Posted by **Jen** on Sunday, July 31, 2011 at 10:56pm.

The number of dry cleaning orders picked up at Sunny Fresh Dry Cleaners was sampled over 12 hour periods. Below is the sample:

142 171 125 91 140 125 97 125 162 142 125 117 89 125 140 128

From this data set, compute the sample mean, median, mode and midrange. Compute the 1st

quartile and 3rd and interpret their meanings.

I'm pretty sure i did this part correct, but im confused with the second part....

the mean is 2044/16 = 127.75

the median is 125 + 125 = 250/2 = 125

the range is 171 - 89 = 82

The 1st quartile (lower quartile) is 34 and the 3rd quartile (upper quartile) is 61. The lower quartile is the middle value of the lower half. The upper quartile is the middle value of the upper half.

- Math-Ms. Sue -
**Ms. Sue**, Sunday, July 31, 2011 at 11:11pm
How can a quartile be less than any of your data?

Study this site about quartiles. You should also study your text materials.

http://www.onlinemathlearning.com/quartile.html

You can also use this site.

http://www.alcula.com/calculators/statistics/quartiles/

- Math-Ms. Sue -
**MathMate**, Sunday, July 31, 2011 at 11:13pm
The mean, median and the range are correct.

Don't know how you got 34 and 61 for the quartiles when the minimum value is 89.

Your definition of the quartiles is correct, although in practice there might be different ways to calculate them.

- Math-Ms. Sue -
**Jen**, Sunday, July 31, 2011 at 11:16pm
I apologize Ms. Sue, I was reading the wrong problem...I believe the 1st quartile is 117 and the 3rd quartile is 140....am i correct??

- Math-Ms. Sue -
**Ms. Sue**, Sunday, July 31, 2011 at 11:19pm
Jen -- Please THINK and PROOFREAD before you post your questions!!!!!

- Math-Ms. Sue -
**Jen**, Sunday, July 31, 2011 at 11:23pm
I did....how is that incorrect???

- Math-Ms. Sue -
**MathMate**, Monday, August 1, 2011 at 5:17am
There are 16 observations, so the median is the mean of the two middle numbers, namely 125 and 125, which you did correctly.

The lower quartile is the median of the lower half, excluding the median, meaning the median of the lower eight observations. This works out to be the mean of 117 and 125 = 121.

The upper quartile can be worked out similarly. So work it out and post for confirmation if you wish.

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