Let the mean and the variance of 6 observation $a, b$, $68,44,48,60$ be $55$ and $194 $, respectively if $a>b$, then $a+3 b$ is

The mean and standard deviation of the marks of $10$ students were found to be $50$ and $12$ respectively. Later, it was observed that two marks $20$ and $25$ were wrongly read as $45$ and $50$ respectively. Then the correct variance is $…………$.

The variance of the data $2, 4, 6, 8, 10$ is

Let $ \bar x , M$ and $\sigma^2$ be respectively the mean, mode and variance of $n$ observations $x_1 , x_2,…,x_n$ and $d_i\, = – x_i – a, i\, = 1, 2, …. , n$, where $a$ is any number.
Statement $I$: Variance of $d_1, d_2,…..d_n$ is $\sigma^2$.
Statement $II$ : Mean and mode of $d_1 , d_2, …. d_n$ are $-\bar x -a$ and $- M – a$, respectively

If $\sum_{i=1}^{5}(x_i-10)=5$ and $\sum_{i=1}^{5}(x_i-10)^2=5$ then standard deviation of observations $2x_1 + 7, 2x_2 + 7, 2x_3 + 7, 2x_4 + 7$ and $2x_5 + 7$ is equal to-