Question

N. the marks scored by 5 students in a test for 50 marks are 20, 25, 30, 35, 40. find the s.d for the marks. if the marks are converted for 100 marks, find the s.d. for newly obtained

Answer 1

Given:

The marks scored by 5 students in a test for 50 marks are 20, 25, 30, 35, 40.

To Find:

Standard deviation in this case and Standard deviation if the marks are converted for 100 marks.

Calculation:

Mean, x = (20 + 25 + 30 + 35 + 40)/5 = 150/5 = 30

Standard deviation = √∑(Xi - x)²/N

⇒ σ = √{(20 - 30)² + (25 - 30)² + (30 - 30)² + (35 - 30)² + (40 - 30)²}/5

⇒ σ = √{10² + 5² + 0 + 5² + 10²}/5

⇒ σ = √{100 + 25 + 25 + 100}/5

⇒ σ = √250/5

⇒ σ = √50

⇒ σ = 7.07

- So the standard deviation is 7.07

- To convert these marks from 100, each value is doubled.

- When each value is multiplied by a no, then the value of standard deviation also gets doubled

⇒ New standard deviation, σ' = 2 × 7.07 = 14.14