Class XI Chapter 15 – Statistics Maths ______________________________________________________________________________ Question 6: Find the mean and standard deviation using short-cut method. x 60 61 62 63 64 65 66 67 68 i f 2 1 12 29 25 12 10 4 5 i Solution 6: The data is obtained in tabular form as follows. x i f x i i 64 2 y fy 1 i i f i 1 60 2 â€“4 16 â€“8 32 61 1 â€“3 9 â€“3 9 62 12 â€“2 4 â€“24 48 63 29 â€“1 1 â€“29 29 64 25 0 0 0 0 65 12 1 1 12 12 66 10 2 4 20 40 67 4 3 9 12 36 68 5 4 16 20 80 100 220 0 286 9 i i i Mean, 1fy 0 x=A h=64+ 1 64 0 64 N 100 2 9 9 2 h 2 2 Variance, N f 2 iy i fiy i N i1 i1 1 2 100 286 0 100 2.86 = 2.86 1.69 Standard deviation fi 2 y 1 Question 7: Find the mean and variance for the following frequency distribution. Classes 0-30 30-60 60-90 90-120 120-150 150-180 180-210 Frequencies 2 3 5 10 3 5 2 Solution 7: Class Frequency f i Mid-point x i xi 105 yi 30 2 y i fi y i fi 2 y i Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 15 – Statistics Maths ______________________________________________________________________________ 0-30 2 15 â€“3 9 â€“6 18 30-60 3 45 â€“2 4 â€“6 12 60-90 5 75 â€“1 1 â€“5 5 90-120 10 105 0 0 0 0 120-150 3 135 1 1 3 3 150-180 5 165 2 4 10 20 180-210 2 195 3 9 6 18 30 2 76 Mean, 7 i i i1fy 2 x=A+ h=105+ 30 105 2 107 N 30 2 7 7 2 h 2 Variance, N f 2 iy i fiy i N i1 i1 2 30 30 76 2 2 30 2280 4 2276 2 2 Question 8: Find the mean and variance for the following frequency distribution. Classes 0-10 10-20 20-30 30-40 40-50 Frequencies 5 8 15 16 6 Solution 8: Class Frequency f i Mid-point x x i i 25 2 yi y i fi y i 10 fi 0-10 5 5 â€“2 4 â€“10 20 10-20 8 15 â€“1 1 â€“8 8 20-30 15 25 0 0 0 0 30-40 16 35 1 1 16 16 40-50 6 45 2 4 12 24 50 10 68 Mean, 5 i i i1fy 10 x=A+ h=25+ 10 25 2 27 N 50 2 y i Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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