What is the third Quartile Of the following distribution?. 10, 25, 18, 31, 16, 27, 5, 13, 32, 24, 15, 21 , 18 , 18, 24, 4, 8, 11, 11, 23

The third Quartile of the given distribution is 24. I
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windyyork windyyork · Answer 2 · 2019-06-18T01:15:41-04:00

Answer: The third quartile of the distribution is 23.

Step-by-step explanation:

First we write the data in ascending order:

4,5,8,10, 11,11, 13,15,16, 18, 18, 18, 21, 23, 24, 24, 25, 27, 31, 32

Since there are 20 terms:

First half is for First Quartile :

4,5,8,10, 11,11, 13,15,16, 18

Second half is for third Quartile:

18, 18, 21, 23, 24, 24, 25, 27, 31, 32.

So, Value of third quartile would be

\(Q_3=\dfrac{5^{th}+6^{th}}{2}\\\\Q_3=\dfarc{24+24}{2}\\\\Q_3=\dfrac{48}{2}\\\\Q_3=24\)

Hence, the third quartile of the distribution is 23.