Question
Find all quartiles for the data given below about marks scored by $15$ students in class test $8,6,7,0,2,4,6,5,5,4,8,9,3,6,7$.
✓
Answer
Arranging the observations on marks in ascending order.
$0, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9$ Here, $n = 15$
First Quartile:
$\mathrm{Q}_1=$ Value of $\left(\frac{n+1}{4}\right)$ th observation
$=$ Value of $\left(\frac{15+1}{4}\right)=\left(\frac{16}{4}\right)=4$ th observation
$=4$ Marks
Hence, first quartile $=4$ marks.
Second Quartile:
$\mathrm{Q}_2=$ Value of $2\left(\frac{n+1}{4}\right)$ th observation
$=$ Value of $2(4)$
$=8$ th observation $=6$ marks
Hence, second quartile $=6$ marks.
Third Quartile:
$\mathrm{Q}_3=$ Value of $3\left(\frac{n+1}{4}\right)$ th observation
= Value of $3(4)=12$ th observation $=7$ marks
Hence, third quartile $=7$ marks.
$0, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9$ Here, $n = 15$
First Quartile:
$\mathrm{Q}_1=$ Value of $\left(\frac{n+1}{4}\right)$ th observation
$=$ Value of $\left(\frac{15+1}{4}\right)=\left(\frac{16}{4}\right)=4$ th observation
$=4$ Marks
Hence, first quartile $=4$ marks.
Second Quartile:
$\mathrm{Q}_2=$ Value of $2\left(\frac{n+1}{4}\right)$ th observation
$=$ Value of $2(4)$
$=8$ th observation $=6$ marks
Hence, second quartile $=6$ marks.
Third Quartile:
$\mathrm{Q}_3=$ Value of $3\left(\frac{n+1}{4}\right)$ th observation
= Value of $3(4)=12$ th observation $=7$ marks
Hence, third quartile $=7$ marks.
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