Question :
Let \(x_1\), \(x_2\), ….. , \(x_n\), be n observations such that \(\sum{x_i}^2\) = 400 and \(\sum{x_i}\) = 80. Then, a possible value of among the following is
(a) 12
(b) 9
(c) 18
(d) 15
Solution :
Given \(\sum{x_i}^2\) = 400 and \(\sum{x_i}\) = 80
\(\because\) \(\sigma^2\) \(\ge\) 0
\(\therefore\) \(\sum{x_i}^2\over n\) – \(({\sum{x_i}\over n})^2\) \(\ge\) 0
\(\implies\) \(400\over n\) – \(6400\over n^2\) \(\ge\) 0
\(\therefore\) n \(\ge\) 16
Similar Questions
The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is
The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observation of the set is increased by 2, then the median of the new is
A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 g and a standard deviation of 2 g. Later, it was found that the measuring scale was misaligned and always under reported every fish weight by 2 g. The correct mean and standard deviation in gram of fishes are respectively.
In a series of 2n observations, half of them equals a and remaining half equal -a. If the standard deviation of the observation is 2, then |a| equal to
The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then, find the values of a and b?
