Question 551·Medium·Math

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The table below shows the number of text messages each of the nine employees at a small company sent on an average workday in both January and February.

Employee	January	February
A	45	50
B	60	58
C	39	41
D	52	55
E	48	47
F	63	67
G	59	62
H	42	45
I	56	54

By how many messages was the median number of messages sent per day in February greater than the median number sent per day in January?

Your answer

A median is the middle value after the data are sorted. The cue here is two columns of unsorted counts and a question asking how much greater one median is. Enter each month's values as a separate Desmos list, find both medians, then subtract in the order the question gives. Comparing one employee's January and February entries instead can miss both middle values.

Hints

Hint 1
With nine values, the median is the fifth value after sorting, not the value in the fifth row of the table. Which nine numbers belong in the January list?
Hint 2
Desmos's median function sorts a list for you. Give the February values their own list so you can find that month's middle independently of January's. Which month's median should come first in the subtraction?

Step-by-step

Find each month's median in Desmos
Step 1
Find January's middle value
A median is the middle value after ordering the numbers. With nine values in each month, use the fifth value of each month separately, not the fifth employee's row. Type $a=[45,60,39,52,48,63,59,42,56]$ and $\operatorname{median}(a)$ . Desmos shows $52$ . In order, January's values are $39,42,45,48,52,56,59,60,63$ , so $52$ is fifth.
Step 2
Find February's middle value
Type February's values as a separate list, $b=[50,58,41,55,47,67,62,45,54]$ , then type $\operatorname{median}(b)$ . Desmos shows $54$ . In order, February's values are $41,45,47,50,54,55,58,62,67$ , so the median is again the fifth value. The employees' rows don't stay in numerical order.
Step 3
Find how much greater February's median was
Type $\operatorname{median}(b)-\operatorname{median}(a)$ to subtract January from February, as “greater than” asks. Desmos prints $2$ , so February's median was $2$ messages per day greater. Grid in 2.

Question 551·Medium·Math

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