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Chapter 32: Statistics – Exercise 32.5

Statistics – Exercise – 32.5 – Q.1

x f fx x-mean (x-mean)2 f(x – mean)2
4.5 1 4.5 -33.14 1098.45 1098.45
14.5 5 72.5 -23.14 535.59 267.96
24.5 12 294 -13.14 172.73 2072.82
34.5 22 759 -3.14 9.88 217.31
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

 

Statistics – Exercise – 32.5 – Q.2

X F  Fx x-mean F(x-mean) (x-mean)2 F(x-mean)2
0 51 0 -6 -306 36 1836
1 203 203 -5 -1015 25 5075
2 383 766 -4 -1532 16 6128
3 525 1575 -3 -1575 9 4725
4 532 2128 -2 -1064 4 2128
5 408 2040 -1 -408 1 408
6 273 1638 0 0 0 0
7 139 973 1 139 1 139
8 43 344 2 86 4 172
9 27 243 3 81 9 243
10 10 100 4 40 16 160
11 4 44 5 20 25 100
12 2 24 6 12 36 72
  2600 10078   -5522   21186

Here, N = 2600,       Σfixi = 10078

σ2 = 8.14846 – 4.51072

σ2 = 3.64

 

Statistics – Exercise – 32.5 – Q.3

(i)

xi Cum. Freq fi fixi f1x12
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  f1x12
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

 

Statistics – Exercise – 32.5 – Q.4

(i)

  x f   fx x-mean (x- mean)2 f(x – mean)2
3 7 21 -9.79 95.88 671.13
8 10 80 -4.79 22.96 229.6
13 15 195 0.21 0.04 0.65
18 10 180 5.21 27.13 271.26
23 6 138 10.21 104.21 625.26
  48 614     1797.02

Here, N = 48, and Σfixi = 614

Statistics – Exercise – 32.5 – Q.4(i)

(ii)

xi fi  f1x12
2 4 16
3 9 81
4 16 256
5 14 350
6 11 396
7 6 294
  N = 60 Total = 1393


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