RS AGGARWAL CLASS 9 CHAPTER 18 MEAN, MEDIAN AND MODE OF UNGROUPED DATA EXERCISE 18C

 EXERCISE 18C

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Question 1:

Find the median of
(i) 2, 10, 9, 9, 5, 2, 3, 7, 11
(ii) 15, 6, 16, 8, 22, 21, 9, 18, 25
(iii) 20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22
(iv) 7, 4, 2, 5, 1, 4, 0, 10, 3, 8, 5, 9, 2

Answer 1:

(i) Arranging the numbers in ascending order, we get:
      2, 2, 3, 5, 7, 9, 9, 10, 11
Here, n is 9, which is an odd number.
If n is an odd number, we have:
Median= Value of n+12th observation
Now,
Median=Value of 9+12th observation             =Value of the 5th observation             =7

(ii) Arranging the numbers in ascending order, we get:
6, 8, 9, 15, 16, 18, 21, 22, 25
Here, n is 9, which is an odd number.
If n is an odd number, we have:
Median= Value of n+12th observation
Now,
Median=Value of 9+12th observation             =Value of the 5th observation             =16

(iii) Arranging the numbers in ascending order, we get:
    6, 8, 9, 13, 15, 16, 18, 20, 21, 22, 25
Here, n is 11, which is an odd number.
If n is an odd number, we have:
Median= Value of n+12th observation
Now,
Median=Value of 11+12th observation             =Value of the 6th observation             =16

(iv) Arranging the numbers in ascending order, we get:
   0, 1, 2, 2, 3, 4, 4, 5, 5, 7, 8, 9, 10
Here, n is 13, which is an odd number.
If n is an odd number, we have:
Median= Value of n+12th observation
Now,
Median=Value of 13+12th observation             =Value of the 7th observation             =4

Question 2:

Find the median of
(i) 17, 19, 32, 10, 22, 21, 9, 35
(ii) 72, 63, 29, 51, 35, 60, 55, 91, 85, 82
(iii) 10, 75, 3, 15, 9, 47, 12, 48, 4, 81, 17, 27

Answer 2:

(i) Arranging the numbers in ascending order, we get:
9, 10, 17, 19, 21, 22, 32, 35
Here, n is 8, which is an even number.
If n is an even number, we have:
Median=Mean of n2th & n2+1th observations
Now,
Median =Mean of 82th & 82+1th observations              =Mean of the 4th & 5th observations              =1219+21              = 20

(ii) Arranging the numbers in ascending order, we get:
   29, 35, 51, 55, 60, 63, 72, 82, 85, 91
Here, n is 10, which is an even number.
If n is an even number, we have:
Median=Mean of n2th & n2+1th observations
Now,
Median =Mean of 102th & 102+1th observations              =Mean of the 5th & 6th observations              =1260+63              =61.5

(iii) Arranging the numbers in ascending order, we get:
    3, 4, 9, 10, 12, 15, 17, 27, 47, 48, 75, 81
Here, n is 12, which is an even number.
If n is an even number, we have:
Median=Mean of n2th & n2+1th observations
Now,
Median =Mean of 122th & 122+1th observations              =Mean of the 6th & 7th observations              =1215+17              =16

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Question 3:

The marks of 15 students in an examination are:
25, 19, 17, 24, 23, 29, 31, 40, 19, 20, 22, 26, 17, 35, 21.
Find the median score.

Answer 3:

Arranging the marks of 15 students in ascending order, we get:
17, 17, 19, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 35, 40
Here, n is 15, which is an odd number.
We know:
 Median=Value of (n+12)th observation
Thus, we have:
Median score=Value of (15+12) th observation                        =Value of the 8th observation                        =23

Question 4:

The heights (in cm) of 9 students of a class are 148, 144, 152, 155, 160, 147, 150, 149, 145.
Find the median height.

Answer 4:

Arranging the given data in ascending order:
144, 145, 147, 148, 149, 150, 152, 155, 160

Number of terms = 9 (odd)
 Median=n+12th term                  =9+12th term                  =5th term                  =149

Hence, the median height is 149.

Question 5:

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.

Answer 5:

Arranging the weights (in kg) in ascending order, we have:
9.8, 10.6, 12.7, 13.4, 14.3, 15, 16.5, 17.2
Here, n is 8, which is an even number.
Thus, we have:
Median=Mean of n2th & n2+1th observations
Median weight=Mean of 82th & 82+1th observations                           =Mean of 4th & 5th observations                           =1213.4+14.3                          =13.85               

Hence, the median weight is 13.85 kg.

Question 6:

The ages (in years) of 10 teachers in a school are:
32, 44, 53, 47, 37, 54, 34, 36, 40, 50.
Find the median age.

Answer 6:

Arranging the ages (in years) in ascending order, we have:
32, 34, 36, 37, 40, 44, 47, 50, 53, 54
Here, n is 10, which is an even number.
Thus, we have:
Median=Mean of n2th & n2+1th observations
Median age =Mean of 102th & 102+1th observations                                           = Mean of 5th & 6th observations                                           =1240+44                                           =42Hence, the median age is 42 years.

Question 7:

If 10, 13, 15, 18, x + 1, x + 3, 30, 32, 35, 41 are ten observation in an ascending order with median 24, find the value of x.

Answer 7:

10, 13, 15, 18, x+1, x+3, 30, 32, 35 and 41 are arranged in ascending order.
Median = 24
We have to find the value of x.
Here, n is 10, which is an even number.
Thus, we have:
Median=Mean of n2th & n2+1th observations
Median=Mean of 102th & 102+1th observations                                  =Mean of 5th & 6th observations                                  =12x+1+x+3                                  =122x+4                                  =(x+2)Given: Median=24x+2=24x=22

Question 8:

The following observations are arranged in ascending order:
26, 29, 42, 53, x, x + 2, 70, 75, 82, 93.
If the median is 65, find the value of x.

Answer 8:

Arranging the given data in ascending order:
26, 29, 42, 53, x, x + 2, 70, 75, 82, 93

Number of terms = 10 (even)

 Median=mean of n2th term and n2+1th term65=mean of 102th term and 102+1th term65=mean of 5th term and 6th term65=mean of x and x+265=x+x+2265×2=2x+2130=2x+22x=130-22x=128x=64

Hence, the value of x is 64.

Question 9:

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.

Answer 9:

Arranging the given data in ascending order:
8, 11, 12, (2x – 8), (2x + 10), 35, 42, 50

Number of terms = 8 (even)

 Median=mean of n2th term and n2+1th term25=mean of 82th term and 82+1th term25=mean of 4th term and 5th term25=mean of 2x-8 and 2x+1025=2x-8+2x+10225×2=4x+250=4x+24x=50-24x=48x=12

Hence, the value of x is 12.

Question 10:

Find the median of the data
46, 41, 77, 58, 35, 64, 87, 92, 33, 55, 90.
In the above data, if 41 and 55 are replaced by 61 and 75 respectively, what will be the new median?

Answer 10:

Arranging the given data in ascending order:
33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92

Number of terms = 11 (odd)

 Median=n+12th term                  =11+12th term                  =6th term                  =58

Hence, the median of the data is 58.

Now, In the above data, if 41 and 55 are replaced by 61 and 75 respectively.
Then, new data in ascending order is:
33, 35, 46, 58, 61, 64, 75, 77, 87, 90, 92

Number of terms = 11 (odd)

 Median=n+12th term                  =11+12th term                  =6th term                  =64

Hence, the new median of the data is 64.

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