Skip to content
Exercises · Q7
Q.

A batsman is to be selected for a cricket team. The choice is between X and Y on the basis of their scores in five previous tests:

X25854080120
Y5070654580

Which batsman should be selected if we want (i) a higher run-getter, or (ii) a more reliable batsman?

Bihar BsebTextbookSubjectiveImportance★★★★★est
81% · 21/26 Questions
🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Mean: X = 70, Y = 62. C.V.: X ≈ 48.4%, Y ≈ 20.8%. Select X for more runs, Y for reliability.

Batsman X — scores 25, 85, 40, 80, 120. Mean =3505=70= \dfrac{350}{5} = 70. Deviations from 70: −45, +15, −30, +10, +50; squares: 2025, 225, 900, 100, 2500; ∑d2=5750\sum d^2 = 5750. σX=57505=1150=33.91\sigma_X = \sqrt{\dfrac{5750}{5}} = \sqrt{1150} = 33.91. C.V.X=33.9170×100=48.4%C.V._X = \dfrac{33.91}{70}\times100 = 48.4\%.

Batsman Y — scores 50, 70, 65, 45, 80. Mean =3105=62= \dfrac{310}{5} = 62. Deviations from 62: −12, +8, +3, −17, +18; squares: 144, 64, 9, 289, 324; ∑d2=830\sum d^2 = 830. σY=8305=166=12.88\sigma_Y = \sqrt{\dfrac{830}{5}} = \sqrt{166} = 12.88. C.V.Y=12.8862×100=20.8%C.V._Y = \dfrac{12.88}{62}\times100 = 20.8\%. …

Start your 14-day free trial to unlock the full solution →

Unlock everything free for 14 days

  • Full step-by-step solutions
  • Concept-first explanations
  • Methods, shortcuts & mistakes
  • PYQ mapping + timed mock tests
Start 14-day free trial →See Plans & Pricing →

Full access for 14 days. No credit card required.

←Previous questionQ6 — In the previous question, calculate the relative measures of variation…→Next questionQ8 — To check the quality of two brands of light bulbs, their life in burni…