Exercise
5.3
1. Fill in the blanks.
(i) The median
of the data 12, 14, 23, 25, 34, 11, 42, 45, 32, 22, 44 is _________.
(ii) The
median of first ten even natural numbers is ________.
2. Find the median of the given data:
35, 25, 34, 36, 45, 18, 28.
Solution:
Arranging the given data in ascending order 18, 25, 28, 34, 35,
36, 45.
Here the number of observations n = 7, which is odd.
∴ Median = ( [n + 1] /
2)th term = ([7 + 1] / 2)th term
= (8 / 2)th term = 4th term
Hence Median = 34
3. The weekly sale of motor bikes in
a showroom for the past 14 weeks given below. 10, 6, 8, 3, 5, 6, 4, 7, 12, 13, 16,
10, 4, 7. Find the median of the data.
Solution:
Arranging the given data in ascending order 3, 4, 4, 5, 6, 6, 7,
7, 8, 10, 10, 12, 13, 16.
Here number of data n
= 14, which is even
∴ Median = 1/2 {(n / 2)th term + (n / 2 + 1)th term
= 1/2 {(14 / 2)th term + (14 / 2 + 1)th term
= 1/2 {7th
term + 8th term}
= 1/2 {7 + 7} = 1/2 (14)
= 7
∴ Median = 7
4.
Find the median of the 10 observations 36, 33, 45, 28, 39, 45, 54, 23, 56, 25. If
another observation 35 is added to the above data, what would be the new median?
Solution:
Arranging the given 10 observations in ascending order.23, 25,
28, 33, 36, 39, 45, 45, 54, 56. Here number of data n = 10, which is even
∴ Median = 1/2 {(n / 2)th term + (n / 2 + 1)th term
= 1/2 {(10 / 2)th term + (10 / 2 + 1)th term
= 1/2 {5th
term + 6th term}
= 1/2 {36 + 39}
= 1/2 (75) = 37.5
∴ Median = 37.5
If 35 is added to the above data then it will be the 5th term
then number of data n = 11, odd
∴ Median = ([n + 1] /
2)th term = ([11 + 1] / 2)th term
= (12 / 2)th
term = 6th term
New median = 36
Objective type questions
5.
If the median of a, 2a, 4a, 6a, 9a is 8, then find the value of a
is
(i) 8
(ii) 6
(iii) 2
(iv) 10
[Answer: (iii) 2]
Solution: a, 2a, 4a, 6a, 9a
Median = 4a = 8
a = 2
6.
The median of the data 24, 29, 34, 38, 35 and 30, is_____________
(i) 29
(ii) 30
(iii) 34
(iv) 32
[Answer: (iv) 32]
Solution: 24, 29, 30, 34, 35, 38
Median = [30 + 34] / 2 = 64 / 2 = 32
7.
The median first 6 odd natural numbers is ________
(i) 6
(ii) 7
(iii) 8
(iv) 14
[Answer: (i) 6]
Solution: 1, 3, 5, 7, 9, 11
Median = [5 + 7] / 2 = 12 / 2 = 6
ANSWERS:
Exercise 5.3
1. (i) 25 (ii). 11
2. 34
3. 7
4. 37.5 ; 36
Objective type questions:
5. (iii) 2
6. (iv) 32
7. (i) 6
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