NIMCET 2022
The 10th and 50th percentiles of the observations 32, 49, 23, 29, 118 respectively are
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option B — 23, 32
Detailed Solution
Arrange in ascending order: 23, 29, 32, 49, 118 ( ).
The 50th percentile is the median, the 3rd value: 32.
For the 10th percentile, , so take the 1st value (nearest rank): 23.
✓ Check
21 and 22 are not in the data, and 31 and 33 are not the middle value, so only (23, 32) fits.⚠ Common trap
(C) 23, 33 has the right 10th percentile but the wrong median; the middle of the 5 sorted values is 32.Quick tip
= median; nearest-rank is the value at position
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Statistics — Preparation
This question tests your understanding of Statistics, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Statistics deals with collecting, summarising and interpreting data. This topic covers measures of central tendency (mean, median and mode) for ungrouped and grouped data, and measures of dispersion such as range, mean deviation, variance, standard deviation and the coefficient of variation. Exam questions test calculating these measures, the effect of adding or multiplying every observation by a constant, combined mean and variance of two groups, and comparing the consistency of two data sets. Remember that adding a constant to every value changes the mean but not the variance or standard deviation, while multiplying by k multiplies the standard deviation by |k|. Facts like these solve many questions without any calculation. Practise the statistics questions below, each with a step-by-step solution.