Randall set a personal goal to exercise at least 20 minutes for most of the days during the last two months. He recorded his exercise time each day. Use the box and whisker plot of his data to determine whether he reached his goal. Explain.

Question

gabylovesyou · Answer

attachment

jim_thompson5910 · Answer

Define "most of the days". Do you mean "more than half of the days of the last two months"?

gabylovesyou · Answer

idk thats how it comes out :S

jim_thompson5910 · Answer

hmm that could be what it means, I'll assume that

jim_thompson5910 · Answer

Looking at this box and whisker plot, where is the median?

gabylovesyou · Answer

20?

jim_thompson5910 · Answer

good

jim_thompson5910 · Answer

what do we know about the median in general?

gabylovesyou · Answer

.................................

jim_thompson5910 · Answer

If I told you to find the median of the set {1,5,7,9,11}, what would the median be?

gabylovesyou · Answer

the middle number in this case is 7

jim_thompson5910 · Answer

good, so the median lies at the exact halfway point of any data set

jim_thompson5910 · Answer

this means that the data set is cut into two equal halves (that don't include the median)

jim_thompson5910 · Answer

so if we know that 20 is the median, then we can say that 50% of the data points are below the median and 50% of the points are above the median

gabylovesyou · Answer

yes "D

gabylovesyou · Answer

so did he reach his goal?

gabylovesyou · Answer

Im confused :S

jim_thompson5910 · Answer

one sec, I'm trying to list out a possible data set to confirm my answer

gabylovesyou · Answer

ok :D

gabylovesyou · Answer

ohhhh ok Thank you! And don't worry :D

jim_thompson5910 · Answer

alright you're welcome

jim_thompson5910 · Answer

oh bugger, found a glitch in my logic...but the answer is still the same. He doesn't reach his goal (the glitch is in the second piece of what I wrote, the first piece should be fine)

jim_thompson5910 · Answer

I'll write the first part again


if we have one data value of 20 (and the rest of the data values are all something else), then this will mean that the target data points that we want will lie above the median and will take up half of the box and whisker plot


But if that's the case, then it won't be "most of the days" since it will approximately be composed of half of the days. 


If we don't have a value of 20 (and we have something like 18 and 22 in the middle), then we run into the same problem. About only half of the targeted times are reached, which is far short of the goal of "most days"

gabylovesyou · Answer

ok :D thanks

jim_thompson5910 · Answer

yw