Quartiles

A

aburchett

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Jan 19, 2011
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The number of surfer’s special burritos served was sampled during a dinner period 5:00 p.m. – 8:30 p.m. at a taco shop on a weekday. Below is the sample:
12 7 5 14 9 2 12 11 5 15 20 14 9 21 14
From this data set, compute the sample mean, median, mode and midrange. Compute the 1st quartile and 3rd and interpret their meanings.

My work:
Mean-(the average) (12+7+5+14+9+2+12+11+5+15+20+14+9+21+14)/15 = 170/15= 11.333
Median-(middle value when placed in order from least to greatest- 2,5,5,7,9,9,11,12,12,14,14,14,15,20,21) so Median= 12 (this is also Q2)
Mode-(number repeated the most), so Mode= 14
Midrange-(maximum value + minimum value divided by 2), so MIdrange= (21+2)/2=23/2=11.5
Q1-(median of data values less than 12) 2,5,5,7,9,9,11, so Q1=7
Q3-(median of data values greater than 12) 14,14,14,15,20,21, the median will be halfway between the 2 middle values: (14+15)/2=14.5

Is this correct? or would you include the 12s when figuring out the Q1 and Q3?
 
Just a couple things.

1) Are you SURE a "midrange" is a point value?
2) I would include the 12's. Actually, I would determine the quartiles without reference to the 12s.
 
The first quartile and the 25th percentile are one and the same. However, different people calculate differently. I have seen one text offer the explanation that the 1st quartile is the median of the lower half of the distribution. But, then he goes on to include the mid score as part of the lower half, if there is an odd number of data points. It is my interpretation that the 1st quartile is that point below which 25% of the population lies. If this is correct, we could take 25% of the number of data points, 15, to arrive at the 1st quartile being the point that is 3.75 points from the bottom. Using your data set...

2,5,5,7,9,9,11,12,12,14,14,14,15,20,21

and counting up from the 1st entry we are at the 2nd five when we count to 3. What about the 0.75? I think it is going to depend on what your teacher says. Some people would say that we take 0.75 times 2 (7-5) getting 1.5 and add that to the 5. So the 1st quartile is 5 + 1.5 or 6.5. Other people will calculate differently.
 
Thanks. My instructor says that the formula for Q1= (N+1/4)th term and for Q3=[3(N+1)/4]th term. So this would mean that Q1= (N+1/4)th term=15+1/4=16/4=4th term, the 4th term is 7, so Q1=7 and then Q3=[3(N+1)/4]th term=3(15+1)/4=3(16)/4=48/4=12th term and the 12th term is 14, so Q3=14.
 
Not everyone agrees with that definition, but i that's what it takes to pass the exam, it won't cause any permanent scars.
 
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