Question

Find the standard deviation and coefficient of variation for the following data
44,55,56,60,63,70

Answer 1

Solution :-

  
    x                                                      (x - Arithmetic Mean)²
  44                                                          (44 - 58)² = 196      55                                                          (55 - 58)² = 9       56                                                          (56 - 58)² = 4     60                                                          (60 - 58)² = 4     63                                                          (63 - 58)² = 25      70                                                          (70 - 58)² = 144____________________________________________________________  ∑x = 348                                            ∑(x - Arithmetic Mean)² =  382            ____________________________________________________________

Arithmetic Mean = ∑x/N

⇒ 348/6

Arithmetic Mean = 58

Standard Deviation = √∑(x - Arithmetic Mean)²/N

⇒ √382/6

⇒ √63.66666666

Standard Deviation = 7.979 or 7.98 (Approximately)

Coefficient of Variation = (Standard Deviation × 100)/Arithmetic Mean

⇒ (7.98 × 100)/58

Coefficient of Variation = 13.7586 or 13.76 % (Approximately)

Answer.