1
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $$-$$a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. Then the value of a2 + b2 is equal to :
A
425
B
250
C
925
D
650
2
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?
A
b2 = 3(a2 + c2) + 9d2
B
b2 = 3(a2 + c2) $$-$$ 9d2
C
b2 = 3(a2 + c2 + d2)
D
b2 = a2 + c2 + 3d2
3
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
If $$\sum\limits_{i = 1}^n {\left( {{x_i} - a} \right)} = n$$ and $$\sum\limits_{i = 1}^n {{{\left( {{x_i} - a} \right)}^2}} = na$$
(n, a > 1) then the standard deviation of n
observations x1 , x2 , ..., xn is :
A
$$a$$ – 1
B
$$n\sqrt {a - 1}$$
C
$$\sqrt {n\left( {a - 1} \right)}$$
D
$$\sqrt {a - 1}$$
4
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
If the mean and the standard deviation of the
data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation :
A
x2 – 20x + 18 = 0
B
2x2 – 20x + 19 = 0
C
x2 – 10x + 18 = 0
D
x2 – 10x + 19 = 0
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