NIMCET 2022 — Mathematics PYQ

Calculation of Percentiles 
Step 1: Arrange the observations in ascending order 
The given observations are $32,49,23,29,118$. When arranged in ascending order, the observations become $23,29,32,49,118$. 
Step 2: Calculate the position of the 10th percentile 
The position of the $P$-th percentile is calculated using the formula $L=\frac{P}{100}\times N$, where $N$ is the total number of observations. For the $10$-th percentile, $P=10$ and $N=5$. The position is calculated as $L_{10}=\frac{10}{100}\times 5=\frac{50}{100}=0.5$. Since the position is not a whole number, the $10$-th percentile is the value of the observation at the next whole number position, which is the $1$-st position. The $1$-st observation in the sorted list is $23$. 
Step 3: Calculate the position of the 50th percentile 
For the $50$-th percentile, $P=50$ and $N=5$. The position is calculated as $L_{50}=\frac{50}{100}\times 5=\frac{250}{100}=2.5$. Since the position is not a whole number, the $50$-th percentile is the value of the observation at the next whole number position, which is the $3$-rd position. The $3$-rd observation in the sorted list is $32$. 
Final Answer 
The $10$-th and $50$-th percentiles of the given observations are $23$ and $32$, respectively.