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JEE Main Math Class 12 Statistics Part 1 Questions
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© examsnet.com
Question : 6
Total: 115
Let
S
be the set of all values of
a
1
for which the mean deviation about the mean of 100 consecutive positive integers
a
1
,
a
2
,
a
3
,
.
.
.
.
,
a
100
is 25 . Then
S
is
[30-Jan-2023 Shift 2]
φ
{
99
}
ℕ
{
9
}
Validate
Solution:
let
a
1
be any natural number
a
1
,
a
1
+
1
,
a
1
+
2
,
.
.
.
.
,
a
1
+
99
are values of
a
i
′
S
x
=
a
1
+
(
a
1
+
1
)
+
(
a
1
+
2
)
+
.
.
.
.
+
a
1
+
99
100
=
100
a
1
+
(
1
+
2
+
.
.
.
.
+
99
)
100
=
a
1
+
99
×
100
2
×
100
=
a
1
+
99
2
Mean deviation about mean
=
100
∑
1
=
1
|
x
i
−
x
|
100
=
2
(
99
2
+
97
2
+
95
2
+
.
.
.
.
+
1
2
)
100
=
1
+
3
+
.
.
.
.
+
99
100
=
50
2
[
1
+
99
]
100
=
25
So, it is true for every natural no. '
a
1
′
© examsnet.com
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