Class 11 RD Sharma Solutions – Chapter 32 Statistics – Exercise 32.5 Improve Improve Like Article Like Save Share Report Question 1. Find the standard deviation for the following distribution: x: y: 4.5 1 14.5 5 24.5 34.5 12 22 44.5 17 54.5 64.5 9 4 Solution: x 4.5 14.5 f fx x-mean 1 4.5 -33.14 5 72.5 -23.14 (x-mean)2 1098.45 535.59 f(x-mean)2 1098.45 2677.96 24.5 34.5 12 294 -13.14 22 759 -3.14 172.73 9.88 2072.82 217.31 44.5 17 756.5 6.86 47.02 799.35 54.5 9 490.5 16.86 284.16 2557.47 64.5 4 258 26.86 721.31 2885.22 N = 70 2635 12308.57 Here, N = 70, We have, Question 2. Calculate the mean and variance. x: y: 0 51 1 2 203 383 3 525 4 532 5 408 6 273 7 139 8 9 43 27 10 10 11 4 12 2 Solution: X F Fx x-mean F(x-mean) (x-mean)2 F(x-mean)2 0 1 51 203 0 -6 203 -5 -306 -1015 36 25 1836 5075 2 3 383 525 766 -4 1575 -3 -1532 -1575 16 9 6128 4725 4 5 6` 532 408 273 2128 -2 2040 -1 1638 0 -1064 -408 0 4 1 0 2128 408 0 7 8 139 43 973 1 344 2 139 86 1 4 139 172 9 10 27 10 243 3 100 4 81 40 9 16 243 160 11 12 4 2 44 5 24 6 20 12 25 36 100 72 2600 10078-5522 21186 Here, N = 2600, Since, Question 3. Find the mean, and the standard deviation for the following data: (i) Year render: No. of persons (cumulative) 10 15 20 32 30 51 40 50 60 78 97 109 (ii) Marks: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Frequency: 1 6 6 8 8 2 2 3 0 2 1 0 0 0 1 Solution: (i) xi Cumulative frequency fi fixi fixi2 10 15 15 150 1500 20 32 17 340 6800 30 51 19 570 17100 40 78 27 1080 43200 50 97 19 950 47500 60 109 12 720 43200 N = 109 Total = 3810 Total = 159300 (ii) xi fi fixi fixi2 2 1 2 4 3 6 18 54 4 6 24 96 5 8 40 200 6 8 48 288 7 2 14 98 8 2 16 128 9 3 27 243 10 0 0 0 11 2 22 242 12 1 12 144 13 0 0 0 14 0 0 0 15 0 0 0 16 1 16 256 N = 40 Total = 239 Total = 1753 Question 4. Find the standard deviation for the following data: (i) x: y: 3 7 8 10 13 18 15 10 23 6 (ii) x 2 3 4 5 6 7 f 4 9 16 14 11 6 Solution: (i) x f 3 7 8 10 fx x-mean (x-mean)2 21 -9.79 95.88 80 -4.79 22.96 f(x-mean)2 671.13 229.60 13 15 18 10 195 0.21 0.04 180 5.21 27.13 0.65 271.26 23 6 138 10.21 104.21 625.26 48 614 1797.92 Here, N = 48, and (ii) xi fi fixi2 2 4 16 3 9 81 4 16 256 5 14 350 6 11 396 7 6 294 N = 60 Total = 1393 Last Updated : 13 Jul, 2023 Like Article Save Article Previous Class 11 RD Sharma Solutions - Chapter 32 Statistics - Exercise 32.4 Next Class 11 RD Sharma Solutions- Chapter 32 Statistics - Exercise 32.6 Share your thoughts in the comments Add Your Comment Please Login to comment...