Central Tendency & DispersionPYQ June 24Question 3146 of 473
All Questions

Consider the data sets: X=[−6,2,−2,6]\displaystyle X = [-6, 2, -2, 6], Y=[4,8,2,6]\displaystyle Y = [4, 8, 2, 6] Z=[103,100,102,101]\displaystyle Z = [103, 100, 102, 101] Let SX,SY,SZ\displaystyle S_X, S_Y, S_Z be the standard deviations of the sets X,Y\displaystyle X, Y and Z\displaystyle Z respectively. We have the relations,

Options

ASX<SY<SZ\displaystyle S_X < S_Y < S_Z
BSX>SY>SZ\displaystyle S_X > S_Y > S_Z
CSX<SZ<SY\displaystyle S_X < S_Z < S_Y
DSX<SY=SZ\displaystyle S_X < S_Y = S_Z
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — SX>SY>SZ\displaystyle S_X > S_Y > S_Z

All Options:

  • ASX<SY<SZ\displaystyle S_X < S_Y < S_Z
  • BSX>SY>SZ\displaystyle S_X > S_Y > S_Z
  • CSX<SZ<SY\displaystyle S_X < S_Z < S_Y
  • DSX<SY=SZ\displaystyle S_X < S_Y = S_Z

Detailed Solution & Explanation

**Compute SX\displaystyle S_X:** Data: −6,2,−2,6\displaystyle -6, 2, -2, 6 Xˉ=−6+2−2+64=0\bar{X} = \frac{-6+2-2+6}{4} = 0 σX2=(−6)2+(2)2+(−2)2+(6)24=36+4+4+364=804=20\sigma_X^2 = \frac{(-6)^2+(2)^2+(-2)^2+(6)^2}{4} = \frac{36+4+4+36}{4} = \frac{80}{4} = 20 SX=20≈4.47S_X = \sqrt{20} \approx 4.47 **Compute SY\displaystyle S_Y:** Data: 4,8,2,6\displaystyle 4, 8, 2, 6 Yˉ=4+8+2+64=5\bar{Y} = \frac{4+8+2+6}{4} = 5 σY2=(4−5)2+(8−5)2+(2−5)2+(6−5)24=1+9+9+14=204=5\sigma_Y^2 = \frac{(4-5)^2+(8-5)^2+(2-5)^2+(6-5)^2}{4} = \frac{1+9+9+1}{4} = \frac{20}{4} = 5 SY=5≈2.24S_Y = \sqrt{5} \approx 2.24 **Compute SZ\displaystyle S_Z:** Data: 103,100,102,101\displaystyle 103, 100, 102, 101 Zˉ=103+100+102+1014=4064=101.5\bar{Z} = \frac{103+100+102+101}{4} = \frac{406}{4} = 101.5 σZ2=(1.5)2+(−1.5)2+(0.5)2+(−0.5)24=2.25+2.25+0.25+0.254=54=1.25\sigma_Z^2 = \frac{(1.5)^2+(-1.5)^2+(0.5)^2+(-0.5)^2}{4} = \frac{2.25+2.25+0.25+0.25}{4} = \frac{5}{4} = 1.25 SZ=1.25≈1.12S_Z = \sqrt{1.25} \approx 1.12 **Comparison:** SX≈4.47>SY≈2.24>SZ≈1.12S_X \approx 4.47 > S_Y \approx 2.24 > S_Z \approx 1.12 ∴SX>SY>SZ\therefore S_X > S_Y > S_Z Hence, **Option B** is the correct answer.

More Questions from Central Tendency & Dispersion

If the range of 28,22,40,20,15,50\displaystyle 28, 22, 40, 20, 15, 50 is

If the S.D. of the 1st\displaystyle 1^{st} n\displaystyle n natural numbers is 30\displaystyle \sqrt{30} then the value of n\displaystyle n is

If the variance of 5,7,9\displaystyle 5, 7, 9 and 11\displaystyle 11 is 4\displaystyle 4, then the coefficient of variation is:

A helicopter flies from A to B at the rate of 500 km/hr. and comes back at the rate 700 km/hr. The average speed of the helicopter is

If Arithmetic Mean (A.M.) and Geometric Mean (G.M.) of two numbers are 6.50 and 6 respectively, then the two numbers are

Which of the following is not a method of dispersion?

Ready to Master Central Tendency & Dispersion?

Practice all 473 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free