Find the mean of the following data : 30,32,24,34,26,28,30,35,33,25 show that the sum of the deviations of all the given observations from the mean is zero
Answers
Step-by-step explanation:
Mean (
x
)=
∑i
∑x
i
=
10
30+32+24+34+26+28+30+35+33+25
=
10
297
⇒
x
=29.7
deviation d
i
=
x
−x
i
d
1
=29.7−30=−0.3
d
2
=29.7−32=−2.3
d
3
=29.7−24=5.7
d
4
=29.7−34=−5.7
d
4
=29.7−26=−4.3
d
5
=29.7−26=3.7
d
6
=29.7−28=1.7
d
7
=29.7−30=−0.3
d
8
=29.7−35=−5.3
d
9
=29.7−33=−3.3
d
10
=29.7−25=4.7
Sum of deviations =∑d
i
=(0.3)+(−2.3)+5.7+(−4.3)+3.7+1.7+(−0.3)+(−5.3)+(−3.3)+4.7
Answer:
Mean (
x
)=
∑i
∑x
i
=
10
30+32+24+34+26+28+30+35+33+25
=
10
297
⇒
x
=29.7
deviation d
i
=
x
−x
i
d
1
=29.7−30=−0.3
d
2
=29.7−32=−2.3
d
3
=29.7−24=5.7
d
4
=29.7−34=−5.7
d
4
=29.7−26=−4.3
d
5
=29.7−26=3.7
d
6
=29.7−28=1.7
d
7
=29.7−30=−0.3
d
8
=29.7−35=−5.3
d
9
=29.7−33=−3.3
d
10
=29.7−25=4.7
Sum of deviations =∑d
i
=(0.3)+(−2.3)+5.7+(−4.3)+3.7+1.7+(−0.3)+(−5.3)+(−3.3)+4.7