A standard deviation measures how spread out scores are around their mean. For two dot plots on the same scale, find each center, then compare all the dots, not only the tallest stacks. Enter one score per dot in Desmos lists to check the comparison. A tall stack at the center can hide scores that sit much farther away.
Hints
- Hint 1
The mean is the average score. When dots have matching counts at equal distances on either side of a score, that score is the mean. Where do the dots balance in each plot?
- Hint 2
Each dot represents one score, so a stack of three dots needs three entries in a Desmos list. After entering both classes, compare their standard deviations. Don't leave out repeated scores.
Step-by-step
Read the centers, then check the spread in Desmos
Step 1Find each class's center
Both plots balance around : in Class R, pairs with ; in Class S, pairs with . The other dots balance in matching counts too. So each class has a mean, or average score, of . The same mean doesn't guarantee the same spread.
- Step 2
Find Class R's standard deviation
Type , then . Each dot is one score, so repeat scores to match the stacks. Desmos shows about points for R's standard deviation.
- Step 3
Find Class S's standard deviation and compare
Type , then . Desmos shows about , greater than . The four scores at don't settle the comparison: S also has six scores or points from the mean, while every R score is within points. Standard deviation accounts for every score's distance from the mean. So Class R's standard deviation is less than Class S's. Choice A.