ExamBro
ExamBro
AP EAMCET · Maths · Statistics

The standard deviation of the scores 505, 510, \(515,520, \ldots \ldots ., 595\) is

  1. A \(500+5 \sqrt{30}\)
  2. B \(505+\sqrt{30}\)
  3. C \(5 \sqrt{30}\)
  4. D \(5+\sqrt{30}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(5 \sqrt{30}\)

Step-by-step Solution

Detailed explanation

Given, scores 505, 510, 515, 520, ... 595 the mean of these 19 scores \(=550=\bar{X}\) So, \[ \begin{aligned} \sum_{i=1}^{19}\left(x_i-\bar{x}\right)^2 & =2\left(45^2+40^2+35^2+\ldots+5^2\right) \\ & =2 \times 5^2 \times\left[1^2+2^2+3^2+\ldots+9^2\right] \end{aligned} \] So,…