Question 8·Medium·One-Variable Data Distributions; Measures of Center and Spread
The dot plots show the quiz scores (in points) for two different classes.
Which choice best compares the standard deviations of the quiz scores for these two classes?
When comparing standard deviations from dot plots, focus on spread, not the number of dots. First check whether the distributions are centered at about the same value; if they are, the plot with dots farther from that center (more extreme low and high values) has the larger standard deviation. The more tightly clustered plot has the smaller standard deviation.
Hints
Look for the center
Estimate the score each dot plot is centered around (where the dots would balance).
Compare distances from the center
Notice which class has dots farther away from the center value, especially at the extremes.
Connect spread to standard deviation
Remember: a distribution with values more spread out from its mean has a larger standard deviation.
Desmos Guide
Enter the Class R scores as a list
From the dot plot, create a list with repeats for each dot, such as:
R={71,72,72,72,73,73,74,74,74,75}
Enter the Class S scores as a list
From the dot plot, create a list with repeats for each dot, such as:
S={65,68,68,73,73,73,73,78,78,81}
Compute and compare standard deviations
Type stdev(R) and stdev(S).
Compare the two values and choose the answer choice that matches which class has the smaller standard deviation.
Step-by-step Explanation
Identify the center of each distribution
In Class R, the dots cluster around (many scores at , , and ).
In Class S, the dots also balance around (there are dots equally far below and above , such as and , and and ). This indicates the mean is the same for both classes (centered at ).
Compare how spread out the scores are from the center
For Class R, all scores lie between and , so the farthest any score is from is points.
For Class S, scores extend from to , so some scores are as far as points from .
Because standard deviation measures the typical distance from the mean, the class with values farther from the mean has the larger standard deviation.
Select the matching comparison
Therefore, Class S has the larger standard deviation, so the standard deviation for Class R is less than the standard deviation for Class S.