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```Chapter 32: Statistics – Exercise 32.6

Statistics – Exercise – 32.6 – Q.1

CI
f
x
u = (x – A)/h
fu
u2
fu2

0 – 10
14
5
-2
-28
4
56

10 – 20
13
15
-1
-13
1
13

20 – 30
27
25
0
0
0
0

30 – 40
21
35
1
21
1
21

40 – 50
15
45
2
30
4
60

90

10

150

Statistics – Exercise – 32.6 – Q.2

CI
f
x
u = (x – A)/h
f*u
u2
fu2

0 – 30
9
15
-3
-27
9
81

30 – 60
17
45
-2
-34
4
68

60 – 90
43
75
-1
-43
1
43

90 – 120
82
105
0
0
0
0

120 – 150
81
135
1
81
1
81

150 – 180
44
165
2
88
4
176

180 – 210
24
195
3
72
9
216

300

137

665

Statistics – Exercise – 32.6 – Q.3

CI
f
x
u = (x – A)/h
f*u
u2
fu2

0 – 10
18
5
-3
-54
9
162

10 – 20
16
15
-2
-32
4
64

20 – 30
15
25
-1
-15
1
15

30 – 40
12
35
0
0
0
0

40 – 50
10
45
1
10
1
10

50 – 60
5
55
2
10
4
20

60 – 70
2
65
3
6
9
18

70 – 80
1
75
4
4
16
16

79

-71

305

Statistics – Exercise – 32.6 – Q.4

We have,

and,

σ = 5.1

⟹ σ2 = 26.01

When the incorrect observation 50 is replaced by 40:

we have, Incorrect Σxi = 4000

∴Corrected Σxi = 4000 - 50 + 40 = 3990

and,

Statistics – Exercise – 32.6 – Q.5

CI
Freq
Mid Value
ui
fiui
fiui2

31 – 35
2
33
-4
-8
32

36 – 40
3
38
-3
-9
27

41 – 45
8
43
-2
-16
32

46 – 50
12
48
-1
-12
12

51 – 55
16
53
0
0
0

56 – 60
5
58
1
5
5

61 – 65
2
63
2
4
8

66 – 70
2
68
3
6
18

N = 50

Total = – 30
Total = 134

Statistics – Exercise – 32.6 – Q.6

Converting the given data into continuous frequency distribution by subtracing 0.5 from the lower limit and adding 0.5 to the upper limit of each dass interval.

Class interval
fi
Mid-value xi

fiui
ui2
fiui2

1 – 2
6
1.5
-4
-24
16
96

3 – 4
4
3.5
-4
-8
4
16

5 – 6
5
5.5
0
0
0
0

7 – 8
1
7.5
2
2
4
4

N = Σfi = 16

Σfiui = – 30

Σfiui2 = 116

Statistics – Exercise – 32.6 – Q.7

CI
xi
fi
ui
fiui
fiui2

200 – 201
200.5
13
-15
-19.5
29.25

201 – 202
201.5
27
-1
-27
27

202 – 203
202.5
18
-0.5
-9
4.5

203 – 204
203.5
10
0
0
0

204 – 205
204.5
1
0.5
0.5
0.25

205 – 206
205.5
1
1
1
1

N = 70

Total = – 54
Total = 62

Statistics – Exercise – 32.6 – Q.8

Mean = 40

SD = 10

n = 100

Σxi = 40 × 100 = 4000

Corrected Sum = 4000 - 30 - 70 + 3 + 27 = 3930

Variance = 100

Statistics – Exercise – 32.6 – Q.9

Mean = 45

Variance = 16

n = 10

Σxi = 450

Corrected Sum = 450 - 52 + 25 = 423

Corrected Mean = 42.3

Variance = 16

Corrected Variance = 6.62*6.62 = 43.82
```

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