1
JEE Main 2024 (Online) 30th January Evening Shift
Numerical
+4
-1

The variance $$\sigma^2$$ of the data

$$x_i$$ 0 1 5 6 10 12 17
$$f_i$$ 3 2 3 2 6 3 3

is _________.

2
JEE Main 2024 (Online) 29th January Morning Shift
Numerical
+4
-1

If the mean and variance of the data $$65,68,58,44,48,45,60, \alpha, \beta, 60$$ where $$\alpha> \beta$$, are 56 and 66.2 respectively, then $$\alpha^2+\beta^2$$ is equal to _________.

3
JEE Main 2024 (Online) 27th January Evening Shift
Numerical
+4
-1

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12 . If $$\mu$$ and $$\sigma^2$$ denote the mean and variance of the correct observations respectively, then $$15\left(\mu+\mu^2+\sigma^2\right)$$ is equal to __________.

4
JEE Main 2023 (Online) 13th April Evening Shift
Numerical
+4
-1

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 _________