What is the first quartile of the data set below? . . 275, 257, 301, 218, 265, 242, 201 . 201. 218. 257. 270
The answers to your question about the first quartile of the data set would be: 201, 230, 257, 270
Q1 = 2nd observation in the ascending array = 218
Had 301 been 201, Q1 would have been 201.
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Answer:
218
Step-by-step explanation:
Let's first arrange the 11 numbers in ascending order:
\(201,201,218,218,242,257,257,265,270,275,301\)
Which number is the first quartile?
Its is given by the formula \(C=\frac{n}{4}\)
Where, \(n\) is the number of numbers [in our case \(n=11\) ] and decimal value of \(n\) is rounded up.
So, \(C=\frac{11}{4}=2.75\)
Rounding gives us \(C=3\)
This means that the 3rd number in the list is the first quartile. Hence, we see that 218 is the 3rd number and it is the first quartile.