Solutions to Quiz 01

Notes:

1. If you had trouble understanding the definition of the percentile, think of the water-filling analogy again. The 20th percentile, for example, is the water level corresponding to “20% full”.
2. What I laid out here are recommended solutions. There could be other solutions.
3. Update on 2025-09-13: Corrected portions indicated in bold. Thank you to Cendric Hou for pointing out the mistakes!

For V26:

1. It is hard to tell if all songs would fit although we might be tempted to say that 3.5*500 = 1750 MB < 2000 MB. It depends on the sizes of the music files beyond the median. If you have a lot of very long songs (say classic, orchestral, or jazz pieces), then your songs in total might actually exceed 2000 MB in size.

   • Note: If you were tempted to say 3.5*500 = 1750 MB < 2000 MB, then you are thinking that 3.5 MB is the mean and that the mean happens to be equal to the median (which is not guaranteed).

2. The total count is 65.

   • The median can be found in the interval 16-19 because (3+14)/65 \(\approx\) 0.26 and (3+14+23)/65 \(\approx\) 0.62.
   • The 25th percentile can be found in the interval 13-16 because 3/65 \(\approx\) 0.04 and (3+14)/65 \(\approx\) 0.26.
   • The 75th percentile can be found in the interval 19-22 because (3+14+23)/65 \(\approx\) 0.62 and (3+14+23+12)/65 = 0.8.
   • So a rough value for the median would be some number between 16 to 19. A rough value for the IQR would be somewhere between 19-16 = 3 and 22-13 = 9.

For V27:

1. It is hard to tell if all pictures would fit although we might be tempted to say that 2.5*500 = 1250 MB < 1500 MB. It depends on the sizes of the pictures beyond the median. If you have a lot of high resolution pictures (think about how many times you have to delete pictures on your phone), then your pictures in total might actually exceed 1500 MB in size.

   • Note: If you were tempted to say 3.5*500 = 1750 MB < 2000 MB, then you are thinking that 3.5 MB is the mean and that the mean happens to be equal to the median (which is not guaranteed).

2. The total count is.

   • The median can be found in the interval 5000-6000 because (6+8+14)/80 = 0.35 and (6+8+14+18)/80 = 0.575.
   • The 25th percentile can be found in the interval 4000-5000 because (6+8)/80 = 0.175 and (6+8+14)/80 = 0.35.
   • The 75th percentile can be found in the interval 6000-7000 because (6+8+14+18)/80 = 0.575 and (6+8+14+18+17)/80 = 0.7875.
   • So a rough value for the median would be some number between 5000 to 6000. A rough value for the IQR would be somewhere between 6000-5000 = 1000 and 7000-4000 = 3000.