Class XI Chapter 15 – Statistics Maths ______________________________________________________________________________ 2 5 5 2 h 2 Variance, N f 2 iy i fiy i N i1 i1 16 2 100 199 25 10000 16 19900 625 10000 16 19275 10000 30.84 Standard deviation 5.55 2 Exercise 15.3 : Question 1: From the data given below state which group is more variable, A or B? Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Group A 9 17 32 33 40 10 9 Group B 10 20 30 25 43 15 7 Solution 1: Firstly, the standard deviation of group A is calculated as follows. Marks Group A Mid-point xi 45 2 yi y i f x 10 i i 10-20 9 15 â€“3 9 â€“27 81 20-30 17 25 â€“2 4 â€“34 68 30-40 32 35 â€“1 1 â€“32 32 40-50 33 45 0 0 0 0 50-60 40 55 1 1 40 40 60-70 10 65 2 4 20 40 70-80 9 75 3 9 27 81 150 â€“6 342 Here, h = 10, N = 150, A = 45 7 xi 1 -610 i Mean=A+ h=45+ 45 0.4 44.6 N 150 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 ______________________________________________________________________________ h N 100 150 342 6 22500 1 51264 225 227.84 2 7 7 2 2 1 N f 2 iy i fiyi i1 i1 1 2 2 Standard deviation 227.84 15.09 The standard deviation of group B is calculated as follows. Marks Group B Mid-point xi 45 2 yi y i f x 10 i i 10-20 10 15 â€“3 9 â€“30 90 20-30 20 25 â€“2 4 â€“40 80 30-40 30 35 â€“1 1 â€“30 30 40-50 25 45 0 0 0 0 50-60 43 55 1 1 43 43 60-70 15 65 2 4 30 60 70-80 7 75 3 9 21 63 150 â€“6 366 7 i i 1fy -610 i Mean=A+ h=45+ 45 0.4 44.6 N 150 2 7 7 2 2 h 2 2 N f 2 iy i fiy i N i1 i1 100 150 366 6 2 22500 1 54864 243.84 225 Standard deviation 243.84 15.61 1 Since the mean of both the groups is same, the group with greater standard deviation will be more variable. Thus, group B has more variability in the marks. 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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