Selina Concise Class 9 Maths Chapter 19 Mean and Median Exercise 19B Solutions
EXERCISE – 19B
(1) Find the median of:
(i) 25, 16, 26, 16, 32, 31, 19, 28 and 35
Solution:
First we will arrange given numbers in ascending order
16, 16, 19, 25, 26, 28, 31, 32 and 35
Total numbers are 9.
And 9 is the odd number
∴ n = 9 (odd)
So, we will use the formula,
M = (n +1/2)th term
= (9 + 1/2)th term
M = (10/2)th term
Median = 5th term.
Median = 26
(ii) 241, 243, 347, 350, 327, 299, 261, 292, 271, 258, and 257.
Solution:
First we will arrange given number in ascending order.
241, 243, 257, 258, 261, 271, 292, 299, 327, 347, 350.
Total numbers are 11 and 11 is the odd number.
∴ n = 11 (odd)
So, we will use the formula,
M = (n +1/2)th term
M = (11 + 1/2)th term
= (12/2)th term
= 6th term
Median = 271
(iii) 63, 17, 50, 9, 25, 43, 21, 50, 14, and 34.
Solution:
First we will arrange given numbers in ascending order
9, 14, 17, 21, 25, 34, 43, 50, 50, 63
Total numbers are 10 and 10 is the even number
∴ n = 10 (even)
So, we will use the formula,
M = 25 + 34/2
M = 59/2
Median = 29.5
(iv) 233, 173, 189, 208, 194, 194, 185, 200 and 220.
Solution:
First we will arrange given numbers in ascending order.
173, 185, 189, 194, 194, 200, 204, 208, 220, 223.
Total numbers are 10 and 10 is the even number.
∴ n = 10 (even)
So, we will use the formula,
Median = 194 + 200/2
Median = 394/2
Median = 197
(2) The following data have been arranged in ascending order. If their median is 63, find the value of x.
34, 37, 53, 55, x, x + 2, 77, 83, 89 and 100.
Solution:
The given numbers are –
34, 37, 53, 55, x, x + 2, 77, 83, 89 and 100.
Total numbers are 10 and 10 is the even number.
∴ n = 10 (even)
Now,
We will use the formula,
Median = 2x + 2/2
= 2 ( x + 1)/2
Median = x + 1
63 = x + 1
63 – 1 = x
62 = x
∴ x = 62
(3) In 10 numbers, arranged in increasing order, the 7th number is increased by 8, how much will the median be changed?
Solution:
Let 10 numbers are –
X1, x2, x3, ——— x10
The 7th number is increased by 8.
X1, x2, x3, ———– (x7 + 8), x8, x9, x10.
Median = x5 + x6/ 2
∴ Median remains Same.
Median will not changed.
(4) out of 10 students, who appears in a test, three secured less than 30 marks and 3 secured more than 75 marks, The marks secured by the remaining 4 Students are 35, 48, 66 and 40. Find the median score of the whole group.
Solution:
Let, The 10 students are
X1, x2, x3, x4, x5, x6, x7, x8, x9 and x10.
∴ The three students Secured less than 30 marks
X1, x2, x3 = 30.
∴ The 3 Students secured more than 75 marks.
X8, x9, x10 = 75.
And remaining 4 students Secured 35, 48, 66 and 40 marks.
X4, x5, x6, x7 = 35, 48, 66, and 40.
∴ n = 10 (even)
Now,
Median = 40 + 48/2
= 88/2
Median = 44
(5) The median of observations 10, 11, 13, 17, x + 5, 20, 22, 24 and 53 ( arranged in ascending order) is 18; find the value of x.
Solution:
Given numbers are –
10, 11, 13, 17, x + s, 20, 22, 24 and 53.
∴ n = 9 (odd)
Here is your solution of Selina Concise Class 9 Maths Chapter 19 Mean and Median Exercise 19B
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