SOLUTION: Respected Sir / Mam , Please help me to solve this question. I will be very grateful for your help . My question is What is the value of the first quartile for observations 15,

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Question 485381: Respected Sir / Mam ,
Please help me to solve this question. I will be very grateful for your help .
My question is
What is the value of the first quartile for observations 15,
18,10,20,23,28,12,16 ?
As the answer given is : 15.75
Please provide me the steps for this question.
Thank you
Found 2 solutions by Edwin McCravy, deborabr:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
The 1st quartile is the median of the numbers below the 
median of the whole data set.

There is no way the answer could be 15.75.  So you should point
this out to your teacher.  Very little educational material is
free of typos.  Where there are humans, there is usually some 
human error.

Arrange the data in ascending order:

10,12,15,16,18,20,23,28

Find the median of the whole data set. Since there are an even 
number of numbers in the data set, the median is the average of 
its two middle numbers (16+18)÷2 = 34÷2 or 17.

Next we find the median of the numbers below the median of the
whole data set, 17.  These numbers are 10,12,15,16. Since there 
are also an even number of numbers in this data set, the median
is the average of its two middle numbers (12+15)÷2 = 27÷2 or 13.5.

Edwin
Answer by deborabr(181)   (Show Source): You can put this solution on YOUR website!
put the numbers in ascending order: 10,12,15,16,18,20,23,28
use the formula: L=(K/100)N
where:
L= the position of the number in the sequence
K= the quartile (first=25, second=50 and third=75
here we want to know the first quartile so K=25
N= the quantity of numbers in the sequence
and here we have 11 numbers --> 10,12,15,16,18,20,23,28
substituting we have:
L=(25/100)11
L=(25/100)11/1
L=275/100
L=2,75
rounding 2,75 we get 3, is the position of the number in the sequence and the third number is 15. The first quartile is 15
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