1
JEE Main 2022 (Online) 27th July Morning Shift
Numerical
+4
-1

The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is _____________.

2
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1

The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If $$\sigma$$ is the standard deviation of the data after omitting the two wrong observations from the data, then $$38 \sigma^{2}$$ is equal to ___________.

3
JEE Main 2022 (Online) 28th June Evening Shift
Numerical
+4
-1

Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of students can fail is _________.

4
JEE Main 2022 (Online) 28th June Morning Shift
Numerical
+4
-1

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _____________.