AP Statistics : Data
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Example Questions
Example Question #1 : How To Do Logarithmic Transformations
Example Question #1 : How To Do Logarithmic Transformations
What transformation should be done to the data set, with its residual shown below, to linearize the data?
Add 
take the log of the dependent variable
multiply the independent variable by
multiply the dependent variable by a constant k.
Nothing, the data set is already linear
take the log of the dependent 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.
Example Question #1 : Graphing Data
A basketball coach wants to determine if a player's height can be used to predict the number of points that player scores in a season. Before using a statistical test to determine the precise relationship of the variables, the coach wants a visual of the data to see if there is likely to be a relationship. Which of the following should the coach create?
Histogram
Bar chart
Scatterplot
Bell curve
Z-score
Scatterplot
A scatterplot is a diagram that shows the values of two variables and provides a general illustration of the relationship between them.
Example Question #2 : Graphing Data
Based on the scatter plot below, is there a correlation between the 
Yes; negative exponential relationship
Yes; negative linear relationship
No; there is no correlation
Yes; positive linear relationship
Yes; negative linear relationship
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.
Example Question #3 : Graphing Data
Order the correlation coefficients to fit the order of the following graphs (two coefficients will not be used)
The first graph is random scatter, no correlation, the second is perfect linear, corellation 
Example Question #3 : Graphing Data
Find the range of the data in the stem-and-leaf plot.
To find the range, subtract the minimum value from the maximum value
minimum:
maximum:
So,
maximum - minimum =
Example Question #2 : How To Interpret Stemplots
Find the median of the stem and leaf plot.
The median is the middle value of the set in increasing order.
In this set of 11 entries, the median is the 6th entry of the set in increasing order, or 26.
Example Question #3 : How To Interpret Stemplots
How many entries are in this stem and leaf plot?
The number of entries is the number of digits on the right hand side of the column.
Since there are 21 total digits, there are 21 total entris that make up the stem and leaf plot.
Example Question #2 : Graphing Data
What is the interquartile range of the following data set?
This stemplot is read as follows: the stem is the tens digit and each digit in the "leaves" section is a ones digit. Put them together to have a data point.
53, 65, 68, 69, 70, 72, 72, 79, 83, 84, 85, 87, 89, 90, 94
In the particular case there are 15 data points therefore the median is 79. Thus the first quartile is 69 and the third quartile is 87.
Finding the interquartile range is subtracting the first quartile from the 3rd quartile.
Example Question #4 : Graphing Data
Based on the histogram, which of the following sets of values was most common in the sample?
58-64
54-60
62-68
66-72
64-70
62-68
You can see from the histogram that the two most frequent ranges for values are 62-64 and 64-66, with 5 values in each group. And from the answer choices, you should see that only one choice, 62-68, contains both of the high-frequency bars. It also contains the next-highest bar (66-68, with a total of 4), so at 14 total values the range 62-68 has the highest frequency of any of these six-inch-range sets in the choices.
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