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
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When the incorrect observation 50 is replaced by 40:
we have, Incorrect Σxi = 4000
∴Corrected Σxi = 4000 - 50 + 40 = 3990
and,
.png "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.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 |
.png "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.8
Mean = 40
SD = 10
n = 100
Σxi = 40 × 100 = 4000
Corrected Sum = 4000 - 30 - 70 + 3 + 27 = 3930
Variance = 100
.png "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
Corrected Variance = 6.62*6.62 = 43.82