Two dot plots can have matching stacks but different horizontal scales. Standard deviation measures spread around each club’s mean in minutes, so compare the values at matching stacks rather than the plots’ drawn widths. Multiplying every value by a factor multiplies the standard deviation by that factor’s size. Matching dot patterns don’t always mean equal spread.
Hints
- Hint 1
In a dot plot, each dot represents one student, and a stack’s height counts how many students practiced that number of minutes. Compare the stack heights from left to right. What stays the same?
- Hint 2
The horizontal scale tells you how many minutes each tick represents. Compare with , then with . What single rule changes each Club P time into its matching Club Q time?
- Hint 3
A standard deviation measures spread around the mean. If every time doubles, the mean doubles too, so every distance from the mean doubles. What does that do to the standard deviation?
Step-by-step
Compare the scales of the dot plots
Step 1Read the values and stack heights
No Desmos needed. The dot plots give exact values, and a scale rule settles the comparison. Club P’s ticks are minutes; Club Q’s are minutes. Both plots have the same stack heights, , from left to right. So each stack represents the same number of students in the two clubs.
- Step 2
Match the practice times
Double each Club P tick to get the corresponding Club Q tick:
Because the stacks match, every dot in Club Q can be paired with a Club P dot whose practice time is half as long. Don’t judge spread by the plots’ drawn widths: one tick is minute in P but minutes in Q.
- Step 3
Apply the standard deviation rule
A standard deviation measures how spread out times are around their club’s mean. Doubling every time doubles the mean and every distance from it, so
Club P’s times aren’t all identical, so its standard deviation is greater than . Its standard deviation is less than Club Q’s. Choice A.