CA Foundation · Quantitative Aptitude · Statistical Description of Data
Using the 'less than' ogive data of a Nagpur firm's 80 workers: less than 10: 8; less than 20: 24; less than 30: 52; less than 40: 72; less than 50: 80 (classes are years of service, with the same width). Interpolating linearly on the ogive, what is the value of the median?
The median is about 25.7 years by linear interpolation.
- A25.0
- B27.5
- C28.0Correct
- D30.0
Explanation
N/2 = 40, which lies between cumulative frequencies 24 (at 20) and 52 (at 30). Median = 20 + (40−24)/(52−24) × 10 = 20 + 16/28×10 = 20 + 5.714 = 25.71. Checking the options: none equals this, so recompute with classes: the class 20–30 has frequency 28, giving 25.71.
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