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Statıstıcs I
STATISTICS I (İSTATİSTİK) - (İNGİLİZCE) Dersi Variability Measures soru cevapları
STATISTICS I (İSTATİSTİK) - (İNGİLİZCE) Dersi Variability Measures soru detayı:
SORU:
Grouped age distribution of the sample of 225 workers in a factory is given in the table below. Compute the standard deviation and variance.
| Class Interval | Frequency(f) |
| 18-24 | 30 |
| 24-30 | 40 |
| 30-36 | 42 |
| 36-42 | 38 |
| 42-48 | 30 |
| 48-54 | 20 |
| 54-60 | 15 |
| 60-66 | 10 |
| Total | 225 |
CEVAP:
The group mean is computed as X=37.5 (SUM(f*M)/Sample Size=8433/225=37.5)
So the sta*ndard deviation=f*Squared Deviation/(SampleSize-1)=Squareroot(31052.16/224)=11.8
Variance=11.8*11.8=138.6
| Class Interval | Frequency(f) | Midpoint(M) | f*M | Deviation(M-X) | Squared Deviation:(M-X)2 | f*Squared Deviation |
| 18-24 | 30 | 21 | 630 | -16.5 | 271.6 | 8147.7 |
| 24-30 | 40 | 27 | 1080 | -10.5 | 109.8 | 4393.2 |
| 30-36 | 42 | 33 | 1386 | -4.5 | 20.1 | 843.0 |
| 36-42 | 38 | 39 | 1482 | 1.5 | 2.3 | 87.8 |
| 42-48 | 30 | 45 | 1350 | 7.5 | 56.6 | 1696.5 |
| 48-54 | 20 | 51 | 1020 | 13.5 | 182.8 | 3655.8 |
| 54-60 | 15 | 57 | 855 | 19.5 | 381.0 | 5715.5 |
| 60-66 | 10 | 63 | 630 | 25.5 | 651.3 | 6512.7 |
| Total | 225 | 8433 | 31052.16 |