Question 29·Medium·One-Variable Data Distributions; Measures of Center and Spread
Each dot plot shows the number of pages read by each student in two book clubs during the same weekend.
Which choice best describes how the mean and the standard deviation of the numbers of pages read for Book Club A compare with those for Book Club B?
When two dot plots have the same shape but one is shifted left or right, treat it as “adding a constant” to every value. A horizontal shift changes the mean by the shift amount but does not change the standard deviation, because the spread around the mean is unchanged. So first identify the shift amount from the axis labels, then apply these center-and-spread rules.
Hints
Compare matching dot stacks
Look for a pages-read value in Book Club A and find where the same number of dots appears in Book Club B.
Determine the horizontal shift
How many pages to the right is Book Club B compared with Book Club A? Check the leftmost dots (or any matching stack).
Recall what a shift does
Think about what happens to the mean and the standard deviation when the same number is added to every data value.
Desmos Guide
Enter the data for Book Club A as a list
In Desmos, create a list for Book Club A by repeating each pages-read value the number of times it appears as dots. For example, if there are 4 dots at 5 pages, include four 5s in the list.
Enter the data for Book Club B as a list
Create a second list for Book Club B the same way, using the dot plot for Book Club B.
Compare the means and standard deviations
Compute mean(listA) and mean(listB), and compute stdev(listA) and stdev(listB).
Use the results to pick the choice that matches the mean difference and whether the standard deviations are the same or different.
Step-by-step Explanation
Identify the shift between the distributions
Compare matching stacks of dots: for example, Book Club A has 1 dot at 3 pages and Book Club B has 1 dot at 13 pages; Book Club A has 4 dots at 5 pages and Book Club B has 4 dots at 15 pages.
Each value in Book Club B is exactly 10 more than the corresponding value in Book Club A.
Use how adding a constant affects center and spread
Adding the same constant to every data value:
- increases the mean by that constant
- does not change the standard deviation, because all values are still the same distances from the mean as before (just shifted together).
Choose the statement that matches
So, Book Club B’s mean is 10 greater than Book Club A’s mean, and the standard deviations are equal.
Therefore, the correct choice is: The mean for Book Club B is 10 greater than the mean for Book Club A, and the standard deviations are equal.