Find the median of the following data
83, 37, 70, 29, 45, 63, 41, 70, 34, 54
Answers
Given numbers are
83, 37, 70, 29, 45, 63, 41, 70, 34, 54
Arrange the numbers is ascending order
29, 34, 37, 41, 45, 54, 63, 70, 70, 83
n = 10 (even)
∴ Median =
n
t
h
2
v
a
l
u
e
+
(
n
2
+
1
)
t
h
v
a
l
u
e
2
nth2value+(n2+1)thvalue2
=
10
t
h
2
v
a
l
u
e
+
(
10
2
+
1
)
t
h
v
a
l
u
e
2
10th2value+(102 +1)thvalue2
=
5
t
h
v
a
l
u
e
+
6
t
h
v
a
l
u
e
2
5thvalue+6thvalue2
=
45
+
54
2
=
99
2
=
49.5
45+542=992=49.5
Given : Observations :83, 37, 70, 29, 45, 63, 41, 70, 34, 54
Arranging given numbers in ascending order:
29 , 34 , 37 , 41 , 45 , 54 , 63 , 70 , 70 , 83
Number of observations, (n) = 10 (even)
Median = ½[value of (n/2)th + (n/2 +1)th observations]
Median = ½ [value of (10/2 th + (10/2 + 1 th) observations]
Median = ½ [value of (5th + 6th) observations]
Median = (45 + 54)/2
Median = 99/2 th
Median = 49.5
Hence, the median of the given data is 49.5 .
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