Page 1 1. Find the mean, median and mode of the following data: Class 0 10 10 20 20 30 30 40 40 50 50 60 60 70 Frequency 4 4 7 10 12 8 5 Sol: To find the mean let us put the data in the table given below: Class Frequency (fi) Class mark (x i) fi xi 0 10 4 5 20 10 20 4 15 60 20 30 7 25 175 30 40 10 35 350 40 50 12 45 540 50 60 8 55 440 60 70 5 65 325 Total fi = 50 fi xi = 1910 Mean = i i i i i f x f = = 38.2 Thus, the mean of the given data is 38.2. Now, to find the median let us put the data in the table given below: Class Frequency (fi) Cumulative Frequency (cf) 0 10 4 4 10 20 4 8 20 30 7 15 30 40 10 25 40 50 12 37 50 60 8 45 60 70 5 50 Total N = = 50 Now, N = 50 = 25. The cumulative frequency just greater than 25 is 37 and the corresponding class is 40 50. Thus, the median class is 40 50. l = 40, h = 10, N = 50, f = 12 and cf = 25. Now, Median = l + × h Page 2 1. Find the mean, median and mode of the following data: Class 0 10 10 20 20 30 30 40 40 50 50 60 60 70 Frequency 4 4 7 10 12 8 5 Sol: To find the mean let us put the data in the table given below: Class Frequency (fi) Class mark (x i) fi xi 0 10 4 5 20 10 20 4 15 60 20 30 7 25 175 30 40 10 35 350 40 50 12 45 540 50 60 8 55 440 60 70 5 65 325 Total fi = 50 fi xi = 1910 Mean = i i i i i f x f = = 38.2 Thus, the mean of the given data is 38.2. Now, to find the median let us put the data in the table given below: Class Frequency (fi) Cumulative Frequency (cf) 0 10 4 4 10 20 4 8 20 30 7 15 30 40 10 25 40 50 12 37 50 60 8 45 60 70 5 50 Total N = = 50 Now, N = 50 = 25. The cumulative frequency just greater than 25 is 37 and the corresponding class is 40 50. Thus, the median class is 40 50. l = 40, h = 10, N = 50, f = 12 and cf = 25. Now, Median = l + × h = 40 + × 10 = 40 Thus, the median is 40. We know that, Mode = 3(median) 2(mean) = 3 × 40 2 × 38.2 = 120 76.4 = 43.6 Hence, Mean = 38.2, Median = 40 and Mode = 43.6 2. Find the mean, median and mode of the following data: Class 0 20 20 40 40 60 60 80 80 100 100 120 120 140 Frequency 6 8 10 12 6 5 3 Sol: To find the mean let us put the data in the table given below: Class Frequency (fi) Class mark (x i) fi xi 0 20 6 10 60 20 40 8 30 240 40 60 10 50 500 60 80 12 70 840 80 100 6 90 540 100 120 5 110 550 120 140 3 130 390 Total fi = 50 fi xi = 3120 Mean = i i i i i f x f = = 62.4 Thus, the mean of the given data is 62.4. Now, to find the median let us put the data in the table given below: Class Frequency (fi) Cumulative Frequency (cf) 0 20 6 6 20 40 8 14 40 60 10 24 60 80 12 36 80 100 6 42 100 120 5 47 120 140 3 50 Total N = = 50 Page 3 1. Find the mean, median and mode of the following data: Class 0 10 10 20 20 30 30 40 40 50 50 60 60 70 Frequency 4 4 7 10 12 8 5 Sol: To find the mean let us put the data in the table given below: Class Frequency (fi) Class mark (x i) fi xi 0 10 4 5 20 10 20 4 15 60 20 30 7 25 175 30 40 10 35 350 40 50 12 45 540 50 60 8 55 440 60 70 5 65 325 Total fi = 50 fi xi = 1910 Mean = i i i i i f x f = = 38.2 Thus, the mean of the given data is 38.2. Now, to find the median let us put the data in the table given below: Class Frequency (fi) Cumulative Frequency (cf) 0 10 4 4 10 20 4 8 20 30 7 15 30 40 10 25 40 50 12 37 50 60 8 45 60 70 5 50 Total N = = 50 Now, N = 50 = 25. The cumulative frequency just greater than 25 is 37 and the corresponding class is 40 50. Thus, the median class is 40 50. l = 40, h = 10, N = 50, f = 12 and cf = 25. Now, Median = l + × h = 40 + × 10 = 40 Thus, the median is 40. We know that, Mode = 3(median) 2(mean) = 3 × 40 2 × 38.2 = 120 76.4 = 43.6 Hence, Mean = 38.2, Median = 40 and Mode = 43.6 2. Find the mean, median and mode of the following data: Class 0 20 20 40 40 60 60 80 80 100 100 120 120 140 Frequency 6 8 10 12 6 5 3 Sol: To find the mean let us put the data in the table given below: Class Frequency (fi) Class mark (x i) fi xi 0 20 6 10 60 20 40 8 30 240 40 60 10 50 500 60 80 12 70 840 80 100 6 90 540 100 120 5 110 550 120 140 3 130 390 Total fi = 50 fi xi = 3120 Mean = i i i i i f x f = = 62.4 Thus, the mean of the given data is 62.4. Now, to find the median let us put the data in the table given below: Class Frequency (fi) Cumulative Frequency (cf) 0 20 6 6 20 40 8 14 40 60 10 24 60 80 12 36 80 100 6 42 100 120 5 47 120 140 3 50 Total N = = 50 Now, N = 50 = 25. The cumulative frequency just greater than 25 is 36 and the corresponding class is 60 80. Thus, the median class is 60 80. l = 60, h = 20, N = 50, f = 12 and cf = 24. Now, Median = l + × h = 60 + × 20 = 60 + 1.67 = 61.67 Thus, the median is 61.67. We know that, Mode = 3(median) 2(mean) = 3 × 61.67 2 × 62.4 = 185.01 124.8 = 60.21 Hence, Mean = 62.4, Median = 61.67 and Mode = 60.21 3. Find the mean, median and mode of the following data: Class 0 50 50 100 100 150 150 200 200 250 250 300 300 - 350 Frequency 2 3 5 6 5 3 1 Sol: To find the mean let us put the data in the table given below: Class Frequency (fi) Class mark (x i) fi xi 0 50 2 25 50 50 100 3 75 225 100 150 5 125 625 150 200 6 175 1050 200 250 5 225 1125 250 300 3 275 825 300 350 1 325 325 Total fi = 25 fi xi = 4225 Mean = i i i i i f x f = = 169 Thus, mean of the given data is 169. Page 4 1. Find the mean, median and mode of the following data: Class 0 10 10 20 20 30 30 40 40 50 50 60 60 70 Frequency 4 4 7 10 12 8 5 Sol: To find the mean let us put the data in the table given below: Class Frequency (fi) Class mark (x i) fi xi 0 10 4 5 20 10 20 4 15 60 20 30 7 25 175 30 40 10 35 350 40 50 12 45 540 50 60 8 55 440 60 70 5 65 325 Total fi = 50 fi xi = 1910 Mean = i i i i i f x f = = 38.2 Thus, the mean of the given data is 38.2. Now, to find the median let us put the data in the table given below: Class Frequency (fi) Cumulative Frequency (cf) 0 10 4 4 10 20 4 8 20 30 7 15 30 40 10 25 40 50 12 37 50 60 8 45 60 70 5 50 Total N = = 50 Now, N = 50 = 25. The cumulative frequency just greater than 25 is 37 and the corresponding class is 40 50. Thus, the median class is 40 50. l = 40, h = 10, N = 50, f = 12 and cf = 25. Now, Median = l + × h = 40 + × 10 = 40 Thus, the median is 40. We know that, Mode = 3(median) 2(mean) = 3 × 40 2 × 38.2 = 120 76.4 = 43.6 Hence, Mean = 38.2, Median = 40 and Mode = 43.6 2. Find the mean, median and mode of the following data: Class 0 20 20 40 40 60 60 80 80 100 100 120 120 140 Frequency 6 8 10 12 6 5 3 Sol: To find the mean let us put the data in the table given below: Class Frequency (fi) Class mark (x i) fi xi 0 20 6 10 60 20 40 8 30 240 40 60 10 50 500 60 80 12 70 840 80 100 6 90 540 100 120 5 110 550 120 140 3 130 390 Total fi = 50 fi xi = 3120 Mean = i i i i i f x f = = 62.4 Thus, the mean of the given data is 62.4. Now, to find the median let us put the data in the table given below: Class Frequency (fi) Cumulative Frequency (cf) 0 20 6 6 20 40 8 14 40 60 10 24 60 80 12 36 80 100 6 42 100 120 5 47 120 140 3 50 Total N = = 50 Now, N = 50 = 25. The cumulative frequency just greater than 25 is 36 and the corresponding class is 60 80. Thus, the median class is 60 80. l = 60, h = 20, N = 50, f = 12 and cf = 24. Now, Median = l + × h = 60 + × 20 = 60 + 1.67 = 61.67 Thus, the median is 61.67. We know that, Mode = 3(median) 2(mean) = 3 × 61.67 2 × 62.4 = 185.01 124.8 = 60.21 Hence, Mean = 62.4, Median = 61.67 and Mode = 60.21 3. Find the mean, median and mode of the following data: Class 0 50 50 100 100 150 150 200 200 250 250 300 300 - 350 Frequency 2 3 5 6 5 3 1 Sol: To find the mean let us put the data in the table given below: Class Frequency (fi) Class mark (x i) fi xi 0 50 2 25 50 50 100 3 75 225 100 150 5 125 625 150 200 6 175 1050 200 250 5 225 1125 250 300 3 275 825 300 350 1 325 325 Total fi = 25 fi xi = 4225 Mean = i i i i i f x f = = 169 Thus, mean of the given data is 169. Now, to find the median let us put the data in the table given below: Class Frequency (fi) Cumulative Frequency (cf) 0 50 2 2 50 100 3 5 100 150 5 10 150 200 6 16 200 250 5 21 250 300 3 24 300 350 1 25 Total N = = 25 Now, N = 25 = 12.5. The cumulative frequency just greater than 12.5 is 16 and the corresponding class is 150 200. Thus, the median class is 150 200. l = 150, h = 50, N = 25, f = 6 and cf = 10. Now, Median = l + × h = 150 + × 50 = 150 + 20.83 = 170.83 Thus, the median is 170.83. We know that, Mode = 3(median) 2(mean) = 3 × 170.83 2 × 169 = 512.49 338 = 174.49 Hence, Mean = 169, Median = 170.83 and Mode = 174.49 4. Find the mean, median and mode of the following data: Marks obtained 25 - 35 35 45 45 55 55 65 65 75 75 - 85 No. of students 7 31 33 17 11 1 Sol: To find the mean let us put the data in the table given below: Marks obtained Number of students (fi) Class mark (x i) fi xi 25 35 7 30 210 35 45 31 40 1240 Page 5 1. Find the mean, median and mode of the following data: Class 0 10 10 20 20 30 30 40 40 50 50 60 60 70 Frequency 4 4 7 10 12 8 5 Sol: To find the mean let us put the data in the table given below: Class Frequency (fi) Class mark (x i) fi xi 0 10 4 5 20 10 20 4 15 60 20 30 7 25 175 30 40 10 35 350 40 50 12 45 540 50 60 8 55 440 60 70 5 65 325 Total fi = 50 fi xi = 1910 Mean = i i i i i f x f = = 38.2 Thus, the mean of the given data is 38.2. Now, to find the median let us put the data in the table given below: Class Frequency (fi) Cumulative Frequency (cf) 0 10 4 4 10 20 4 8 20 30 7 15 30 40 10 25 40 50 12 37 50 60 8 45 60 70 5 50 Total N = = 50 Now, N = 50 = 25. The cumulative frequency just greater than 25 is 37 and the corresponding class is 40 50. Thus, the median class is 40 50. l = 40, h = 10, N = 50, f = 12 and cf = 25. Now, Median = l + × h = 40 + × 10 = 40 Thus, the median is 40. We know that, Mode = 3(median) 2(mean) = 3 × 40 2 × 38.2 = 120 76.4 = 43.6 Hence, Mean = 38.2, Median = 40 and Mode = 43.6 2. Find the mean, median and mode of the following data: Class 0 20 20 40 40 60 60 80 80 100 100 120 120 140 Frequency 6 8 10 12 6 5 3 Sol: To find the mean let us put the data in the table given below: Class Frequency (fi) Class mark (x i) fi xi 0 20 6 10 60 20 40 8 30 240 40 60 10 50 500 60 80 12 70 840 80 100 6 90 540 100 120 5 110 550 120 140 3 130 390 Total fi = 50 fi xi = 3120 Mean = i i i i i f x f = = 62.4 Thus, the mean of the given data is 62.4. Now, to find the median let us put the data in the table given below: Class Frequency (fi) Cumulative Frequency (cf) 0 20 6 6 20 40 8 14 40 60 10 24 60 80 12 36 80 100 6 42 100 120 5 47 120 140 3 50 Total N = = 50 Now, N = 50 = 25. The cumulative frequency just greater than 25 is 36 and the corresponding class is 60 80. Thus, the median class is 60 80. l = 60, h = 20, N = 50, f = 12 and cf = 24. Now, Median = l + × h = 60 + × 20 = 60 + 1.67 = 61.67 Thus, the median is 61.67. We know that, Mode = 3(median) 2(mean) = 3 × 61.67 2 × 62.4 = 185.01 124.8 = 60.21 Hence, Mean = 62.4, Median = 61.67 and Mode = 60.21 3. Find the mean, median and mode of the following data: Class 0 50 50 100 100 150 150 200 200 250 250 300 300 - 350 Frequency 2 3 5 6 5 3 1 Sol: To find the mean let us put the data in the table given below: Class Frequency (fi) Class mark (x i) fi xi 0 50 2 25 50 50 100 3 75 225 100 150 5 125 625 150 200 6 175 1050 200 250 5 225 1125 250 300 3 275 825 300 350 1 325 325 Total fi = 25 fi xi = 4225 Mean = i i i i i f x f = = 169 Thus, mean of the given data is 169. Now, to find the median let us put the data in the table given below: Class Frequency (fi) Cumulative Frequency (cf) 0 50 2 2 50 100 3 5 100 150 5 10 150 200 6 16 200 250 5 21 250 300 3 24 300 350 1 25 Total N = = 25 Now, N = 25 = 12.5. The cumulative frequency just greater than 12.5 is 16 and the corresponding class is 150 200. Thus, the median class is 150 200. l = 150, h = 50, N = 25, f = 6 and cf = 10. Now, Median = l + × h = 150 + × 50 = 150 + 20.83 = 170.83 Thus, the median is 170.83. We know that, Mode = 3(median) 2(mean) = 3 × 170.83 2 × 169 = 512.49 338 = 174.49 Hence, Mean = 169, Median = 170.83 and Mode = 174.49 4. Find the mean, median and mode of the following data: Marks obtained 25 - 35 35 45 45 55 55 65 65 75 75 - 85 No. of students 7 31 33 17 11 1 Sol: To find the mean let us put the data in the table given below: Marks obtained Number of students (fi) Class mark (x i) fi xi 25 35 7 30 210 35 45 31 40 1240 45 55 33 50 1650 55 65 17 60 1020 65 75 11 70 770 75 85 1 80 80 Total fi = 100 fi xi = 4970 Mean = i i i i i f x f = = 49.7 Thus, mean of the given data is 49.7. Now, to find the median let us put the data in the table given below: Class Frequency (fi) Cumulative Frequency (cf) 25 35 7 7 35 45 31 38 45 55 33 71 55 65 17 88 65 75 11 99 75 85 1 100 Total N = = 100 Now, N = 100 = 50. The cumulative frequency just greater than 50 is 71 and the corresponding class is 45 55. Thus, the median class is 45 55. l = 45, h = 10, N = 100, f = 33 and cf = 38. Now, Median = l + × h = 45 + × 10 = 45 + 3.64 = 48.64 Thus, the median is 48.64. We know that, Mode = 3(median) 2(mean) = 3 × 48.64 2 × 49.70 = 145.92 99.4 = 46.52 Hence, Mean = 49.70, Median = 48.64 and Mode = 46.52Read More

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