Question

each of the dot plots shown represents the number of glue sticks brought in by each student for two classes, class a and class b. which statement best compares the standard deviations of the numbers of glue sticks brought in by each student for these two classes?
a) the standard deviation of the number of glue sticks brought in by each student for class a is less than the standard deviation of the number of glue sticks brought in by each student for class b.
b) the standard deviation of the number of glue sticks brought in by each student for class a is equal to the standard deviation of the number of glue sticks brought in by each student for class b.
c) the standard deviation of the number of glue sticks brought in by each student for class a is greater than the standard deviation of the number of glue sticks brought in by each student for class b.
d) there is not enough information to compare these standard deviations.
(class a dot plot: values 1 to 7 with dots increasing; class b dot plot: values 14 to 20 with dots increasing)

Explanation:

Step1: Analyze Dot Plot Shapes

Class A and Class B dot plots have the same distribution shape (symmetric, increasing then decreasing counts). Class B's data is a shift (13 units right) of Class A's (1 - 7 vs 14 - 20, since \(14 = 1 + 13\), \(20 = 7 + 13\)).

Step2: Recall Standard Deviation Property

Standard deviation measures spread (variability), not center. A shift (adding/subtracting a constant) doesn't change the spread. So the standard deviations should be equal.

Answer:

B) The standard deviation of the number of glue sticks brought in by each student for class A is equal to the standard deviation of the number of glue sticks brought in by each student for class B.