A median is the middle value after the data are ordered, and a dot plot puts them in order from left to right. With an odd number of dots, count to the middle one, including every dot in a stack. If every cyclist adds the same distance, the middle cyclist stays in the middle; don't stop at the distance shown on the plot.
Hints
- Hint 1
The median is the middle value in order. With an odd number of cyclists, find the dot that has the same number of dots on each side.
- Hint 2
A stack means more than one cyclist rode that distance. Count each dot in the stack as a separate cyclist when you look for the middle position.
- Hint 3
Adding the same distance to every cyclist keeps their order the same. Once you find the middle distance shown, how much does that cyclist plan to add?
Step-by-step
Count the middle dot, then shift it
Step 1Find the middle position
No Desmos needed. Read the middle dot from the plot. The median is the middle value in order. With cyclists, four are on each side, so the fifth dot is the median.
- Step 2
Read the fifth dot
The dots above , , and fill positions through . Both dots above count: they fill positions and . So the median distance shown is miles.
- Step 3
Find next month's median
Because each cyclist adds miles, no one changes position in the ordered list. The fifth distance becomes
Adding the same amount to every value adds it to the median. The median next month is miles. Choice B.
Lessons that teach this
- SAT Data AnalysisBeginnerCoreFind and interpret center
- SAT Data AnalysisIntermediateCoreRead distributions and data displays
- SAT Data AnalysisIntermediateAnalyze changed data and outliers
- DesmosIntermediateCoreMean, median, and frequency tables in Desmos
- DesmosIntermediateCoreSpread, standard deviation, and box plots in Desmos