Question

Find the third quartile for the following data.

$\begin{array}{cc}\text{Observation}& \text{Frequency}\\ 3& 6\\ 8& 1\\ 12& 1\\ 19& 4\\ 22& 8\\ 29& 6\\ 31& 3\\ 42& 5\end{array}$

• A. 21.5
• B. 23.75
• C. 28.25
• D. 29.5

Answer 1

The correct option is D

29.5

The given observations are in the
ascending order.

$\begin{array}{ccc}\text{Observation}& \text{Frequency}& \text{Cumulative}\\ & & \text{Frequency}\\ 3& 6& 6\\ 8& 1& 7\\ 12& 1& 8\\ 19& 4& 12\\ 22& 8& 20\\ 29& 6& 26\\ 31& 3& 29\\ 42& 5& 34\end{array}$

Here, N =34
$Q_3=\text{size of 3}\left(\frac{N+1}{4}\right)thobservation=\text{size of 26.25th observation}$
The 26th observation is 29 and the
27th observation is 31

$\therefore Q_3=29+0.25\times (31-29)=29+0.25\times 2=29.5$