Question 46·Easy·One-Variable Data Distributions; Measures of Center and Spread
The dot plot shows the number of miles cycled by each of 9 cyclists during a training ride.
Next month, each cyclist plans to cycle 2 more miles than shown.
Which choice is the median number of miles cycled next month?
For median questions, first determine whether there are an odd or even number of data points to know what “middle” means. If every data value is increased by the same amount, the median increases by that amount too, so you can find the original median and then apply the shift.
Hints
Locate the median position
Because there are 9 data values, the median is the 5th value when the data are ordered from least to greatest.
Read the current median from the plot
Count dots from the smallest miles value to find which miles value the 5th dot lands on.
Use the effect of adding a constant
If you add 2 to every data value, the median increases by 2 as well.
Desmos Guide
Enter the data in Desmos
Enter a list matching the dots, for example: L=[12,13,14,15,15,16,17,18,19].
Find the current median, then add 2
Type median(L) to get the current median, then add 2 to that result to get next month’s median.
Step-by-step Explanation
Find the current median from the dot plot
There are 9 data points, so the median is the 5th value when the distances are ordered from least to greatest.
Counting the dots from left to right, the 5th dot is at 15 miles, so the current median is 15 miles.
Adjust the median for next month
If each cyclist rides 2 more miles, every value in the data set increases by 2, so the median also increases by 2.
The median next month is miles, so the correct choice is 17.