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Data Handling – II (Central Values Exercise 23.3) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download
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Page 1
Find the median of the following data (1 – 8)
1. 83, 37, 70, 29, 45, 63, 41, 70, 34, 54
Solution:
First we have to arrange given data into ascending order,
29, 34, 37, 41, 45, 54, 63, 70, 70, 83
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (45 + 54)/2
= 49.5
Hence median for given data = 49.5
2. 133, 73, 89, 108, 94,104, 94, 85, 100, 120
Solution:
First we have to arrange given data into ascending order,
73, 85, 89, 94, 100, 104, 108, 120, 133
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (94 + 100)/2
= 97
Hence median for given data = 97
3. 31, 38, 27, 28, 36, 25, 35, 40
Solution:
First we have to arrange given data into ascending order
25, 27, 28, 31, 35, 36, 38, 40
Given number of observations, n = 8 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 4
th
term + value of 5
th
term)/2
= (31 + 35)/2
Page 2
Find the median of the following data (1 – 8)
1. 83, 37, 70, 29, 45, 63, 41, 70, 34, 54
Solution:
First we have to arrange given data into ascending order,
29, 34, 37, 41, 45, 54, 63, 70, 70, 83
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (45 + 54)/2
= 49.5
Hence median for given data = 49.5
2. 133, 73, 89, 108, 94,104, 94, 85, 100, 120
Solution:
First we have to arrange given data into ascending order,
73, 85, 89, 94, 100, 104, 108, 120, 133
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (94 + 100)/2
= 97
Hence median for given data = 97
3. 31, 38, 27, 28, 36, 25, 35, 40
Solution:
First we have to arrange given data into ascending order
25, 27, 28, 31, 35, 36, 38, 40
Given number of observations, n = 8 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 4
th
term + value of 5
th
term)/2
= (31 + 35)/2
= 33
Hence median for given data = 33
4. 15, 6, 16, 8, 22, 21, 9, 18, 25
Solution:
First we have to arrange given data into ascending order
6, 8, 9, 15, 16, 18, 21, 22, 25
Given number of observations, n = 9 (odd)
Therefore median = ((n+1)/2)
th
term
Median = value of 5
th
term
= 16
5. 41, 43,127, 99, 71, 92, 71, 58, 57
Solution:
First we have to arrange given data into ascending order
41, 43, 57, 58, 71, 71, 92, 99, 127
Given number of observations, n = 9 (odd)
Therefore median = ((n+1)/2)
th
term
Median = value of 5
th
term
= 71
6. 25, 34, 31, 23, 22, 26, 35, 29, 20, 32
Solution:
First we have to arrange given data into ascending order,
20, 22, 23, 25, 26, 29, 31, 32, 34, 35
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (26 + 29)/2
= 27.5
Hence median for given data = 27.5
7. 12, 17, 3, 14, 5, 8, 7, 15
Page 3
Find the median of the following data (1 – 8)
1. 83, 37, 70, 29, 45, 63, 41, 70, 34, 54
Solution:
First we have to arrange given data into ascending order,
29, 34, 37, 41, 45, 54, 63, 70, 70, 83
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (45 + 54)/2
= 49.5
Hence median for given data = 49.5
2. 133, 73, 89, 108, 94,104, 94, 85, 100, 120
Solution:
First we have to arrange given data into ascending order,
73, 85, 89, 94, 100, 104, 108, 120, 133
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (94 + 100)/2
= 97
Hence median for given data = 97
3. 31, 38, 27, 28, 36, 25, 35, 40
Solution:
First we have to arrange given data into ascending order
25, 27, 28, 31, 35, 36, 38, 40
Given number of observations, n = 8 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 4
th
term + value of 5
th
term)/2
= (31 + 35)/2
= 33
Hence median for given data = 33
4. 15, 6, 16, 8, 22, 21, 9, 18, 25
Solution:
First we have to arrange given data into ascending order
6, 8, 9, 15, 16, 18, 21, 22, 25
Given number of observations, n = 9 (odd)
Therefore median = ((n+1)/2)
th
term
Median = value of 5
th
term
= 16
5. 41, 43,127, 99, 71, 92, 71, 58, 57
Solution:
First we have to arrange given data into ascending order
41, 43, 57, 58, 71, 71, 92, 99, 127
Given number of observations, n = 9 (odd)
Therefore median = ((n+1)/2)
th
term
Median = value of 5
th
term
= 71
6. 25, 34, 31, 23, 22, 26, 35, 29, 20, 32
Solution:
First we have to arrange given data into ascending order,
20, 22, 23, 25, 26, 29, 31, 32, 34, 35
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (26 + 29)/2
= 27.5
Hence median for given data = 27.5
7. 12, 17, 3, 14, 5, 8, 7, 15
Solution:
First we have to arrange given data into ascending order,
3, 5, 7, 8, 12, 14, 15, 17
Given number of observations, n = 8 (even)
Therefore median = (n/2)
th
term + ((n +1)/2)
th
term
Median = (value of 4
th
term + value of 5
th
term)/2
= (8 + 12)/2
= 10
Hence median for given data = 10
8. 92, 35, 67, 85, 72, 81, 56, 51, 42, 69
Solution:
First we have to arrange given data into ascending order,
35, 42, 51, 56, 67, 69, 72, 81, 85, 92
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (67 + 69)/2
= 68
Hence median for given data = 68
9. Numbers 50, 42, 35, 2x +10, 2x – 8, 12, 11, 8, 6 are written in descending order and
their median is 25, find x.
Solution:
Here, the number of observations n is 9.
Since n is odd, the median is the n+12th observation, i.e., the 5
th
observation.
As the numbers are arranged in the descending order, we therefore observe from the
last.
Median = 5
th
observation.
=> 25 = 2x – 8
=> 2x = 25 + 8
=> 2x = 33
=> x = (33/2)
x = 16.5
Page 4
Find the median of the following data (1 – 8)
1. 83, 37, 70, 29, 45, 63, 41, 70, 34, 54
Solution:
First we have to arrange given data into ascending order,
29, 34, 37, 41, 45, 54, 63, 70, 70, 83
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (45 + 54)/2
= 49.5
Hence median for given data = 49.5
2. 133, 73, 89, 108, 94,104, 94, 85, 100, 120
Solution:
First we have to arrange given data into ascending order,
73, 85, 89, 94, 100, 104, 108, 120, 133
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (94 + 100)/2
= 97
Hence median for given data = 97
3. 31, 38, 27, 28, 36, 25, 35, 40
Solution:
First we have to arrange given data into ascending order
25, 27, 28, 31, 35, 36, 38, 40
Given number of observations, n = 8 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 4
th
term + value of 5
th
term)/2
= (31 + 35)/2
= 33
Hence median for given data = 33
4. 15, 6, 16, 8, 22, 21, 9, 18, 25
Solution:
First we have to arrange given data into ascending order
6, 8, 9, 15, 16, 18, 21, 22, 25
Given number of observations, n = 9 (odd)
Therefore median = ((n+1)/2)
th
term
Median = value of 5
th
term
= 16
5. 41, 43,127, 99, 71, 92, 71, 58, 57
Solution:
First we have to arrange given data into ascending order
41, 43, 57, 58, 71, 71, 92, 99, 127
Given number of observations, n = 9 (odd)
Therefore median = ((n+1)/2)
th
term
Median = value of 5
th
term
= 71
6. 25, 34, 31, 23, 22, 26, 35, 29, 20, 32
Solution:
First we have to arrange given data into ascending order,
20, 22, 23, 25, 26, 29, 31, 32, 34, 35
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (26 + 29)/2
= 27.5
Hence median for given data = 27.5
7. 12, 17, 3, 14, 5, 8, 7, 15
Solution:
First we have to arrange given data into ascending order,
3, 5, 7, 8, 12, 14, 15, 17
Given number of observations, n = 8 (even)
Therefore median = (n/2)
th
term + ((n +1)/2)
th
term
Median = (value of 4
th
term + value of 5
th
term)/2
= (8 + 12)/2
= 10
Hence median for given data = 10
8. 92, 35, 67, 85, 72, 81, 56, 51, 42, 69
Solution:
First we have to arrange given data into ascending order,
35, 42, 51, 56, 67, 69, 72, 81, 85, 92
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (67 + 69)/2
= 68
Hence median for given data = 68
9. Numbers 50, 42, 35, 2x +10, 2x – 8, 12, 11, 8, 6 are written in descending order and
their median is 25, find x.
Solution:
Here, the number of observations n is 9.
Since n is odd, the median is the n+12th observation, i.e., the 5
th
observation.
As the numbers are arranged in the descending order, we therefore observe from the
last.
Median = 5
th
observation.
=> 25 = 2x – 8
=> 2x = 25 + 8
=> 2x = 33
=> x = (33/2)
x = 16.5
10. Find the median of the following observations: 46, 64, 87, 41, 58, 77, 35, 90, 55, 92,
33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?
Solution:
Arranging the given data in ascending order, we have:
33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92
Here, the number of observations n is 11 (odd).
Since the number of observations is odd, therefore,
Therefore median = ((n+1)/2)
th
term
Median = value of 5
th
term
= 58.
Hence, median = 58.
If 92 is replaced by 99 and 41 by 43, then the new observations arranged in ascending
order are:
33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99
New median = Value of the 6
th
observation = 58.
11. Find the median of the following data: 41, 43, 127, 99, 61, 92, 71, 58, 57, If 58 is
replaced by 85, what will be the new median?
Solution:
Arranging the given data in ascending order, we have:
41, 43, 57, 58, 61, 71, 92, 99,127
Here, the number of observations, n, is 9(odd).
Therefore median = ((n+1)/2)
th
term
Median = value of 5
th
term
Hence, the median = 61.
If 58 is replaced by 85, then the new observations arranged in ascending order are:
41, 43, 57, 61, 71, 85, 92, 99, 12
New median = Value of the 5
th
observation = 71.
12. The weights (in kg) of 15 students are: 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44,
45, 42, 30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg,
find the new median.
Solution:
Arranging the given data in ascending order, we have:
Page 5
Find the median of the following data (1 – 8)
1. 83, 37, 70, 29, 45, 63, 41, 70, 34, 54
Solution:
First we have to arrange given data into ascending order,
29, 34, 37, 41, 45, 54, 63, 70, 70, 83
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (45 + 54)/2
= 49.5
Hence median for given data = 49.5
2. 133, 73, 89, 108, 94,104, 94, 85, 100, 120
Solution:
First we have to arrange given data into ascending order,
73, 85, 89, 94, 100, 104, 108, 120, 133
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (94 + 100)/2
= 97
Hence median for given data = 97
3. 31, 38, 27, 28, 36, 25, 35, 40
Solution:
First we have to arrange given data into ascending order
25, 27, 28, 31, 35, 36, 38, 40
Given number of observations, n = 8 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 4
th
term + value of 5
th
term)/2
= (31 + 35)/2
= 33
Hence median for given data = 33
4. 15, 6, 16, 8, 22, 21, 9, 18, 25
Solution:
First we have to arrange given data into ascending order
6, 8, 9, 15, 16, 18, 21, 22, 25
Given number of observations, n = 9 (odd)
Therefore median = ((n+1)/2)
th
term
Median = value of 5
th
term
= 16
5. 41, 43,127, 99, 71, 92, 71, 58, 57
Solution:
First we have to arrange given data into ascending order
41, 43, 57, 58, 71, 71, 92, 99, 127
Given number of observations, n = 9 (odd)
Therefore median = ((n+1)/2)
th
term
Median = value of 5
th
term
= 71
6. 25, 34, 31, 23, 22, 26, 35, 29, 20, 32
Solution:
First we have to arrange given data into ascending order,
20, 22, 23, 25, 26, 29, 31, 32, 34, 35
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (26 + 29)/2
= 27.5
Hence median for given data = 27.5
7. 12, 17, 3, 14, 5, 8, 7, 15
Solution:
First we have to arrange given data into ascending order,
3, 5, 7, 8, 12, 14, 15, 17
Given number of observations, n = 8 (even)
Therefore median = (n/2)
th
term + ((n +1)/2)
th
term
Median = (value of 4
th
term + value of 5
th
term)/2
= (8 + 12)/2
= 10
Hence median for given data = 10
8. 92, 35, 67, 85, 72, 81, 56, 51, 42, 69
Solution:
First we have to arrange given data into ascending order,
35, 42, 51, 56, 67, 69, 72, 81, 85, 92
Given number of observations, n = 10 (even)
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
= (67 + 69)/2
= 68
Hence median for given data = 68
9. Numbers 50, 42, 35, 2x +10, 2x – 8, 12, 11, 8, 6 are written in descending order and
their median is 25, find x.
Solution:
Here, the number of observations n is 9.
Since n is odd, the median is the n+12th observation, i.e., the 5
th
observation.
As the numbers are arranged in the descending order, we therefore observe from the
last.
Median = 5
th
observation.
=> 25 = 2x – 8
=> 2x = 25 + 8
=> 2x = 33
=> x = (33/2)
x = 16.5
10. Find the median of the following observations: 46, 64, 87, 41, 58, 77, 35, 90, 55, 92,
33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?
Solution:
Arranging the given data in ascending order, we have:
33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92
Here, the number of observations n is 11 (odd).
Since the number of observations is odd, therefore,
Therefore median = ((n+1)/2)
th
term
Median = value of 5
th
term
= 58.
Hence, median = 58.
If 92 is replaced by 99 and 41 by 43, then the new observations arranged in ascending
order are:
33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99
New median = Value of the 6
th
observation = 58.
11. Find the median of the following data: 41, 43, 127, 99, 61, 92, 71, 58, 57, If 58 is
replaced by 85, what will be the new median?
Solution:
Arranging the given data in ascending order, we have:
41, 43, 57, 58, 61, 71, 92, 99,127
Here, the number of observations, n, is 9(odd).
Therefore median = ((n+1)/2)
th
term
Median = value of 5
th
term
Hence, the median = 61.
If 58 is replaced by 85, then the new observations arranged in ascending order are:
41, 43, 57, 61, 71, 85, 92, 99, 12
New median = Value of the 5
th
observation = 71.
12. The weights (in kg) of 15 students are: 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44,
45, 42, 30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg,
find the new median.
Solution:
Arranging the given data in ascending order, we have:
27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 44, 45
Here, the number of observations n is 15(odd).
Since the number of observations is odd, therefore,
Therefore median = ((n+1)/2)
th
term
Median = value of 8
th
term
Hence, median = 35 kg.
If 44 kg is replaced by 46 kg and 27 kg by 25 kg, then the new observations arranged in
ascending order are:
25, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 45, 46
? New median = Value of the 8
th
observation = 35 kg.
13. The following observations have been arranged in ascending order. If the median
of the data is 63, find the value of x: 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95
Solution:
Here, the number of observations n is 10. Since n is even,
Therefore median = (n/2)
th
term + ((n + 1)/2)
th
term
Median = (value of 5
th
term + value of 6
th
term)/2
63 = x + (x + 2)/2
63 = (2x + 2)/2
63 = 2 (x + 1)/2
63 = x + 1
x = 63 – 1
x = 62
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The "RD Sharma Solutions: Data Handling – II (Central Values Exercise 23.3) Class 7 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 7 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study RD Sharma Solutions: Data Handling – II (Central Values Exercise 23.3) on the App
Students of Class 7 can study RD Sharma Solutions: Data Handling – II (Central Values Exercise 23.3) alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the RD Sharma Solutions: Data Handling – II (Central Values Exercise 23.3),
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of RD Sharma Solutions: Data Handling – II (Central Values Exercise 23.3) is prepared as per the latest Class 7 syllabus.
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