 16+12=28$.  The only possible answer outside of this range is $\displaystyle 30$.

A residual plot shows the difference between the actual and expected value, or residual. This goes on the y-axis. The plot shows these residuals in relation to the independent variable.

Taking the log of a data set whose residual is nonrandom is effective in increasing the correleation coefficient and results in a more linear relationship.

A scatterplot is a diagram that shows the values of two variables and provides a general illustration of the relationship between them.

The data points follow an overall linear trend, as opposed to being randomly distributed. Though there are a few outliers, there is a general relationship between the two variables.

A line could accurately predict the trend of the data points, suggesting there is a linear correlation. Since the y-values decrease as the x-values increase, the correlation must be negative. We can see that a line connecting the upper-most and lower-most points would have a negative slope.

An exponential relationship would be curved, rather than straight.

The first graph is random scatter, no correlation, the second is perfect linear, corellation $\displaystyle -1$, the last two have fairly strong positive and negative corellations, the student should know that a corellation of $\displaystyle 0.3$ is much weaker than them

To find the range, subtract the minimum value from the maximum value

minimum: $\displaystyle 11$

maximum: $\displaystyle 48$

So,

maximum - minimum = $\displaystyle 48-11 = 37$