Page 10 - Lesson note-5-Ch 14 Statistics ( Measure of Central Tendency)

Question 4:
The weights (in kg) of 8 children are
13.4, 10.6, 12.7, 17.2, 14.3, 15, 16.5, 9.8.
Find the median weight.
Solution:
By arranging the numbers in ascending order, We get
9.8, 1.6, 12.7, 13.4, 14.3, 15, 16.5, 17.2
We know that n = 8 which is even

1 ℎ +( +1) ℎ
Median = [ 2 2 ]
2 2
Median = ½ {4th term + 5th term)
By substituting the values
Median = ½ (13.4 + 14.3)
Median = ½ (27.7)
Median = 13.85kg
Therefore, the median weight is 13.85kg.

Question 5:
If 10, 13, 15, 18, x + 1, x + 3, 30, 32, 35, 41 are ten observations in an ascending order
with median 24, find the value of x.
Solution:
By arranging the numbers in ascending order,we get
10, 13, 15, 18, x + 1, x + 3, 30, 32, 35, 41
We know that n = 10 which is even
So we get

1 ℎ +( +1) ℎ
Median = [ 2 2 ]
2 2
Median = ½ {5th term + 6th term)
By substituting the values
Median = ½ (x + 1 + x + 3)
Median = ½ (2x + 4)
Median = x + 2
It is given that median = 24
So we get x + 2 = 24
x = 24 – 2 = 22
Therefore, the value of x is 22.

Question 6. The numbers 50, 42, 35, (2x + 10), (2x – 8), 12, 11, 8 have been written in
a descending order. If their median is 25, find the value of x.
Solution:
We know that no of terms= 8 which is even
It is given that median = 25

1 ℎ +( +1) ℎ
We can write it as Median = [ 2 2 ] = 25
2 2
By substituting the values ½ {(8/2)th term + (8/2 + 1)th term} = 25
So we get ½ {4th value + 5th value} = 25