Dot plots of the same objects measured in different units call for a standard deviation scaling rule. Match the dots to find how every measurement changes, then apply that change to their distances from the mean. Don't assume the standard deviations have the same numerical value because the rods themselves haven't changed.
Hints
- Hint 1
A dot plot shows each measurement as a dot, including repeats. Match the two dots at centimeters with the two at millimeters. What multiplication connects the matching measurements?
- Hint 2
The mean is the average. The dots balance around centimeters in the top plot and millimeters in the bottom plot. Compare how far a matching pair of dots sits from those means.
Step-by-step
Scale the distances from the mean
Step 1Match the measurements
No Desmos needed. The unit change gives the spread comparison directly. The two dots at centimeters match the two at millimeters, and the pattern continues across both plots. Since centimeter equals millimeters, every rod's numerical length is multiplied by in Lab M's plot.
- Step 2
Find each plot's center
In Lab C's plot, the dots at and balance, as do those at and ; two more sit at . So the mean, or average, is centimeters. The matching pattern in Lab M's plot balances around millimeters.
- Step 3
Compare spread, not physical length
A standard deviation measures spread around the mean. For example, centimeters is centimeters below , while millimeters is millimeters below . Multiplying every measurement by multiplies every distance from its mean, and its standard deviation, by . So Lab M's standard deviation is times Lab C's. Choice A.