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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.1

 

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.2

 

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.3

 

Statistics – Exercise – 32.6 – Q.4

We have,

Statistics – Exercise – 32.6 – Q.4

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.4(ii)

 

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.5

 

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.6(i)

 

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.7

 

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.8(i)

 

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

Statistics – Exercise – 32.6 – Q.9

Corrected Variance = 6.62*6.62 = 43.82


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