JEE Mains · Maths · STD 11 - 13. statistics
The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation \( \alpha \) in this data is replaced by \( \beta \), then the mean and variance become 10.1 and 1.99, respectively. Then \( \alpha+\beta \) equals.
- A 10
- B 15
- C 5
- D 20
Answer & Solution
Correct Answer
(D) 20
Step-by-step Solution
Detailed explanation
Let first 10 numbers are \(x_1, x_2, \ldots \ldots . x_9, \alpha\) \(\Rightarrow \alpha+\sum_{ i =1}^9 x _{ i }=100 \Rightarrow \sum_{ i =1}^9 x _{ i }=100-\alpha\) Variance \(=\left(\frac{\sum x _{ i }^2}{ n }\right)-\left(\frac{\sum x _{ i }}{ n }\right)^2\)…
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