CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion
A variable x has mean 20 and standard deviation 4. A new variable is defined as y = 3x − 5. The mean and standard deviation of y are respectively:
The mean of y is 55 and its standard deviation is 12. The mean follows the full transformation, 3 × 20 − 5 = 55. Standard deviation ignores the shift of origin but is multiplied by the scale factor 3, giving 3 × 4 = 12.
- A55 and 7
- B60 and 12
- C55 and 12Correct
- D60 and 7
Explanation
Mean of y = 3(20) − 5 = 55. The SD is unaffected by change of origin (the −5) but is multiplied by the absolute value of the scale factor, so SD of y = 3 × 4 = 12. An SD of 7 wrongly applies the −5 shift to the SD as well.
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 harmonic mean of the three observations 2, 3 and 6 is:
- For a distribution of 100 measurements with mean = 60 and standard deviation = 8, approximately how many observations are expected to lie wi…
- The marks obtained by five students in a test are 45, 52, 48, 55, and 50. What is the arithmetic mean of their marks?
- For a distribution of daily sales, the first quartile is ₹24 thousand and the third quartile is ₹36 thousand. What is the coefficient of qua…
- For a variable x, the mean is 50 and the standard deviation is 8. A new variable y is defined as y = 5 − 3x. What is the variance of y?
- Firm A has 40 employees with a mean monthly salary of ₹30,000. Firm B has 60 employees with a mean monthly salary of ₹25,000. What is the co…