CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion
For a frequency distribution of the daily output (in units) of a Coimbatore workshop, Q1 = 46 and Q3 = 74. What are the quartile deviation and its coefficient?
Quartile deviation is half the interquartile range, so (74 − 46)/2 = 14 units. The coefficient of quartile deviation is (Q3 − Q1)/(Q3 + Q1) = 28/120, which equals 0.2333.
- AQuartile deviation = 28; coefficient = 0.2333
- BQuartile deviation = 14; coefficient = 0.2333Correct
- CQuartile deviation = 14; coefficient = 0.4667
- DQuartile deviation = 14; coefficient = 0.5000
Explanation
Quartile deviation = (Q3 − Q1)/2 = (74 − 46)/2 = 14. Coefficient = (Q3 − Q1)/(Q3 + Q1) = 28/120 = 0.2333. Option A gives the interquartile range 28 instead of the semi-interquartile range, and option C uses 28/60, a wrong denominator.
Did you get it right without looking?
One question tells you little. A timed set on Measures of Central Tendency and Dispersion shows your real accuracy, how long you take and where you lose marks.
More Measures of Central Tendency and Dispersion questions
- The following 11 observations are already arranged in ascending order: 12, 15, 18, 22, 25, 28, 30, 35, 40, 45, 50. Using the position formul…
- The mean deviation about the mean of the observations 4, 8, 10, 14 and 24 is:
- The mean of five observations is 24. If each of the first three observations is increased by 10 and each of the remaining two is decreased b…
- The sales of a Surat textile firm rose by 25% in one year and by 80% in the next year. What is the average annual growth rate, measured usin…
- The coefficient of variation of a series is 40% and its standard deviation is 16. What is the arithmetic mean of the series?
- The monthly sales of a Surat textile shop have a mean of ₹50,000 and a standard deviation of ₹7,500. What is the coefficient of variation of…