Page 1 1. If the mean of 5 observation , 2, 4, 6 x x x x and 8 x , find the value of x. Sol: Mean of given observations = 11 = 55 = 5x + 20 5x = 55 20 5x = 35 x = x = 7 Hence, the value of x is 7. 2. If the mean of 25 observations is 27 and each observation is decreased by 7, what will be new mean? Sol: Mean of given observations = Mean of 25 observations = 27 Sum of 25 observations = 27 × 25 = 675 If 7 is subtracted from every number, then the sum = 675 (25 × 7) = 675 175 = 500 Then, new mean = = 20 Thus, the new mean will be 20. 3. Compute the mean for following data: Class 1 3 3 5 5 - 7 7 9 Frequency 12 22 27 19 Sol: The given data is shown as follows: Class Frequency (fi) Class mark (x i) fi xi 1 3 12 2 24 3 5 22 4 88 5 7 27 6 162 7 9 19 8 152 Total fi = 80 fi xi = 426 Page 2 1. If the mean of 5 observation , 2, 4, 6 x x x x and 8 x , find the value of x. Sol: Mean of given observations = 11 = 55 = 5x + 20 5x = 55 20 5x = 35 x = x = 7 Hence, the value of x is 7. 2. If the mean of 25 observations is 27 and each observation is decreased by 7, what will be new mean? Sol: Mean of given observations = Mean of 25 observations = 27 Sum of 25 observations = 27 × 25 = 675 If 7 is subtracted from every number, then the sum = 675 (25 × 7) = 675 175 = 500 Then, new mean = = 20 Thus, the new mean will be 20. 3. Compute the mean for following data: Class 1 3 3 5 5 - 7 7 9 Frequency 12 22 27 19 Sol: The given data is shown as follows: Class Frequency (fi) Class mark (x i) fi xi 1 3 12 2 24 3 5 22 4 88 5 7 27 6 162 7 9 19 8 152 Total fi = 80 fi xi = 426 The mean of given data is given by = i i i i i f x f = = 5.325 Thus, the mean of the following data is 5.325. 4. Find the mean using direct method: Class 0 10 10 20 20 30 30 40 40 50 50 60 Frequency 7 5 6 12 8 2 Sol: Class Frequency (fi) Mid values (x i) fi × xi 0 10 7 5 35 10 20 5 15 75 20 30 6 25 150 30 40 12 35 420 40 50 8 45 360 50 60 2 55 110 fi = 40 i i f x = 1150 Mean, = i i i f x f 1150 40 = 28.75 = 28.75 5. Find the mean of the following data, using direct method: Class 25 35 35 45 45 55 55 65 65 75 Frequency 6 10 8 12 4 Sol: Class Frequency (fi) Mid values (x i) (fi × xi) 25 35 6 30 180 35 45 10 40 400 45 55 8 50 400 55 65 12 60 720 65 75 4 70 280 fi = 40 i i f x = 1980 Page 3 1. If the mean of 5 observation , 2, 4, 6 x x x x and 8 x , find the value of x. Sol: Mean of given observations = 11 = 55 = 5x + 20 5x = 55 20 5x = 35 x = x = 7 Hence, the value of x is 7. 2. If the mean of 25 observations is 27 and each observation is decreased by 7, what will be new mean? Sol: Mean of given observations = Mean of 25 observations = 27 Sum of 25 observations = 27 × 25 = 675 If 7 is subtracted from every number, then the sum = 675 (25 × 7) = 675 175 = 500 Then, new mean = = 20 Thus, the new mean will be 20. 3. Compute the mean for following data: Class 1 3 3 5 5 - 7 7 9 Frequency 12 22 27 19 Sol: The given data is shown as follows: Class Frequency (fi) Class mark (x i) fi xi 1 3 12 2 24 3 5 22 4 88 5 7 27 6 162 7 9 19 8 152 Total fi = 80 fi xi = 426 The mean of given data is given by = i i i i i f x f = = 5.325 Thus, the mean of the following data is 5.325. 4. Find the mean using direct method: Class 0 10 10 20 20 30 30 40 40 50 50 60 Frequency 7 5 6 12 8 2 Sol: Class Frequency (fi) Mid values (x i) fi × xi 0 10 7 5 35 10 20 5 15 75 20 30 6 25 150 30 40 12 35 420 40 50 8 45 360 50 60 2 55 110 fi = 40 i i f x = 1150 Mean, = i i i f x f 1150 40 = 28.75 = 28.75 5. Find the mean of the following data, using direct method: Class 25 35 35 45 45 55 55 65 65 75 Frequency 6 10 8 12 4 Sol: Class Frequency (fi) Mid values (x i) (fi × xi) 25 35 6 30 180 35 45 10 40 400 45 55 8 50 400 55 65 12 60 720 65 75 4 70 280 fi = 40 i i f x = 1980 Mean, = i i i f x f = = 49.5 = 49.5 6. Find the mean of the following data, using direct method: Class 0 100 100 200 200 300 300 400 400 500 Frequency 6 9 15 12 8 Sol: Class Frequency (fi) Mid values (x i) (fi × xi) 0 - 100 6 50 300 100 200 9 150 1350 200 300 15 250 3750 300 400 12 350 4200 400 500 8 450 3600 fi = 50 i i f x = 13200 Mean, = i i i f x f = = 264 = 264 7. Using an appropriate method, find the mean of the following frequency distribution: Class 84 90 90 96 96 102 102 108 108 114 114 120 Frequency 8 10 16 23 12 11 Which method did you use, and why? Sol: Class Frequency (fi) Mid values (x i) (fi xi) 84 90 8 87 696 90 96 10 93 930 96 102 16 99 1584 102 108 23 105 2415 108 114 12 111 1332 114 120 11 117 1287 Total fi = 80 fi xi = 8244 The mean of the data is given by, Page 4 1. If the mean of 5 observation , 2, 4, 6 x x x x and 8 x , find the value of x. Sol: Mean of given observations = 11 = 55 = 5x + 20 5x = 55 20 5x = 35 x = x = 7 Hence, the value of x is 7. 2. If the mean of 25 observations is 27 and each observation is decreased by 7, what will be new mean? Sol: Mean of given observations = Mean of 25 observations = 27 Sum of 25 observations = 27 × 25 = 675 If 7 is subtracted from every number, then the sum = 675 (25 × 7) = 675 175 = 500 Then, new mean = = 20 Thus, the new mean will be 20. 3. Compute the mean for following data: Class 1 3 3 5 5 - 7 7 9 Frequency 12 22 27 19 Sol: The given data is shown as follows: Class Frequency (fi) Class mark (x i) fi xi 1 3 12 2 24 3 5 22 4 88 5 7 27 6 162 7 9 19 8 152 Total fi = 80 fi xi = 426 The mean of given data is given by = i i i i i f x f = = 5.325 Thus, the mean of the following data is 5.325. 4. Find the mean using direct method: Class 0 10 10 20 20 30 30 40 40 50 50 60 Frequency 7 5 6 12 8 2 Sol: Class Frequency (fi) Mid values (x i) fi × xi 0 10 7 5 35 10 20 5 15 75 20 30 6 25 150 30 40 12 35 420 40 50 8 45 360 50 60 2 55 110 fi = 40 i i f x = 1150 Mean, = i i i f x f 1150 40 = 28.75 = 28.75 5. Find the mean of the following data, using direct method: Class 25 35 35 45 45 55 55 65 65 75 Frequency 6 10 8 12 4 Sol: Class Frequency (fi) Mid values (x i) (fi × xi) 25 35 6 30 180 35 45 10 40 400 45 55 8 50 400 55 65 12 60 720 65 75 4 70 280 fi = 40 i i f x = 1980 Mean, = i i i f x f = = 49.5 = 49.5 6. Find the mean of the following data, using direct method: Class 0 100 100 200 200 300 300 400 400 500 Frequency 6 9 15 12 8 Sol: Class Frequency (fi) Mid values (x i) (fi × xi) 0 - 100 6 50 300 100 200 9 150 1350 200 300 15 250 3750 300 400 12 350 4200 400 500 8 450 3600 fi = 50 i i f x = 13200 Mean, = i i i f x f = = 264 = 264 7. Using an appropriate method, find the mean of the following frequency distribution: Class 84 90 90 96 96 102 102 108 108 114 114 120 Frequency 8 10 16 23 12 11 Which method did you use, and why? Sol: Class Frequency (fi) Mid values (x i) (fi xi) 84 90 8 87 696 90 96 10 93 930 96 102 16 99 1584 102 108 23 105 2415 108 114 12 111 1332 114 120 11 117 1287 Total fi = 80 fi xi = 8244 The mean of the data is given by, = i i i i i f x f = = 103.05 Thus, the mean of the following data is 103.05. 8. If the mean of the following frequency distribution is 24, find the value of p. Class 0 10 10 20 20 30 30 40 40 - 50 Frequency 3 4 P 3 2 Sol: The given data is shown as follows: Class Frequency (fi) Mid values (x i) (fi xi) 0 10 3 5 15 10 20 4 15 60 20 30 p 25 25p 30 40 3 35 105 40 50 2 45 90 Total fi = 12 + p fi xi = 270 + 25p The mean of the given data is given by, = i i i i i f x f 24 = 24 (12 + p) = 270 + 25p 288 + 24p = 270 + 25p 25p 24p = 288 270 p = 18 Hence, the value of p is 18. 9. The following distribution shows the daily pocket allowance of children of a locality. If the mean pocket allowance is 18 , find the missing frequency f. Daily pocket allowance 11 13 13 15 15 17 17 19 19 - 21 21 23 23 25 Page 5 1. If the mean of 5 observation , 2, 4, 6 x x x x and 8 x , find the value of x. Sol: Mean of given observations = 11 = 55 = 5x + 20 5x = 55 20 5x = 35 x = x = 7 Hence, the value of x is 7. 2. If the mean of 25 observations is 27 and each observation is decreased by 7, what will be new mean? Sol: Mean of given observations = Mean of 25 observations = 27 Sum of 25 observations = 27 × 25 = 675 If 7 is subtracted from every number, then the sum = 675 (25 × 7) = 675 175 = 500 Then, new mean = = 20 Thus, the new mean will be 20. 3. Compute the mean for following data: Class 1 3 3 5 5 - 7 7 9 Frequency 12 22 27 19 Sol: The given data is shown as follows: Class Frequency (fi) Class mark (x i) fi xi 1 3 12 2 24 3 5 22 4 88 5 7 27 6 162 7 9 19 8 152 Total fi = 80 fi xi = 426 The mean of given data is given by = i i i i i f x f = = 5.325 Thus, the mean of the following data is 5.325. 4. Find the mean using direct method: Class 0 10 10 20 20 30 30 40 40 50 50 60 Frequency 7 5 6 12 8 2 Sol: Class Frequency (fi) Mid values (x i) fi × xi 0 10 7 5 35 10 20 5 15 75 20 30 6 25 150 30 40 12 35 420 40 50 8 45 360 50 60 2 55 110 fi = 40 i i f x = 1150 Mean, = i i i f x f 1150 40 = 28.75 = 28.75 5. Find the mean of the following data, using direct method: Class 25 35 35 45 45 55 55 65 65 75 Frequency 6 10 8 12 4 Sol: Class Frequency (fi) Mid values (x i) (fi × xi) 25 35 6 30 180 35 45 10 40 400 45 55 8 50 400 55 65 12 60 720 65 75 4 70 280 fi = 40 i i f x = 1980 Mean, = i i i f x f = = 49.5 = 49.5 6. Find the mean of the following data, using direct method: Class 0 100 100 200 200 300 300 400 400 500 Frequency 6 9 15 12 8 Sol: Class Frequency (fi) Mid values (x i) (fi × xi) 0 - 100 6 50 300 100 200 9 150 1350 200 300 15 250 3750 300 400 12 350 4200 400 500 8 450 3600 fi = 50 i i f x = 13200 Mean, = i i i f x f = = 264 = 264 7. Using an appropriate method, find the mean of the following frequency distribution: Class 84 90 90 96 96 102 102 108 108 114 114 120 Frequency 8 10 16 23 12 11 Which method did you use, and why? Sol: Class Frequency (fi) Mid values (x i) (fi xi) 84 90 8 87 696 90 96 10 93 930 96 102 16 99 1584 102 108 23 105 2415 108 114 12 111 1332 114 120 11 117 1287 Total fi = 80 fi xi = 8244 The mean of the data is given by, = i i i i i f x f = = 103.05 Thus, the mean of the following data is 103.05. 8. If the mean of the following frequency distribution is 24, find the value of p. Class 0 10 10 20 20 30 30 40 40 - 50 Frequency 3 4 P 3 2 Sol: The given data is shown as follows: Class Frequency (fi) Mid values (x i) (fi xi) 0 10 3 5 15 10 20 4 15 60 20 30 p 25 25p 30 40 3 35 105 40 50 2 45 90 Total fi = 12 + p fi xi = 270 + 25p The mean of the given data is given by, = i i i i i f x f 24 = 24 (12 + p) = 270 + 25p 288 + 24p = 270 + 25p 25p 24p = 288 270 p = 18 Hence, the value of p is 18. 9. The following distribution shows the daily pocket allowance of children of a locality. If the mean pocket allowance is 18 , find the missing frequency f. Daily pocket allowance 11 13 13 15 15 17 17 19 19 - 21 21 23 23 25 Number of children 7 6 9 13 f 5 4 Sol: The given data is shown as follows: Daily pocket Number of children (fi) Class mark (xi) fi xi 11 13 7 12 84 13 15 6 14 84 15 17 9 16 144 17 19 13 18 234 19 21 f 20 20f 21 23 5 22 110 23 25 4 24 96 Total fi = 44 + f fi xi = 752 + 20f The mean of the given data is given by, = i i i i i f x f 18 = 18 (44 + f) = 752 + 20f 792 + 18f = 752 + 20f 20f 18f = 792 752 2f = 40 f = 20 Hence, the value of f is 20. 10. The mean of following frequency distribution is 54. Find the value of p. Class 0 20 20 40 40 60 60 80 80 100 Frequency 7 p 10 9 13 Sol: The given data is shown as follows: Class Frequency (fi) Class mark (x i) fi xi 0 20 7 10 70 20 40 p 30 30p 40 60 10 50 500 60 80 9 70 630 80 100 13 90 1170 Total fi = 39 + p fi xi = 2370 + 30pRead More

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