if the mean & median of a data are 3.5 &3.7 then what is the mode.
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Answer:
We arrange given data in ascending order 1,2,3,3,3,4,5,5,6,7
Mean=
n
Σx
i
=
10
(1+2+3+3+3+4+5+5+6+7)
=
10
39
=3.9
Here number of observations, n=10 which is even.
So Median=
⎝
⎜
⎜
⎛
2
(
2
n
)
th
+(
2
n
+1)
th
⎠
⎟
⎟
⎞
th
observation
=
2
2
10
+(
2
10
+1)
=
2
1
(5
th
term+(5+1)
th
term)
=
2
1
(5
th
term+6
th
term)
=
2
1
(3+4)
=
2
1
×7
=3.5
Hence the median is 3.5.
In the given set, 3 occurs the maximum number of times.
Hence the mode is 3.
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