Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > RD Sharma Solutions: Data Handling – II (Central Values Exercise 23.2)
Data Handling – II (Central Values Exercise 23.2) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download
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Page 1
1. A die was thrown 20 times and the following scores were recorded:
5, 2, 1, 3, 4, 4, 5, 6, 2, 2, 4, 5, 5, 6, 2, 2, 4, 5, 5, 1
Prepare the frequency table of the scores on the upper face of the die and find the
mean score.
Solution:
The frequency table for the given data is as follows:
x: 1 2 3 4 5 6
f: 2 5 1 4 6 2
To compute arithmetic mean we have to prepare the following table:
Scores (x
i
) Frequency (f
i
) x
i
f
i
1 2 2
2 5 10
3 1 3
4 4 16
5 6 30
6 2 12
Total S f
i
= 20 S f
i
x
i
Mean score = S f
i
x
i
/ S f
i
= 73/20
= 3.65
2. The daily wages (in Rs) of 15 workers in a factory are given below:
200, 180, 150, 150, 130, 180, 180, 200, 150, 130, 180, 180, 200, 150, 180
Prepare the frequency table and find the mean wage.
Solution:
Wages (x
i
) 130 150 180 200
Number of workers (f
i
) 2 4 6 3
To compute arithmetic mean we have to prepare the following table:
Page 2
1. A die was thrown 20 times and the following scores were recorded:
5, 2, 1, 3, 4, 4, 5, 6, 2, 2, 4, 5, 5, 6, 2, 2, 4, 5, 5, 1
Prepare the frequency table of the scores on the upper face of the die and find the
mean score.
Solution:
The frequency table for the given data is as follows:
x: 1 2 3 4 5 6
f: 2 5 1 4 6 2
To compute arithmetic mean we have to prepare the following table:
Scores (x
i
) Frequency (f
i
) x
i
f
i
1 2 2
2 5 10
3 1 3
4 4 16
5 6 30
6 2 12
Total S f
i
= 20 S f
i
x
i
Mean score = S f
i
x
i
/ S f
i
= 73/20
= 3.65
2. The daily wages (in Rs) of 15 workers in a factory are given below:
200, 180, 150, 150, 130, 180, 180, 200, 150, 130, 180, 180, 200, 150, 180
Prepare the frequency table and find the mean wage.
Solution:
Wages (x
i
) 130 150 180 200
Number of workers (f
i
) 2 4 6 3
To compute arithmetic mean we have to prepare the following table:
x
i
f
i
x
i
f
i
130 2 260
150 4 600
180 6 1080
200 3 600
Total S f
i
= N = 15 S f
i
x
i
= 2540
Mean score = S f
i
x
i
/ S f
i
= 2540/15
= 169.33
3. The following table shows the weights (in kg) of 15 workers in a factory:
Weight (in Kg) 60 63 66 72 75
Number of workers 4 5 3 1 2
Calculate the mean weight.
Solution:
Calculation of mean:
x
i
f
i
x
i
f
i
60 4 240
63 5 315
66 3 198
72 1 72
75 2 150
Total S f
i
= N = 15 S f
i
x
i
= 975
Mean score = S f
i
x
i
/ S f
i
= 975/15
= 65 kg
4. The ages (in years) of 50 students of a class in a school are given below:
Age (in years) 14 15 16 17 18
Number of students 15 14 10 8 3
Find the mean age.
Solution:
Page 3
1. A die was thrown 20 times and the following scores were recorded:
5, 2, 1, 3, 4, 4, 5, 6, 2, 2, 4, 5, 5, 6, 2, 2, 4, 5, 5, 1
Prepare the frequency table of the scores on the upper face of the die and find the
mean score.
Solution:
The frequency table for the given data is as follows:
x: 1 2 3 4 5 6
f: 2 5 1 4 6 2
To compute arithmetic mean we have to prepare the following table:
Scores (x
i
) Frequency (f
i
) x
i
f
i
1 2 2
2 5 10
3 1 3
4 4 16
5 6 30
6 2 12
Total S f
i
= 20 S f
i
x
i
Mean score = S f
i
x
i
/ S f
i
= 73/20
= 3.65
2. The daily wages (in Rs) of 15 workers in a factory are given below:
200, 180, 150, 150, 130, 180, 180, 200, 150, 130, 180, 180, 200, 150, 180
Prepare the frequency table and find the mean wage.
Solution:
Wages (x
i
) 130 150 180 200
Number of workers (f
i
) 2 4 6 3
To compute arithmetic mean we have to prepare the following table:
x
i
f
i
x
i
f
i
130 2 260
150 4 600
180 6 1080
200 3 600
Total S f
i
= N = 15 S f
i
x
i
= 2540
Mean score = S f
i
x
i
/ S f
i
= 2540/15
= 169.33
3. The following table shows the weights (in kg) of 15 workers in a factory:
Weight (in Kg) 60 63 66 72 75
Number of workers 4 5 3 1 2
Calculate the mean weight.
Solution:
Calculation of mean:
x
i
f
i
x
i
f
i
60 4 240
63 5 315
66 3 198
72 1 72
75 2 150
Total S f
i
= N = 15 S f
i
x
i
= 975
Mean score = S f
i
x
i
/ S f
i
= 975/15
= 65 kg
4. The ages (in years) of 50 students of a class in a school are given below:
Age (in years) 14 15 16 17 18
Number of students 15 14 10 8 3
Find the mean age.
Solution:
Calculation of mean:
x
i
f
i
x
i
f
i
14 15 210
15 14 210
16 10 160
17 8 136
18 3 54
Total S f
i
= N = 50 S f
i
x
i
= 770
Mean score = S f
i
x
i
/ S f
i
= 770/50
= 15.4 years
5. Calculate the mean for the following distribution:
x: 5 6 7 8 9
f: 4 8 14 11 3
Solution:
x
i
f
i
x
i
f
i
5 4 20
6 8 48
7 14 98
8 11 88
9 3 27
Total S f
i
= N = 40 S f
i
x
i
= 281
Mean score = S f
i
x
i
/ S f
i
= 281/40
= 7.025
6. Find the mean of the following data:
x: 19 21 23 25 27 29 31
f: 13 15 16 18 16 15 13
Solution:
Page 4
1. A die was thrown 20 times and the following scores were recorded:
5, 2, 1, 3, 4, 4, 5, 6, 2, 2, 4, 5, 5, 6, 2, 2, 4, 5, 5, 1
Prepare the frequency table of the scores on the upper face of the die and find the
mean score.
Solution:
The frequency table for the given data is as follows:
x: 1 2 3 4 5 6
f: 2 5 1 4 6 2
To compute arithmetic mean we have to prepare the following table:
Scores (x
i
) Frequency (f
i
) x
i
f
i
1 2 2
2 5 10
3 1 3
4 4 16
5 6 30
6 2 12
Total S f
i
= 20 S f
i
x
i
Mean score = S f
i
x
i
/ S f
i
= 73/20
= 3.65
2. The daily wages (in Rs) of 15 workers in a factory are given below:
200, 180, 150, 150, 130, 180, 180, 200, 150, 130, 180, 180, 200, 150, 180
Prepare the frequency table and find the mean wage.
Solution:
Wages (x
i
) 130 150 180 200
Number of workers (f
i
) 2 4 6 3
To compute arithmetic mean we have to prepare the following table:
x
i
f
i
x
i
f
i
130 2 260
150 4 600
180 6 1080
200 3 600
Total S f
i
= N = 15 S f
i
x
i
= 2540
Mean score = S f
i
x
i
/ S f
i
= 2540/15
= 169.33
3. The following table shows the weights (in kg) of 15 workers in a factory:
Weight (in Kg) 60 63 66 72 75
Number of workers 4 5 3 1 2
Calculate the mean weight.
Solution:
Calculation of mean:
x
i
f
i
x
i
f
i
60 4 240
63 5 315
66 3 198
72 1 72
75 2 150
Total S f
i
= N = 15 S f
i
x
i
= 975
Mean score = S f
i
x
i
/ S f
i
= 975/15
= 65 kg
4. The ages (in years) of 50 students of a class in a school are given below:
Age (in years) 14 15 16 17 18
Number of students 15 14 10 8 3
Find the mean age.
Solution:
Calculation of mean:
x
i
f
i
x
i
f
i
14 15 210
15 14 210
16 10 160
17 8 136
18 3 54
Total S f
i
= N = 50 S f
i
x
i
= 770
Mean score = S f
i
x
i
/ S f
i
= 770/50
= 15.4 years
5. Calculate the mean for the following distribution:
x: 5 6 7 8 9
f: 4 8 14 11 3
Solution:
x
i
f
i
x
i
f
i
5 4 20
6 8 48
7 14 98
8 11 88
9 3 27
Total S f
i
= N = 40 S f
i
x
i
= 281
Mean score = S f
i
x
i
/ S f
i
= 281/40
= 7.025
6. Find the mean of the following data:
x: 19 21 23 25 27 29 31
f: 13 15 16 18 16 15 13
Solution:
x
i
f
i
x
i
f
i
19 13 247
21 15 315
23 16 368
25 18 450
27 16 432
29 15 435
31 13 403
Total S f
i
= N = 106 S f
i
x
i
= 2650
Mean score = S f
i
x
i
/ S f
i
= 2650/106
= 25
7. The mean of the following data is 20.6. Find the value of p.
x: 10 15 p 25 3 5
f: 3 10 25 7 5
Solution:
x
i
f
i
x
i
f
i
10 3 30
15 10 150
P 25 25p
25 7 175
3 5 5 175
Total S f
i
= N = 50 S f
i
x
i
= 530 + 25p
Mean score = S f
i
x
i
/ S f
i
20.6 = 530 + 25p/50
530 + 25 p = 20.6 x 50
25 p = 1030 – 530
p = 500/25
p = 20
8. If the mean of the following data is 15, find p.
Page 5
1. A die was thrown 20 times and the following scores were recorded:
5, 2, 1, 3, 4, 4, 5, 6, 2, 2, 4, 5, 5, 6, 2, 2, 4, 5, 5, 1
Prepare the frequency table of the scores on the upper face of the die and find the
mean score.
Solution:
The frequency table for the given data is as follows:
x: 1 2 3 4 5 6
f: 2 5 1 4 6 2
To compute arithmetic mean we have to prepare the following table:
Scores (x
i
) Frequency (f
i
) x
i
f
i
1 2 2
2 5 10
3 1 3
4 4 16
5 6 30
6 2 12
Total S f
i
= 20 S f
i
x
i
Mean score = S f
i
x
i
/ S f
i
= 73/20
= 3.65
2. The daily wages (in Rs) of 15 workers in a factory are given below:
200, 180, 150, 150, 130, 180, 180, 200, 150, 130, 180, 180, 200, 150, 180
Prepare the frequency table and find the mean wage.
Solution:
Wages (x
i
) 130 150 180 200
Number of workers (f
i
) 2 4 6 3
To compute arithmetic mean we have to prepare the following table:
x
i
f
i
x
i
f
i
130 2 260
150 4 600
180 6 1080
200 3 600
Total S f
i
= N = 15 S f
i
x
i
= 2540
Mean score = S f
i
x
i
/ S f
i
= 2540/15
= 169.33
3. The following table shows the weights (in kg) of 15 workers in a factory:
Weight (in Kg) 60 63 66 72 75
Number of workers 4 5 3 1 2
Calculate the mean weight.
Solution:
Calculation of mean:
x
i
f
i
x
i
f
i
60 4 240
63 5 315
66 3 198
72 1 72
75 2 150
Total S f
i
= N = 15 S f
i
x
i
= 975
Mean score = S f
i
x
i
/ S f
i
= 975/15
= 65 kg
4. The ages (in years) of 50 students of a class in a school are given below:
Age (in years) 14 15 16 17 18
Number of students 15 14 10 8 3
Find the mean age.
Solution:
Calculation of mean:
x
i
f
i
x
i
f
i
14 15 210
15 14 210
16 10 160
17 8 136
18 3 54
Total S f
i
= N = 50 S f
i
x
i
= 770
Mean score = S f
i
x
i
/ S f
i
= 770/50
= 15.4 years
5. Calculate the mean for the following distribution:
x: 5 6 7 8 9
f: 4 8 14 11 3
Solution:
x
i
f
i
x
i
f
i
5 4 20
6 8 48
7 14 98
8 11 88
9 3 27
Total S f
i
= N = 40 S f
i
x
i
= 281
Mean score = S f
i
x
i
/ S f
i
= 281/40
= 7.025
6. Find the mean of the following data:
x: 19 21 23 25 27 29 31
f: 13 15 16 18 16 15 13
Solution:
x
i
f
i
x
i
f
i
19 13 247
21 15 315
23 16 368
25 18 450
27 16 432
29 15 435
31 13 403
Total S f
i
= N = 106 S f
i
x
i
= 2650
Mean score = S f
i
x
i
/ S f
i
= 2650/106
= 25
7. The mean of the following data is 20.6. Find the value of p.
x: 10 15 p 25 3 5
f: 3 10 25 7 5
Solution:
x
i
f
i
x
i
f
i
10 3 30
15 10 150
P 25 25p
25 7 175
3 5 5 175
Total S f
i
= N = 50 S f
i
x
i
= 530 + 25p
Mean score = S f
i
x
i
/ S f
i
20.6 = 530 + 25p/50
530 + 25 p = 20.6 x 50
25 p = 1030 – 530
p = 500/25
p = 20
8. If the mean of the following data is 15, find p.
x: 5 10 15 20 25
f: 6 p 6 10 5
Solution:
x
i
f
i
x
i
f
i
5 6 30
10 P 10p
15 6 90
20 10 200
25 5 125
Total S f
i
= 27 + p S f
i
x
i
= 445 + 10p
Mean score = S f
i
x
i
/ S f
i
15 = 445 + 10p/27 + p
445 + 10 p = 405 + 15p
5 p = 445 – 405
p = 40/5
p = 8
9. Find the value of p for the following distribution whose mean is 16.6
x: 8 12 15 p 20 25 30
f: 12 16 20 24 16 8 4
Solution:
x
i
f
i
x
i
f
i
8 12 96
12 16 192
15 20 300
P 24 24p
20 16 320
25 8 200
30 4 120
Total S f
i
= N = 100 S f
i
x
i
= 1228 + 24p
Mean score = S f
i
x
i
/ S f
i
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