(D)
2
2
i
x
x
n
30.
The mean of 100 observations is 50 and their standard deviation is 5. The sum
of all squares of all the observations is
(A)
50000
(B)
250000
(C)
252500
(D)
255000
31.
Let
a
,
b
,
c
,
d
,
e
be the observations with mean
m
and standard deviation
s
.
The standard deviation of the observations
a
+
k
,
b
+
k
,
c
+
k
,
d
+
k
,
e
+
k
is
(A)
s
(B)
k s
(C)
s
+
k
(D)
s
k
32.
Let
x
1
,
x
2
,
x
3
,
x
4
,
x
5
be the observations with mean
m
and standard deviation
s
.
The standard deviation of the observations
kx
1
,
kx
2
,
kx
3
,
kx
4
,
kx
5
is
(A)
k
+
s
(B)
s
k
(C)
k s
(D)
s
33.
Let
x
1
,
x
2
, ...
x
n
be
n
observations. Let
w
i
=
lx
i
+
k
for
i
= 1, 2, ...
n
, where
l
and
k
are constants. If the mean of
x
i
’
s
is 48 and their standard deviation is 12,
the mean of
w
i
’
s
is 55 and standard deviation of
w
i
’
s
is 15, the values of
l
and
k
should be
(A)
l
= 1.25,
k
= – 5
(B)
l
= – 1.25,
k
= 5
(C)
l
= 2.5,
k
= – 5
(D)
l
= 2.5,
k
= 5
34.
Standard deviations for first 10 natural numbers is
(A)
5.5
(B)
3.87
(C)
2.97
(D)
2.87
35.
Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. If 1 is added to each number,
the variance of the numbers so obtained is