Average of following observation 25,39,35,f, 46 is 36 find the unknown data point f.
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Answer:
Arranging given numbers in ascending order,
24,25,26,28,30,30,32,33,34,35
Mean(
x
)=
10
24+25+26+28+30+30+32+33+34+35
=
10
297
=29.7
(i)
⇒ (24−29.7)+(25−29.7)+(26−29.7)+(28−29.7)+(30−29.7)+(30−29.7)+(32−29.7)+(33−29.7)+(34−29.7)+(35−29.7)
⇒ −5.7−4.7−3.7−1.7+0.3+0.3+2.3+3.3+4.3+5.3
⇒ 0
Hence, we proved that the sum of the deviations of all the given observations from the mean is zero.
(ii)
Number of observation =10
Median=
2
1
[(
2
10
)
th
obs+(
2
10
+1)
th
obs]
Median=
2
1
[5
th
obs+6
th
obs]
5
th
=30 and 6
th
obs=30
∴ Median=
2
30+30
=30
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