JEE Mains · Maths · STD 11 - 13. statistics
The mean of the data set comprising of \(16\) observations is \(16.\) If one of the observation valued \(16\) is deleted and three new observations valued \(3, 4\) and \(5\) are added to the data, then the mean of the resultant data, is:
- A \(14\)
- B \(16.8\)
- C \(16\)
- D \(15.8\)
Answer & Solution
Correct Answer
(A) \(14\)
Step-by-step Solution
Detailed explanation
Given, \(\frac{x_{1}+x_{2}+x_{3}+\ldots+x_{16}}{16}=16\) \( \Rightarrow \sum\limits_{i = 1}^{16} {{x_i}} = 16 \times 16\) Sum of new observations \( = \sum\limits_{i = 1}^{18} {{y_i}} = (16 \times 16 - 16) + (3 + 4 + 5) = 252\) Number of observations \(=18\) \(\therefore \) New…
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