Class XI Chapter 15 – Statistics Maths ______________________________________________________________________________ 2 5 5 2 h 2 Variance, N f 2 iy i fiy i N i1 i1 2 10 50 68 2 10 50 1 3300 3400 100 25 25 132 2 2 Question 9: Find the mean, variance and standard deviation using short-cut method Height in cms No. of children 70-75 3 75-80 4 80-85 7 85-90 7 90-95 15 95-100 9 100-105 6 105-**11**0 6 **11**0-**11**5 3 Solution 9: Class Interval Frequency f i Mid-point x i xi 92.5 yi 5 70-75 3 72.5 â€“4 16 â€“12 48 75-80 4 77.5 â€“3 9 â€“12 36 80-85 7 82.5 â€“2 4 â€“14 28 85-90 7 87.5 â€“1 1 â€“7 7 90-95 15 92.5 0 0 0 0 95-100 9 97.5 1 1 9 9 100-105 6 102.5 2 4 12 24 105-**11**0 6 107.5 3 9 18 54 **11**0-**11**5 3 **11**2.5 4 16 12 48 60 6 254 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 ______________________________________________________________________________ 9 i i i Mean, 1fy 6 x=A+ h=92.5+ 5 92.5 0.5 93 N 60 2 9 9 2 2 h 2 Variance, N f 2 iy i fiy i N i1 i1 2 5 60 60 254 6 2 25 15204 105.58 3600 Standard deviation 105.58 10.27 2 Question 10: The diameters of circles (in mm) drawn in a design are given below: Diameters No. of children 33-36 15 37-40 17 41-44 21 45-48 22 49-52 25 Solution 10: Class Interval Frequency f i Mid-point x i xi 42.5 yi 4 32.5-36.5 15 34.5 â€“2 4 â€“30 60 36.5-40.5 17 38.5 â€“1 1 â€“17 17 40.5-44.5 21 42.5 0 0 0 0 44.5-48.5 22 46.5 1 1 22 22 48.5-52.5 25 50.5 2 4 50 100 100 25 199 Here, N = 100, h = 4 Let the assumed mean, A, be 42.5. Mean, 5 i i i1fy 25 x=A+ h=42.5+ 4 43.5 N 100 2 f 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.

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