Question

Find the first quartile for the following data.

$\begin{array}{cc}Observation& Frequency\\ 12& 7\\ 15& 6\\ 18& 13\\ 32& 5\\ 33& 11\\ 45& 14\\ 48& 4\\ 53& 10\end{array}$

• A. 17
• B. 18
• C. 15
• D. 32

Answer 1

The correct option is B

18

The given observations are in the
ascending order.

$\begin{array}{ccc}Observation& Frequency& Cumulative\\ & & Frequency\\ 12& 7& 7\\ 15& 6& 13\\ 18& 13& 26\\ 32& 5& 31\\ 33& 11& 42\\ 45& 14& 56\\ 48& 4& 60\\ 53& 10& 70\end{array}$

Here, N =70
$Q_1=\text{size of}\left(\frac{N+1}{4}\right)thobservation=\text{size of 17.75th observation}$

The first quartile is the observation
whose cumulative frequency is just
above or equal to 17.75.
Hence, the first quartile is 18.