find the mean, median, mode of the following data 24, 25, 26, 26, 23, 28, 26, 30
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Answer:
10th
Maths
Statistics
Median of Grouped Data
Find the mean of the follow...
STATISTICS
Find the mean of the following data 30,32,24,34,26.28,30,35,33,25
(i) Show that the sum of the deviations of all the given observations from the mean is zero.
(ii) Find the median of the given data.
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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
Answer:
Mean=26
mode=26
Median=26