chap1
.pdf
Ɍɚɤ ɤɚɤ ɷɬɢ ɞɚɧɧɵɟ ɩɨɥɭɱɟɧɵ ɜ ɨɞɧɨɦ ɢ ɬɨɦ ɠɟ ɤɨɧɤɪɟɬɧɨɦ ɫɨɰɢɨɥɨɝɢɱɟɫɤɨɦ ɢɫɫɥɟɞɨɜɚɧɢɢ, ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɢɯ ɫɨɩɨɫɬɚɜɢɬɶ. ɂɧɬɟɪɟɫɧɨ, ɱɬɨ ɭ ɪɚɛɨɱɢɯ-ɫɭɞɨɪɟɦɨɧɬɧɢɤɨɜ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ 10-11 ɤɥɚɫɫɨɜ ɫɪɟɞɧɢɣ ɤɜɚɥɢɮɢɤɚɰɢɨɧɧɵɣ ɪɚɡɪɹɞ ɧɚ ɟɞɢɧɢɰɭ ɦɟɧɶɲɟ, ɱɟɦ ɭ ɪɚɛɨɱɢɯ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ 7 ɤɥɚɫɫɨɜ. Ⱦɟɥɨ ɜ ɬɨɦ, ɱɬɨ ɭ ɪɚɛɨɱɢɯ ɫɨ ɫɪɟɞɧɢɦ ɨɛɪɚɡɨɜɚɧɢɟɦ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɫɪɟɞɧɢɣ ɫɬɚɠ (ɩɪɢɦɟɪɧɨ ɧɚ 9 ɥɟɬ), ɚ ɞɥɹ ɞɚɧɧɨɣ ɫɩɟɰɢɚɥɶɧɨɫɬɢ ɫɬɚɠ ɜ ɛɨɥɶɲɟɣ ɦɟɪɟ ɜɥɢɹɟɬ ɧɚ ɤɜɚɥɢɮɢɤɚɰɢɸ, ɱɟɦ ɨɛɪɚɡɨɜɚɧɢɟ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɷɬɨ ɥɨɤɚɥɶɧɵɣ ɜɵɜɨɞ, ɫɭɳɟɫɬɜɭɸɬ ɩɪɨɮɟɫɫɢɢ, ɝɞɟ ɪɟɲɚɸɳɭɸ ɪɨɥɶ ɜ ɤɜɚɥɢɮɢɤɚɰɢɢ ɢɝɪɚɟɬ ɨɛɪɚɡɨɜɚɧɢɟ. Ɉɛɪɚɬɢɦɜɧɢɦɚɧɢɟ ɢɧɚɬɨ, ɱɬɨ ɝɪɭɩɩɚɪɚɛɨɱɢɯɫɨɛɳɢɦɫɪɟɞɧɢɦ ɨɛɪɚɡɨɜɚɧɢɟɦ ɧɟɫɤɨɥɶɤɨɛɨɥɟɟ ɪɚɡɧɨɪɨɞɧɚɩɨɫɜɨɟɦɭɫɨɫɬɚɜɭɜɫɦɵɫɥɟ
[51]
ɤɜɚɥɢɮɢɤɚɰɢɢ (ɫɪ. ɤɨɷɮɮɢɰɢɟɧɬɵɜɚɪɢɚɰɢɢ), ɚɬɚɤɠɟɜɫɦɵɫɥɟɫɬɚɠɚɢɜɨɡɪɚɫɬɚɪɚɛɨɱɢɯ. ɉɨɡɧɚɤɨɦɢɦɫɹɫɨɫɧɨɜɧɵɦɢɫɜɨɣɫɬɜɚɦɢɞɢɫɩɟɪɫɢɢ.
1. ȿɫɥɢɜɫɟɜɚɪɢɚɧɬɵɭɜɟɥɢɱɢɬɶ (ɢɥɢɭɦɟɧɶɲɢɬɶ) ɜɨɞɧɨ ɢɬɨɠɟɱɢɫɥɨ, ɫɤɚɠɟɦ, Įɪɚɡ, ɬɨ D ɭɜɟɥɢɱɢɬɫɹ (ɢɥɢɫɨɨɬɜɟɬɫɬɜɟɧɧɨɭɦɟɧɶɲɢɬɫɹ) ɜĮ2 ɪɚɡ.
Ɇɵ ɫɨɜɟɪɲɚɟɦ ɩɟɪɟɯɨɞ xi o xic axi . ɉɪɢ ɷɬɨɦ, ɨɱɟɜɢɞɧɨ, M x o xc ax , ɚ
DD' = Į2D.
Ɂɚɦɟɬɢɦ, ɱɬɨı |
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2. ɍɜɟɥɢɱɟɧɢɟ (ɢɥɢ ɭɦɟɧɶɲɟɧɢɟ) ɜɫɟɯ ɜɚɪɢɚɧɬ ɧɚ ɨɞɧɭ ɢ ɬɭ ɠɟ ɩɨɫɬɨɹɧɧɭɸ ɜɟɥɢɱɢɧɭ c ɧɟ |
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Ɍɟɩɟɪɶ, xi o xic xi c , ɨɱɟɜɢɞɧɨ, |
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ɢɡɦɟɧɢɬ ɞɢɫɩɟɪɫɢɸ. |
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3.ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ (ɢɥɢ ɭɦɟɧɶɲɟɧɢɢ) ɜɫɟɯ ɱɚɫɬɨɬ ɜ ɨɞɧɨ ɢ ɬɨ ɠɟ ɱɢɫɥɨ ɪɚɡ ɞɢɫɩɟɪɫɢɹ ɧɟ ɢɡɦɟɧɢɬɫɹ.
4.Ⱦɢɫɩɟɪɫɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɪɟɞɧɟɣ ɚɪɢɮɦɟɬɢɱɟɫɤɨɣ ɪɚɜɧɚ ɞɢɫɩɟɪɫɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɪɨɢɡɜɨɥɶɧɨɣ ɩɨɫɬɨɹɧɧɨɣ ɡɚ ɜɵɱɟɬɨɦ ɤɜɚɞɪɚɬɚ ɪɚɡɧɨɫɬɢ ɫɪɟɞɧɟɣ ɚɪɢɮɦɟɬɢɱɟɫɤɨɣ ɢ ɷɬɨɣ ɩɨɫɬɨɹɧɧɨɣ.
ɉɪɟɞɫɬɚɜɥɹɹ (xi |
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ɢɥɢ: D( |
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Ɉɬɫɸɞɚ: D(c) D( |
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ɬ.ɟ D(c) t D(x)
Ɍɚɤɢɦɨɛɪɚɡɨɦ, ɞɢɫɩɟɪɫɢɹɨɬɧɨɫɢɬɟɥɶɧɨɫɪɟɞɧɟɝɨɚɪɢɮɦɟɬɢɱɟɫɤɨɝɨ (ɦɵɟɟɛɭɞɟɦɧɚɡɵɜɚɬɶ ɫɨɛɫɬɜɟɧɧɨ ɞɢɫɩɟɪɫɢɟɣ, ɢɥɢ ɞɥɹ ɩɪɨɫɬɨɬɵ, ɩɪɨɫɬɨ ɞɢɫɩɟɪɫɢɟɣ) ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɨɦ ɦɢɧɢɦɚɥɶɧɨɫɬɢ: ɨɧɚɦɟɧɶɲɟɞɢɫɩɟɪɫɢɢɨɬɧɨɫɢɬɟɥɶɧɨɥɸɛɨɣɞɪɭɝɨɣɜɟɥɢɱɢɧɵ.
5. Ⱦɢɫɩɟɪɫɢɹ ɪɚɜɧɚ ɫɪɟɞɧɟɣ ɚɪɢɮɦɟɬɢɱɟɫɤɨɣ ɤɜɚɞɪɚɬɨɜ ɜɚɪɢɚɧɬɨɜ, ɭɦɟɧɶɲɟɧɧɨɣ ɧɚ ɤɜɚɞɪɚɬɫɪɟɞɧɟɣɚɪɢɮɦɟɬɢɱɟɫɤɨɣ.
[52]
ȼɫɚɦɨɦɞɟɥɟ, ɩɨɥɚɝɚɹɜ(I,4,2) ɫ = 0, ɩɨɥɭɱɢɦ:
Dx2 x2 (I, 4,3)
ɋɥɟɞɫɬɜɢɟɦɫɜɨɣɫɬɜ1 ɢ4 ɹɜɥɹɟɬɫɹɪɚɜɟɧɫɬɜɨ
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ɤɨɬɨɪɨɟɦɨɠɟɬɛɵɬɶɢɫɩɨɥɶɡɨɜɚɧɨɞɥɹɭɩɪɨɳɟɧɢɹɜɵɱɢɫɥɟɧɢɹɞɢɫɩɟɪɫɢɢ.
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ɍɩɪɚɠɧɟɧɢɟ 16. ȼɟɪɧɟɦɫɹ ɤ ɩɪɢɦɟɪɭ 4 §3 ɢ ɡɚɜɟɪɲɢɦ ɟɝɨ ɪɚɫɫɦɨɬɪɟɧɢɟ, ɜɵɱɢɫɥɢɜ D, ı ɢ Cv ɞɥɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨ ɪɨɫɬɭ ɜɡɪɨɫɥɵɯ ɦɭɠɱɢɧ. Ⱦɥɹ ɷɬɨɝɨ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɞɚɧɧɵɟ ɬɚɛɥɢɰɵ 9, ɜ ɫɟɞɶɦɨɣ ɤɨɥɨɧɤɟ ɤɨɬɨɪɨɣ ɩɪɢɜɟɞɟɧɵ ɜɟɥɢɱɢɧɵ, ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɩɪɢɦɟɧɟɧɢɹ ɮɨɪɦɭɥɵ (I,4,4). Ʉɚɤ ɢ ɪɚɧɟɟ, ɫ = 165,5, ɚ Į = 3. Ɉɬɜɟɬ: D = 36,58; ı= 6,05; Cv = 3,8%. ȿɫɥɢ ɱɢɬɚɬɟɥɶ ɜɵɩɨɥɧɢɬ ɜɵɱɢɫɥɟɧɢɟ ɞɢɫɩɟɪɫɢɢ ɢ ɩɨ ɮɨɪɦɭɥɟ (I,4,1), ɬɨ ɨɧ ɫɭɦɟɟɬ ɨɰɟɧɢɬɶ ɩɪɟɢɦɭɳɟɫɬɜɨ (I,4,4).
ɉɨɡɧɚɤɨɦɢɦɫɹ ɫ ɩɪɚɜɢɥɨɦ ɫɥɨɠɟɧɢɹ ɞɢɫɩɟɪɫɢɣ. Ȼɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɢɡɭɱɚɟɦɚɹ ɫɨɜɨɤɭɩɧɨɫɬɶɪɚɡɛɢɬɚɧɚ s ɧɟɩɟɪɟɫɟɤɚɸɳɢɯɫɹɝɪɭɩɩ.
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ɪɚɡ, ɹɫɧɨ, ɱɬɨ ¦Pri |
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Nr , ɬ.ɟ. ɱɢɫɥɭ ɢɧɞɢɜɢɞɨɜ ɜ r-
c x = xi. Ƚɪɭɩɩɨɜɨɟ ɫɪɟɞɧɟɟ
(I,4,5)
Ɇɟɠɝɪɭɩɩɨɜɨɣ ɞɢɫɩɟɪɫɢɟɣ, ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ, ɧɚɡɵɜɚɟɬɫɹ ɫɪɟɞɧɹɹ ɚɪɢɮɦɟɬɢɱɟɫɤɚɹ
ɜɟɥɢɱɢɧɚɤɜɚɞɪɚɬɨɜɨɬɤɥɨɧɟɧɢɣɝɪɭɩɩɨɜɵɯɫɪɟɞɧɢɯ (xr ) ɨɬɨɛɳɟɣɫɪɟɞɧɟɣ x , ɬ.ɟ.
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ɋɪɟɞɧɹɹɚɪɢɮɦɟɬɢɱɟɫɤɚɹɝɪɭɩɩɨɜɵɯɞɢɫɩɟɪɫɢɣ: |
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[53]
Ɍɟɩɟɪɶɦɵɩɨɥɭɱɢɥɢɜɨɡɦɨɠɧɨɫɬɶɫɮɨɪɦɭɥɢɪɨɜɚɬɶɩɪɚɜɢɥɨɫɥɨɠɟɧɢɹɞɢɫɩɟɪɫɢɣ:
V2 V2 |
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ɉɨɤɚɠɟɦ, ɱɬɨɷɬɨɞɟɣɫɬɜɢɬɟɥɶɧɨɬɚɤ. |
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ɂɡ (I, 4, 5): |
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Ɂɚɩɢɲɟɦ s ɬɚɤɢɯɪɚɜɟɧɫɬɜɢɫɥɨɠɢɦɢɯɩɨɱɥɟɧɧɨ, ɬɨɝɞɚ: |
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Ɋɚɡɞɟɥɢɜɨɛɟ ɱɚɫɬɢɪɚɜɟɧɫɬɜɚ (I, 4, 9) ɧɚ N ɢɜɵɱɬɹ ɢɡɧɢɯɩɨ x2 , ɩɨɥɭɱɢɦ ɫɭɱɟɬɨɦ (I, 4, 5-
7): V 2 V 2 G 2 , ɱɬɨɢɬɪɟɛɨɜɚɥɨɫɶ.
ɉɪɢɦɟɪ6.
ɉɭɫɬɶ ɫɨɜɨɤɭɩɧɨɫɬɶ ɢɡ N = 150 ɢɧɞɢɜɢɞɨɜ ɫɨɫɬɨɢɬ ɢɡ ɬɪɟɯ ɝɪɭɩɩ (ɰɟɯɨɜ), ɜ ɩɟɪɜɨɣ N1 = 40, ɜɨɜɬɨɪɨɣ N2 = 50, ɜɬɪɟɬɶɟɣ N3 = 60 ɱɟɥɨɜɟɤ (ɡɞɟɫɶs = 3; r = I, 2, 3).
ɗɦɩɢɪɢɱɟɫɤɢɟɞɚɧɧɵɟɫɜɟɞɟɦɜɬɚɛɥɢɰɭ 10.
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65 7 75 12 85 15 55 6 |
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ɇɚɣɞɟɦɫɩɟɪɜɚ x |
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80 (ɪɭɛ.) |
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Ⱥɧɚɥɨɝɢɱɧɨ: x2 |
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95 ɪɭɛ.; x3 105 ɪɭɛ. |
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35
ȼ ɤɚɱɟɫɬɜɟ ɭɩɪɚɠɧɟɧɢɹ 17 ɩɪɟɞɥɚɝɚɟɦ ɜɵɱɢɫɥɢɬɶ x ɫɧɚɱɚɥɚ ɤɚɤ ɫɪɟɞɧɟɜɡɜɟɲɟɧɧɨɟ x2 , ɚ ɡɚɬɟɦ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ, ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ. ȼ ɨɛɨɢɯ ɫɥɭɱɚɹɯ ɞɨɥɠɟɧ ɩɨɥɭɱɢɬɶɫɹ ɨɞɢɧ ɢ ɬɨɬ ɠɟ
ɪɟɡɭɥɶɬɚɬ: x |
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Ⱦɚɥɟɟ. ɇɚɣɞɟɦ Vr (r= I, 3, 2). ɇɚɩɪɢɦɟɪ, |
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V 2 |
(65 80)2 7 (75 80)2 12 (85 80)2 15 (95 80)2 6 |
90 |
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ɍɩɪɚɠɧɟɧɢɟ 18. ɇɚɣɬɢ V22 ɢ V32 . Ɉɬɜɟɬ: 140; 66 |
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ɋɥɟɞɭɸɳɢɣɲɚɝ. ȼɵɱɢɫɥɢɦɦɟɠɝɪɭɩɩɨɜɭɸɞɢɫɩɟɪɫɢɸ: |
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N r 1 |
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ɢ V 2 |
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ɚɬɚɤɠɟ |
V 2 |
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Ɍɚɤɢɦɨɛɪɚɡɨɦ, V 2 G 2 V 2 .
[54]
ɉɪɢɜɟɞɟɦɩɪɢɦɟɪɵɜɵɱɢɫɥɟɧɢɣɆ, ıɢ Cv ɞɥɹɞɜɭɯɦɟɪɧɵɯɪɚɫɩɪɟɞɟɥɟɧɢɣ.
ɉɪɢɦɟɪ 7. ɉɭɫɬɶ ɩɟɪɜɵɣ ɩɪɢɡɧɚɤ X – ɡɚɪɚɛɨɬɧɚɹ ɩɥɚɬɚ ɪɚɛɨɱɢɯ (ɜ ɪɭɛɥɹɯ), ɚ ɜɬɨɪɨɣ – Y – ɤɜɚɥɢɮɢɤɚɰɢɹ (ɜ ɪɚɡɪɹɞɚɯ). ȼɬɨɪɨɣ ɩɪɢɡɧɚɤ ɞɢɫɤɪɟɬɧɵɣ, ɚ ɩɟɪɜɵɣ ɢɧɬɟɪɜɚɥɶɧɵɣ (ɜɟɥɢɱɢɧɵ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɢɧɬɟɪɜɚɥɨɜ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥ. II). 2131 ɪɚɛɨɱɢɣ, ɩɨɞɜɟɪɝɧɭɬɵɟ ɨɛɫɥɟɞɨɜɚɧɢɸ, ɜɱɚɫɬɧɨɫɬɢ, ɩɨɩɪɢɡɧɚɤɚɦ X ɢY ɪɚɫɩɪɟɞɟɥɢɥɢɫɶɬɚɤ, ɤɚɤ
Ɍɚɛɥɢɰɚ10
ɉɪɢɦɟɪ ɪɚɫɱɟɬɚ ɦɟɠɝɪɭɩɩɨɜɨɣ ɢɜɧɭɬɪɢɝɪɭɩɩɨɜɨɣɞɢɫɩɟɪɫɢɢ
Ɂɚɪɚɛɨɬɧɚɹ |
xi, ɪɭɛ. |
P1i |
P2i |
P3i |
N(xi) |
ɩɥɚɬɚ, ɪɭɛ. |
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60—70 |
65 |
7 |
1 |
0 |
8 |
70—80 |
75 |
12 |
5 |
0 |
17 |
80—90 |
85 |
15 |
9 |
4 |
28 |
90—100 |
95 |
6 |
18 |
8 |
32 |
100—110 |
105 |
0 |
12 |
32 |
44 |
110-120 |
115 |
0 |
5 |
16 |
21 |
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ȼɫɟɝɨ |
— |
40 |
50 |
60 |
150 |
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ɩɨɤɚɡɚɧɨ ɜ ɬɚɛɥ. 11. ɇɚɩɪɢɦɟɪ, 18 ɱɟɥɨɜɟɤ ɢɦɟɸɬ ɩɟɪɜɵɣɪɚɡɪɹɞ ɢɩɨɥɭɱɚɸɬ ɞɨ 80 ɪɭɛ., 28
– ɩɟɪɜɵɣɪɚɡɪɹɞ ɢɡɚɪɩɥɚɬɭ ɜɢɧɬɟɪɜɚɥɟ ɨɬ 80 ɞɨ 100 ɪɭɛ. ȼɫɟɝɨɪɚɛɨɱɢɯɫɩɟɪɜɵɦɪɚɡɪɹɞɨɦ 121,
36
ɫɨ ɜɬɨɪɵɦ 523 ɢ ɬ.ɞ. ȼɫɟɝɨ ɩɨɥɭɱɚɸɳɢɯ ɡɚɪɩɥɚɬɭ ɞɨ 80 ɪɭɛ. – 107 ɱɟɥ., ɨɬ 80 ɞɨ 100 ɪɭɛ. – 216 ɢ ɬ.ɞ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɤɨɥɨɧɤɟ N(xi) ɩɨ ɫɭɬɢ ɩɪɟɞɫɬɚɜɥɟɧɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɪɚɛɨɱɢɯ ɩɨ ɪɚɡɪɹɞɚɦ, ɚ ɜ ɫɬɪɨɤɟ N(yi) – ɩɨ ɡɚɪɚɛɨɬɧɨɣ ɩɥɚɬɟ. ɗɬɨ ɜɚɪɢɚɰɢɨɧɧɵɟ ɪɹɞɵ ɬɢɩɚ ɪɚɧɟɟ ɪɚɫɫɦɨɬɪɟɧɧɵɯ. Ʉɪɨɦɟ ɬɨɝɨ, ɧɚɲɚɬɚɛɥ. 11 ɫɨɞɟɪɠɢɬɫɩɟɰɢɮɢɱɟɫɤɢɟ ɪɹɞɵɬɢɩɚ: ɪɚɫɩɪɟɞɟɥɟɧɢɟɪɚɛɨɱɢɯɫɞɚɧɧɨɣ ɡɚɪɩɥɚɬɨɣ ɩɨ ɪɚɡɪɹɞɚɦ ɢ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɪɚɛɨɱɢɯ ɫ ɞɚɧɧɵɦ ɪɚɡɪɹɞɨɦ ɩɨ ɜɟɥɢɱɢɧɟ ɡɚɪɚɛɨɬɧɨɣ ɩɥɚɬɵ.
ȼ ɫɬɨɥɛɰɚɯ ɩɪɢɜɟɞɟɧɵ ɬɚɤɠɟ ɫɪɟɞɧɢɟ ɡɧɚɱɟɧɢɹ X (ɧɚɩɪɢɦɟɪ, ɫɪɟɞɧɹɹ ɡɚɪɩɥɚɬɚ ɪɚɛɨɱɢɯ ɫ ɩɟɪɜɵɦ ɤɜɚɥɢɮɢɤɚɰɢɨɧɧɵɦ ɪɚɡɪɹɞɨɦ 113,1 ɪɭɛ., ɚ ɫɪɟɞɧɢɣ ɪɚɡɪɹɞ ɪɚɛɨɱɢɯ, ɡɚɪɚɛɨɬɧɚɹ ɩɥɚɬɚ ɤɨɬɨɪɵɯ ɨɬ 180 ɞɨ 200 ɪɭɛ., ɫɨɫɬɚɜɥɹɟɬ 4,03 ɪɚɡɪɹɞɚ). Ⱦɚɥɟɟ ɩɪɟɞɫɬɚɜɥɟɧɵ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ı ɢ
Cv.
Ɇɵ ɩɪɢɜɨɞɢɦ ɷɬɭ ɬɚɛɥɢɰɭ ɧɟ ɫɬɨɥɶɤɨ ɢɡ-ɡɚ ɟɟ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɰɟɧɧɨɫɬɢ, ɫɤɨɥɶɤɨ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵɱɢɬɚɬɟɥɶɦɨɝ
[55]
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Ɍɚɛɥɢɰɚ11 |
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ɉɪɢɦɟɪ ɪɚɫɱɟɬɚM, ı, Cv (ɡɚɪɩɥɚɬɚ) |
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Ɂɚɪɩɥɚɬɚ, ɪɭɛ. |
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ɪɚɡɪɹɞ |
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80- |
100- |
120- |
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140- |
160- |
180- |
200- |
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N(xi) |
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Cv(x) |
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x |
ıx |
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ɞɨ |
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ɫɜɵɲɟ |
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80 |
100 |
120 |
140 |
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160 |
180 |
200 |
220 |
220 |
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1 |
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18 |
28 |
26 |
26 |
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15 |
6 |
1 |
1 |
0 |
121 |
113,1 |
30,44 |
26,9 |
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2 |
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42 |
77 |
128 |
140 |
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67 |
31 |
16 |
13 |
9 |
523 |
125,6 |
34,93 |
27,8 |
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3 |
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33 |
50 |
84 |
139 |
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123 |
20 |
19 |
11 |
8 |
527 |
134,4 |
33,80 |
25,1 |
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4 |
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7 |
45 |
71 |
66 |
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65 |
72 |
44 |
24 |
22 |
416 |
148,6 |
42,35 |
28,4 |
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5 |
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4 |
12 |
49 |
50 |
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57 |
46 |
34 |
38 |
54 |
344 |
167,3 |
48,51 |
29,0 |
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6 |
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3 |
4 |
23 |
53 |
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47 |
29 |
12 |
9 |
20 |
200 |
155,7 |
41,58 |
26,6 |
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N(yi) |
107 |
216 |
381 |
474 |
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374 |
244 |
126 |
96 |
113 |
2131 |
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y |
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2,49 |
2,75 |
3,15 |
3,28 |
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3,59 |
3,85 |
4,03 |
4,16 |
1,60 |
– |
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ıy |
1,13 |
1,18 |
1,39 |
1,41 |
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1,37 |
1,27 |
1,17 |
1,22 |
1,10 |
– |
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Cv( y) |
45,3 |
43,0 |
44,3 |
43,0 |
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38,2 |
33,0 |
29,0 |
29,3 |
23,9 |
– |
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ɩɪɢ ɠɟɥɚɧɢɢ ɩɪɨɜɟɪɢɬɶ ɫɟɛɹ ɢ ɪɚɫɫɱɢɬɚɬɶ ɩɨɤɚɡɚɬɟɥɢ, ɤɨɬɨɪɵɟ ɛɵɥɢ ɪɚɫɫɦɨɬɪɟɧɵ ɜ ɩɪɟɞɵɞɭɳɢɯɩɚɪɚɝɪɚɮɚɯ.
ɑɬɨ ɠɟ ɤɚɫɚɟɬɫɹ ɫɨɞɟɪɠɚɬɟɥɶɧɨɣ ɢɧɬɟɪɩɪɟɬɚɰɢɢ ɞɚɧɧɵɯ, ɤɪɨɦɟ ɞɨɫɬɚɬɨɱɧɨ ɨɱɟɜɢɞɧɵɯ ɭɬɜɟɪɠɞɟɧɢɣ ɬɢɩɚ «ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɪɚɡɪɹɞɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɫɪɟɞɧɹɹ ɡɚɪɚɛɨɬɧɚɹ ɩɥɚɬɚ», ɢɡ ɧɟɟ ɦɨɠɧɨ ɩɨɱɟɪɩɧɭɬɶ ɦɟɧɟɟ ɨɱɟɜɢɞɧɨɟ: ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɡɚɪɚɛɨɬɧɨɣ ɩɥɚɬɵ ɝɪɭɩɩɵ ɪɚɛɨɱɢɯ ɫɬɚɧɨɜɹɬɫɹɜɫɟɛɨɥɟɟɨɞɧɨɪɨɞɧɵɦɢɩɨɭɪɨɜɧɸɤɜɚɥɢɮɢɤɚɰɢɢ (ɦɨɧɨɬɨɧɧɨɟɭɦɟɧɶɲɟɧɢɟ ɋv), ɯɨɬɹ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɪɚɡɪɹɞɚ ɜɚɪɢɚɰɢɹ ɡɚɪɚɛɨɬɧɨɣ ɩɥɚɬɵ ɧɟ ɢɡɦɟɧɹɟɬɫɹ: ɪɚɡɛɪɨɫ ɩɪɢɦɟɪɧɨ ɨɞɢɧ ɢ ɬɨɬ ɠɟ.
ɉɪɢɦɟɪ8.
ɉɪɢ ɢɡɭɱɟɧɢɢ ɫɜɹɡɢ ɦɟɠɞɭ ɩɪɢɡɧɚɤɚɦɢ ɤɜɚɥɢɮɢɤɚɰɢɹ (X) ɢ ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶ ɫɩɟɰɢɚɥɶɧɨɫɬɶɸ(Y), ɜɱɚɫɬɧɨɫɬɢ, ɛɵɥɚɩɨɥɭɱɟɧɚɬɚɤɚɹɬɚɛɥɢɰɚ (ɬɚɛɥɢɰɚ 12).
Ʉɚɤ ɢ ɪɚɧɟɟ, X ɜɵɪɚɠɚɟɬɫɹ ɜ ɪɚɡɪɹɞɚɯ (xi i,i 1,6) . ɉɪɢɡɧɚɤ Y – ɤɚɱɟɫɬɜɟɧɧɵɣ, ɟɝɨ
ɩɨɡɢɰɢɢ: «ɭɞɨɜɥɟɬɜɨɪɟɧ», «ɧɟ ɡɧɚɸ, ɬɪɭɞɧɨ ɫɤɚɡɚɬɶ», «ɧɟ ɭɞɨɜɥɟɬɜɨɪɟɧ» ɨɛɨɡɧɚɱɟɧɵ ɜ ɬɚɛɥɢɰɟ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ y1,y2,y3. ɍɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶ ɝɪɭɩɩɵ ɪɚɛɨɱɢɯ ɨɩɢɫɵɜɚɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɢɧɞɟɤɫɚ
J |
ɫɩɟɰ |
N |
N |
, |
ɝɞɟ N+ – ɱɢɫɥɨ ɭɞɨɜɥɟɬɜɨɪɟɧɧɵɯ, N–– ɧɟɭɞɨɜɥɟɬɜɨɪɟɧɧɵɯ, N0 – ɧɟ |
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N |
N0 N |
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ɜɵɪɚɡɢɜɲɢɯɨɩɪɟɞɟɥɟɧɧɨɟɨɬɧɨɲɟɧɢɟ.
Ɍɚɤ ɤɚɤ ɜ ɞɚɥɶɧɟɣɲɟɦ ɧɚɦ ɩɪɢɞɟɬɫɹ ɧɟɨɞɧɨɤɪɚɬɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɢɧɞɟɤɫɵ ɞɥɹ ɝɪɭɩɩɵ, ɨɬɦɟɬɢɦ, ɱɬɨ J ɩɪɢɧɢɦɚɟɬɡɧɚɱɟɧɢɹ, ɡɚɤɥɸɱɟɧɧɵɟɦɟɠɞɭ –1 ɢ1, ɩɪɢɱɟɦ –1 ɫɨɨɬ-
37
[56]
ɜɟɬɫɬɜɭɟɬ ɫɥɭɱɚɸ, ɤɨɝɞɚ ɜɫɟ ɪɚɛɨɬɧɢɤɢ ɧɟ ɭɞɨɜɥɟɬɜɨɪɟɧɵ, 1 ɨɡɧɚɱɚɟɬ, ɱɬɨɜɫɟɭɞɨɜɥɟɬɜɨɪɟɧɵ, ɚ 0 ɩɨɥɭɱɚɟɬɫɹ ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɱɢɫɥɨ ɭɞɨɜɥɟɬɜɨɪɟɧɧɵɯ ɫɩɟɰɢɚɥɶɧɨɫɬɶɸ ɪɚɜɧɨ ɱɢɫɥɭ ɧɟɭɞɨɜɥɟɬɜɨɪɟɧɧɵɯ. Ⱥɧɚɥɨɝɢɱɧɨ ɤɨɧɫɬɪɭɢɪɭɸɬɫɹ ɢɧɞɟɤɫɵ ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɢ ɪɚɛɨɬɨɣ, ɪɚɡɥɢɱɧɵɦɢɷɥɟɦɟɧɬɚɦɢɪɚɛɨɱɟɣɫɢɬɭɚɰɢɢɢɬ.ɞ.
ȼɨɡɜɪɚɬɢɦɫɹ ɤ ɬɚɛɥ. 12. Ʉɪɨɦɟ «ɨɱɟɜɢɞɧɵɯ» ɭɬɜɟɪɠɞɟɧɢɣ ɬɢɩɚ «ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɤɜɚɥɢɮɢɤɚɰɢɢɭɜɟɥɢɱɢɜɚɟɬɫɹɢɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶɫɩɟɰɢɚɥɶɧɨɫɬɶɸ», ɢɡ ɧɟɟɫɥɟɞɭɟɬ, ɱɬɨɝɪɭɩɩɵ ɢɧɞɢɜɢɞɨɜ ɫ ɪɚɡɧɨɣ ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶɸ ɫɩɟɰɢɚɥɶɧɨɫɬɶɸ ɩɪɢɦɟɪɧɨ ɨɞɢɧɚɤɨɜɵ ɩɨ ɜɚɪɢɚɰɢɢ ɤɜɚɥɢɮɢɤɚɰɢɢ, ɚ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɤɜɚɥɢɮɢɤɚɰɢɢ ɪɟɡɤɨ ɜɨɡɪɚɫɬɚɟɬ ɨɞɧɨɪɨɞɧɨɫɬɶ ɝɪɭɩɩ ɩɨ ɫɬɟɩɟɧɢ ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɢ: ɩɨɫɥɟɞɧɹɹ ɫɤɥɚɞɵɜɚɟɬɫɹ ɢɡ ɜɫɟ ɛɨɥɟɟ ɫɨɝɥɚɫɨɜɚɧɧɵɯ ɢɧɞɢɜɢɞɭɚɥɶɧɵɯ ɨɰɟɧɨɤ.
Ⱦɨɫɢɯɩɨɪɦɵɪɚɫɫɦɚɬɪɢɜɚɥɢɭɩɨɪɹɞɨɱɟɧɧɵɟ (ɤɨɥɢɱɟɫɬɜɟɧɧɵɟ ɢɤɚɱɟɫɬɜɟɧɧɵɟ) ɩɪɢɡɧɚɤɢ. ȼɨɡɧɢɤɚɟɬɜɨɩɪɨɫ, ɱɬɨɦɨɠɟɬɫɥɭɠɢɬɶɦɟɪɨɣɜɚɪɢɚɰɢɢɤɥɚɫɫɢɮɢɤɚɰɢɨɧɧɵɯ ɩɪɢɡɧɚɤɨɜ?
ȼɚɪɢɚɰɢɹ ɤɥɚɫɫɢɮɢɤɚɰɢɨɧɧɵɯ ɩɪɢɡɧɚɤɨɜ. Ɉɱɟɜɢɞɧɨ, ɦɟɪɵ, ɪɚɡɪɚɛɨɬɚɧɧɵɟ ɞɥɹ ɩɪɢɡɧɚɤɨɜ, ɡɧɚɱɟɧɢɹ ɤɨɬɨɪɵɯ ɱɢɫɥɚ, ɨɤɚɡɵɜɚɸɬɫɹ ɬɟɩɟɪɶ ɧɟɩɪɢɝɨɞɧɵɦɢ: ɦɟɠɞɭ ɨɛɴɟɤɬɚɦɢ ɪɚɡɧɵɯ ɤɥɚɫɫɨɜ ɧɟɬ ɭɩɨɪɹɞɨɱɟɧɢɹ (ɜɫɟ ɤɥɚɫɫɵ ɪɚɜɧɨɩɪɚɜɧɵ – ɧɟɥɶɡɹ ɜɵɞɟɥɢɬɶ ɤɨɧɬɢɧɭɭɦ, ɜ ɤɨɬɨɪɨɦ ɦɨɠɧɨ ɛɵɥɨ ɛɵ ɭɩɨɪɹɞɨɱɢɬɶ ɧɚɰɢɨɧɚɥɶɧɭɸ ɢɥɢ ɪɚɫɨɜɭɸ ɩɪɢɧɚɞɥɟɠɧɨɫɬɶ, ɱɥɟɧɫɬɜɨ ɜ ɪɚɡɥɢɱɧɨɝɨ ɪɨɞɚ ɨɪɝɚɧɢɡɚɰɢɹɯɢɥɢɩɪɢɱɢɧɵ
[57]
ɭɜɨɥɶɧɟɧɢɹ ɫ ɩɪɟɞɩɪɢɹɬɢɹ ɢ ɬ.ɞ.), ɧɟɬ ɧɭɥɹ, ɧɟɬ ɢɧɬɟɪɜɚɥɨɜ, ɬɟɪɹɸɬ ɫɦɵɫɥ ɬɚɤɢɟ ɩɨɧɹɬɢɹ, ɤɚɤ ɞɢɚɩɚɡɨɧ, ɪɚɡɦɚɯ, ɨɬɤɥɨɧɟɧɢɟ, ɫɬɨɥɶɩɪɢɜɵɱɧɵɟɢɭɞɨɛɧɵɟ, ɤɨɝɞɚɡɧɚɱɟɧɢɹɩɪɢɡɧɚɤɨɜ – ɱɢɫɥɚ.
Ɍɟɦ ɧɟ ɦɟɧɟɟ ɨɛɴɟɤɬɵ, ɜɯɨɞɹɳɢɟ ɜ ɪɚɡɧɵɟ ɤɥɚɫɫɵ, ɨɛɥɚɞɚɸɬ ɪɚɡɥɢɱɧɵɦɢ ɤɚɱɟɫɬɜɚɦɢ ɜ ɫɦɵɫɥɟ ɢɡɭɱɚɟɦɨɝɨ ɩɪɢɡɧɚɤɚ: ɭ ɧɢɯ ɪɚɡɧɵɣ ɩɨɥ ɢ ɪɚɡɧɚɹ ɧɚɰɢɨɧɚɥɶɧɨɫɬɶ, ɨɧɢ ɩɪɢɧɚɞɥɟɠɚɬ ɤ ɪɚɡɧɵɦɨɪɝɚɧɢɡɚɰɢɹɦɢɥɢɭɤɚɡɵɜɚɸɬɪɚɡɧɵɟɩɪɢɱɢɧɵɭɜɨɥɶɧɟɧɢɹɢɬ.ɞ.
Ɍɚɛɥɢɰɚ12
ɉɪɢɦɟɪ ɪɚɫɱɟɬɚM, ı ɢ Cv (ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶ)
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ɏ |
Y |
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Cvx (%) |
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y1 |
y2 |
y3 |
N(xi) |
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ıx |
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1 |
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66 |
4 |
30 |
100 |
0,36 |
1,09 |
302,8 |
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2 |
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327 |
16 |
77 |
420 |
0,59 |
0,86 |
145,8 |
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3 |
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353 |
25 |
61 |
439 |
0,66 |
0,76 |
115,2 |
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4 |
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295 |
25 |
34 |
354 |
0,74 |
0,65 |
87,8 |
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5 |
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271 |
16 |
15 |
302 |
0,85 |
0,49 |
57,6 |
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6 |
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172 |
3 |
6 |
181 |
0,92 |
0,38 |
41,3 |
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N(yi) |
1484 |
89 |
223 |
1796 |
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3,60 |
3,47 |
2,75 |
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y |
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ıy |
1,51 |
1,22 |
1,24 |
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C y (%) |
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v |
41,9 |
35,2 |
45,1 |
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ɉɨɩɪɨɛɭɟɦ ɨɰɟɧɢɜɚɬɶ ɜɚɪɢɚɰɢɸ ɫ ɩɨɦɨɳɶɸ ɪɚɡɥɢɱɢɹ ɜ ɤɚɱɟɫɬɜɟ. ɑɟɦ ɛɨɥɶɲɟ ɱɢɫɥɨ ɪɚɡɥɢɱɧɵɯ ɩɚɪ ɨɛɴɟɤɬɨɜ, ɬɟɦ, ɨɱɟɜɢɞɧɨ, ɛɨɥɶɲɟ ɜɚɪɢɚɰɢɹ. Ⱦɨɩɭɫɬɢɦ, ɱɬɨ ɭ ɧɚɫ ɜɫɟɝɨ 2 ɤɥɚɫɫɚ ɨɛɴɟɤɬɨɜȺɢȼ (ɧɚɩɪɢɦɟɪ, ɩɪɢɡɧɚɤ «ɩɨɥ»), ɱɢɫɥɟɧɧɨɫɬɶɤɨɬɨɪɵɯ NA ɢ NB ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ (ɨɛɴɟɦ ɫɨɜɨɤɭɩɧɨɫɬɢ N = NA + NB). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɱɢɫɥɨ ɪɚɡɥɢɱɧɵɯ ɩɚɪ ɨɛɴɟɤɬɨɜ NA NB (ɫɤɚɠɟɦ,
38
ɤɚɠɞɵɣ ɦɭɠɱɢɧɚ, ɨɱɟɜɢɞɧɨ, ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɤɚɠɞɨɣ ɠɟɧɳɢɧɵ: ɧɚ ɨɞɧɨɝɨ ɩɪɢɯɨɞɹɬɫɹ NB ɠɟɧɳɢɧ,
ɬ.ɟ. |
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NB ɪɚɡɥɢɱɢɣ, ɚ ɧɚ ɜɫɟɯ NA ɦɭɠɱɢɧ NA NB |
ɪɚɡɥɢɱɢɣ). Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɫɤɨɧɫɬɪɭɢɪɨɜɚɬɶ |
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ɧɨɪɦɢɪɨɜɚɧɧɭɸ ɦɟɪɭ, ɨɩɪɟɞɟɥɢɦ, ɜɤɚɤɨɦ ɫɥɭɱɚɟ ɱɢɫɥɨ ɩɚɪ ɦɚɤɫɢɦɚɥɶɧɨ. |
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Ʉɚɤ ɢɡɜɟɫɬɧɨ, ɫɪɟɞɧɟɟ ɝɟɨɦɟɬɪɢɱɟɫɤɨɟ ɞɜɭɯ ɱɢɫɟɥ ɚ ɢ b ɧɟ ɩɪɟɜɨɫɯɨɞɢɬ ɫɪɟɞɧɟɝɨ |
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ɚɪɢɮɦɟɬɢɱɟɫɤɨɝɨ ɢɪɚɜɧɨ ɟɦɭ, ɟɫɥɢ a |
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ɉɭɫɬɶ a |
N 2 ,b |
N 2 , ɬɨɝɞɚ ɢɦɟɟɦ N |
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NA2 NB2 |
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[58] |
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ɫɥɟɞɨɜɚɬɟɥɶɧɨ, |
(NANB ) |
ɦɚɤɫɢɦɚɥɶɧɨ, |
ɤɨɝɞɚ ɱɢɫɥɟɧɧɨɫɬɢ ɤɥɚɫɫɨɜ ɨɞɢɧɚɤɨɜɵ, ɬ.ɟ. ɪɚɜɧɵ |
N |
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(N |
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, ɚ ɢɫɤɨɦɚɹ ɦɟɪɚ |
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ɂɬɚɤ, ɜɚɪɢɚɰɢɹ ɦɚɤɫɢɦɚɥɶɧɚ, ɤɨɝɞɚ |
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M |
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ɤɥɚɫɫɵ |
ɪɚɜɧɨɧɚɩɨɥɧɟɧɧɵɟ, ɨɧɚ ɩɪɢ |
ɷɬɨɦ ɪɚɜɧɚ |
1. ȼɚɪɢɚɰɢɢ ɧɟɬ, ɟɫɥɢ, ɫɤɚɠɟɦ, N A |
0 |
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(N NB – ɜɫɟɨɛɴɟɤɬɵɨɞɧɨɬɢɩɧɵ), ɦɟɪɚɜɚɪɢɚɰɢɢɩɪɢɷɬɨɦ, ɨɱɟɜɢɞɧɨ, ɨɛɪɚɳɚɟɬɫɹɜɧɭɥɶ.
Ⱥɤɚɤ ɛɵɬɶ, ɟɫɥɢ ɤɥɚɫɫɨɜ ɛɨɥɶɲɟ ɱɟɦ 2, ɧɚɩɪɢɦɟɪ, 3? Ⱦɥɹ ɞɜɭɯ ɤɥɚɫɫɨɜ ɦɟɪɚ ɪɚɜɧɚ ɤɜɚɞɪɚɬɭ ɨɬɧɨɲɟɧɢɹ ɫɪɟɞɧɟɝɨ ɝɟɨɦɟɬɪɢɱɟɫɤɨɝɨ ɤ ɫɪɟɞɧɟɦɭ ɚɪɢɮɦɟɬɢɱɟɫɤɨɦɭ ɱɢɫɥɟɧɧɨɫɬɟɣ
ɤɥɚɫɫɨɜ. |
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Ʉɚɡɚɥɨɫɶ ɛɵ, |
ɜ ɫɥɭɱɚɟ ɬɪɟɯ ɤɥɚɫɫɨɜ Ⱥ, ȼ, ɋ, ɦɟɪɚ ɜɚɪɢɚɰɢɢ |
ɞɨɥɠɧɚ ɛɵɬɶ |
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G / M |
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2 |
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9NANB NC |
. Ʌɟɝɤɨ ɜɢɞɟɬɶ, ɱɬɨ ɷɬɨ ɧɟ ɬɚɤ. Ⱦɨɩɭɫɬɢɦ, ɱɬɨ NA = 0, |
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ɬɨɝɞɚ ɜɟɥɢɱɢɧɚ |
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ɨɛɪɚɳɚɟɬɫɹ ɜ ɧɭɥɶ, ɯɨɬɹ ɫɨɜɨɤɭɩɧɨɫɬɶ ɧɟɨɞɧɨɪɨɞɧɚ: ɨɫɬɚɥɢɫɶ ɨɛɴɟɤɬɵ ɬɢɩɚ ȼ ɢ ɋ. |
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Ʉɚɤɠɟɛɵɬɶ? |
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ɋɨɫɬɚɜɢɦɜɟɥɢɱɢɧɭ |
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D3 |
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NANB NANG |
NB NG |
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Ɉɧɚ ɨɛɪɚɳɚɟɬɫɹ ɜ ɧɭɥɶ, ɟɫɥɢ ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ ɞɜɚ ɤɥɚɫɫɚ ɩɭɫɬɵ (ɫɤɚɠɟɦ, NA = NB =0, ɬ.ɟ. ɫɨɜɨɤɭɩɧɨɫɬɶɨɞɧɨɪɨɞɧɚ, ɫɨɫɬɨɢɬɬɨɥɶɤɨɢɡɨɛɴɟɤɬɨɜɬɢɩɚɋ).
Ɇɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɨɛɫɭɠɞɚɟɦɚɹ ɜɟɥɢɱɢɧɚ ɩɪɢɧɢɦɚɟɬ ɩɪɢ NA = NB = NC, ɤɨɬɨɪɨɟ, ɤɚɤ ɥɟɝɤɨ ɜɢɞɟɬɶ, ɪɚɜɧɨ 1 (ɩɪɢ ɷɬɨɦ ɪɚɡɥɢɱɢɹ ɦɚɤɫɢɦɚɥɶɧɵ). ȼɟɥɢɱɢɧɭ D3 ɦɨɠɧɨ ɩɪɢɧɹɬɶ ɜ
ɤɚɱɟɫɬɜɟɦɟɪɵɜɚɪɢɚɰɢɢ. |
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ɍɩɪɚɠɧɟɧɢɟ 19. ɉɨɤɚɡɚɬɶ, ɱɬɨ ab ac bc d |
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, ɩɪɢɱɟɦ ɪɚɜɟɧɫɬɜɨ ɞɨɫɬɢɝɚɟɬɫɹ |
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ɩɪɢ a=b=c. ɍɤɚɡɚɧɢɟ: ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɪɢɠɞɵ – ɞɥɹ ɜɫɟɯ ɩɚɪ – ɧɟɪɚɜɟɧɫɬɜɨ ɦɟɠɞɭ G2 ɢ M2 . ɂɬɚɤ, 0 d a3 d1, ɩɪɢɱɟɦ ɧɭɥɶ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɞɧɨɪɨɞɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ (ɨɬɫɭɬɫɬɜɢɟ ɜɚɪɢɚɰɢɢ), ɚ
ɟɞɢɧɢɰɚ – ɦɚɤɫɢɦɚɥɶɧɨ ɧɟɨɞɧɨɪɨɞɧɨɣ (ɦɚɤɫɢɦɚɥɶɧɚɹ ɜɚɪɢɚɰɢɹ, ɫɥɭɱɚɣ ɪɚɜɧɨɧɚɩɨɥɧɟɧɧɵɯ ɤɥɚɫɫɨɜ).
ɍɩɪɚɠɧɟɧɢɟ 20. Ɋɚɫɫɦɨɬɪɟɬɶɫɥɭɱɚɣ k 4(N |
N1 N2 N3 N4 ) |
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Ɉɬɜɟɬ: |
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D4 |
8 N1N2 N1N3 N1N4 N2N3 N2N4 N3N4 |
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[59] |
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39
k 1 k
Ɋɚɫɫɦɨɬɪɢɦ ɨɛɳɢɣ ɫɥɭɱɚɣ (ɩɪɨɢɡɜɨɥɶɧɨɟ k). Ɍɟɩɟɪɶ ɱɢɫɥɨ ɪɚɡɥɢɱɢɣ A ¦ ¦Ni N j .
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i 1 j i 1 |
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ɇɚɣɞɟɦɦɚɤɫɢɦɚɥɶɧɨɟȺ, ɤɨɬɨɪɨɟɫɨɨɬɜɟɬɫɬɜɭɟɬɫɥɭɱɚɸ |
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ɬɚɤɢɦɨɛɪɚɡɨɦ, |
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2k |
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k 1 i |
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(I, 4,12) |
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Ⱦɥɹɨɩɢɫɚɧɢɹɜɚɪɢɚɰɢɢɦɨɠɧɨɢɫɩɨɥɶɡɨɜɚɬɶɬɚɤɠɟɢɷɧɬɪɨɩɢɣɧɭɸɦɟɪɭ (ɫɦ. § 5 ɝɥɚɜɵ II). |
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Ʉɜɚɧɬɢɥɢ. |
Ɇɟɞɢɚɧɚ, |
ɤɚɤ ɦɵ ɜɢɞɟɥɢ, |
ɷɬɨ ɡɧɚɱɟɧɢɟ ɩɪɢɡɧɚɤɚ, ɤɨɬɨɪɨɟ ɨɛɥɚɞɚɟɬ ɬɚɤɢɦ |
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ɫɜɨɣɫɬɜɨɦ: 50% ɜɚɪɢɚɧɬɨɜɦɟɧɶɲɟ, ɱɟɦɆɟ, 50% – ɛɨɥɶɲɟ. ȿɫɬɟɫɬɜɟɧɧɵɦ ɨɛɨɛɳɟɧɢɟɦ ɦɟɞɢɚɧɵ ɹɜɥɹɟɬɫɹ ɩɨɧɹɬɢɟ ɤɜɚɧɬɢɥɹ. Ʉɜɚɧɬɢɥɶ ɞɟɥɢɬ ɫɭɦɦɭ ɱɚɫɬɨɬ ɧɚ ɡɚɞɚɧɧɨɟ ɱɢɫɥɨ ɪɚɜɧɵɯ ɱɚɫɬɟɣ. ɑɢɫɥɨ ɱɚɫɬɟɣ ɦɨɠɟɬ ɛɵɬɶ ɪɚɡɥɢɱɧɵɦ, ɨɬɫɸɞɚ ɢ ɪɚɡɧɵɟ ɤɜɚɧɬɢɥɢ – ɤɜɚɪɬɢɥɢ, ɞɟɰɢɥɢ, ɩɟɪɰɟɧɬɢɥɢ.
Ʉɜɚɪɬɢɥɶ. |
Ʉɜɚɪɬɢɥɶ (Qi ) |
ɞɟɥɢɬ ɫɭɦɦɭ ɱɚɫɬɨɬ ɧɚ |
ɱɟɬɵɪɟ ɪɚɜɧɵɟ ɱɚɫɬɢ. Ɉɱɟɜɢɞɧɨ, |
ɤɜɚɪɬɢɥɟɣ ɜɫɟɝɨ ɬɪɢ: Q1,Q2 ,Q3; |
Q1 ɧɚɩɪɢɦɟɪ, ɷɬɨ ɡɧɚɱɟɧɢɟ ɩɪɢɡɧɚɤɚ, ɤɨɬɨɪɨɟ ɨɛɥɚɞɚɟɬ ɬɚɤɢɦ |
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ɫɜɨɣɫɬɜɨɦ: 25% ɜɚɪɢɚɧɬɨɜ ɦɟɧɶɲɟ, ɚ 75% – ɛɨɥɶɲɟ ɟɝɨ. Q2 |
ɷɬɨ Ɇɟ, ɚ Q3 – ɡɧɚɱɟɧɢɟ ɩɪɢɡɧɚɤɚ, |
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75% ɜɚɪɢɚɧɬɨɜɦɟɧɶɲɟɤɨɬɨɪɨɝɨ, ɚ25% – ɛɨɥɶɲɟ. |
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ɉɪɹɦɵɟ x |
Qi (i 1,2,3) ɞɟɥɹɬ ɩɥɨɳɚɞɶ, ɨɝɪɚɧɢɱɟɧɧɭɸɤɪɢɜɨɣ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɧɚ 4 ɪɚɜɧɵɟ |
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ɱɚɫɬɢ: S1 S2 |
S3 S4 |
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ɇɚ ɪɢɫ. 17ɚ ɢɡɨɛɪɚɠɟɧɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ, ɚ ɧɚ ɪɢɫ. 17ɛ ɩɨɤɚɡɚɧɵ ɤɜɚɪɬɢɥɢ ɧɚ ɝɪɚɮɢɤɟ ɤɭɦɭɥɹɬɢɜɧɨɣ ɤɪɢɜɨɣ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɬɨɱɤɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɤɜɚɪɬɢɥɹɦ, ɜɨɨɛɳɟ ɝɨɜɨɪɹ, ɞɟɥɹɬ ɨɬɪɟɡɨɤ >xmin , xmax @ ɧɚ ɱɟɬɵɪɟ ɧɟɪɚɜɧɵɟ ɱɚɫɬɢ. Ɇɟɠɞɭ Q1 ɢ Q3 ɡɚɤɥɸɱɟɧɚ ɩɨɥɨɜɢɧɚ ɜɫɟɯ
ɜɚɪɢɚɧɬɨɜ. ɑɟɦ ɛɨɥɟɟ ɩɥɨɬɧɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ, ɬɟɦ ɨɬɪɟɡɨɤ >Q1,Q3 @ ɦɟɧɶɲɟ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɜɨɟɨɛɪɚɡɧɨɣɦɟɪɨɣ «ɪɚɡɛɪɨɫɚ» ɦɨɠɟɬɫɥɭɠɢɬɶɜɟɥɢɱɢɧɚ 'Q Q3 Q1.
[60]
Ⱦɟɰɢɥɶ. Ⱦɟɰɢɥɶ (D) ɞɟɥɢɬ ɫɭɦɦɭ ɱɚɫɬɨɬ ɧɚ 10 ɪɚɜɧɵɯ ɱɚɫɬɟɣ. ȼɫɟɝɨ ɞɟɰɢɥɟɣ, ɨɱɟɜɢɞɧɨ, ɞɟɜɹɬɶ: D1,D2 ,...D9 . əɫɧɨ, ɱɬɨ D5 Q2 Me. ȼ ɤɚɱɟɫɬɜɟ ɦɟɪɵ ɪɚɡɛɪɨɫɚ ɢɫɩɨɥɶɡɭɟɬɫɹ ɬɚɤɠɟ
ɜɟɥɢɱɢɧɚ 'D D9 D1.
40
Ɋɢɫ. 17. Ʉɜɚɪɬɢɥɢɧɚɝɪɚɮɢɤɟɪɚɫɩɪɟɞɟɥɟɧɢɹ (ɚ) ɢɧɚɝɪɚɮɢɤɟɤɭɦɭɥɹɬɢɜɧɨɣɤɪɢɜɨɣ (ɛ) ɉɟɪɰɟɧɬɢɥɶ, ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ, ɞɟɥɢɬ ɫɭɦɦɭ ɱɚɫɬɨɬ ɧɚ 100 ɪɚɜɧɵɯ ɱɚɫɬɟɣ: C1,C2,…,C99
Ʌɟɝɤɨɜɢɞɟɬɶ, ɱɬɨ, ɧɚɩɪɢɦɟɪ, D1 = C10, Q1 = C25, Me = C30, Q3 = C75 ɢɬ.ɞ.
Ʉɚɤ ɜɵɱɢɫɥɹɬɶ ɤɜɚɧɬɢɥɢ ɜ ɫɥɭɱɚɟ ɢɧɬɟɪɜɚɥɶɧɵɯ ɪɹɞɨɜ? ȼɫɩɨɦɢɧɚɹ ɜɵɜɨɞ ɮɨɪɦɭɥɵ ɞɥɹ
Me(Q2), ɥɟɝɤɨɩɨɧɹɬɶ, ɱɬɨ |
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0,25N Fl 1 |
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ɝɞɟ l – ɧɨɦɟɪɢɧɬɟɪɜɚɥɚ, ɜɤɨɬɨɪɵɣɩɨɩɚɞɚɟɬɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣɤɜɚɧɬɢɥɶ.
[61]
ɍɩɪɚɠɧɟɧɢɟ 21. ȼɵɜɟɫɬɢɮɨɪɦɭɥɵɞɥɹ Q1 ɢ Q3. Ⱥɧɚɥɨɝɢɱɧɨ, ɧɚɩɪɢɦɟɪ,
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Ɉɬɦɟɬɢɦ, ɱɬɨ ɤɜɚɧɬɢɥɶ – ɦɟɪɚ, ɩɪɢɦɟɧɢɦɚɹ ɤ ɫɚɦɵɦ ɪɚɡɥɢɱɧɵɦ ɬɢɩɚɦ ɭɩɨɪɹɞɨɱɟɧɧɵɯ ɞɚɧɧɵɯ. ɉɪɢɜɵɱɢɫɥɟɧɢɢɤɜɚɧɬɢɥɟɣɜɦɟɫɬɨɱɚɫɬɨɬɦɨɠɧɨɢɫɩɨɥɶɡɨɜɚɬɶɱɚɫɬɨɫɬɢ.
ɉɪɢɦɟɪ 9. ɉɨ ɞɚɧɧɵɦ ɬɚɛɥɢɰɵ ʋ 8 ɪɚɫɫɱɢɬɚɬɶ Q1 ɞɥɹ ɝɨɞɨɜɨɝɨ ɫɟɦɟɣɧɨɝɨ ɞɨɯɨɞɚ ɜ ɋɒȺ
(1959 ɝ.). ɇɟɬɪɭɞɧɨɜɢɞɟɬɶ, ɱɬɨ l = 2, xl = x2 = 2000, fl-1 = f1 14, vl = v2 = 21, ɬɟɩɟɪɶ Q1 §3050. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, 25% ɫɟɦɟɣɢɦɟɥɢɞɨɯɨɞ, ɦɟɧɶɲɢɣ 3050 ɞɨɥ.
ɍɩɪɚɠɧɟɧɢɟ 22. ȼɵɱɢɫɥɢɬɶ Q3, ¨Q, D9. ɇɟɪɟɞɤɨ ɱɚɫɬɨɬɵ ɤɪɚɣɧɢɯ ɜɚɪɢɚɧɬɨɜ ɨɱɟɧɶ ɦɚɥɵ, ɜɟɥɢɱɢɧɚ ɜɚɪɢɚɰɢɨɧɧɨɝɨ ɪɚɡɦɚɯɚ ɦɨɠɟɬ ɫɨɡɞɚɬɶ ɜɩɟɱɚɬɥɟɧɢɟ ɛɨɥɶɲɟɣ ɤɨɥɟɛɥɟɦɨɫɬɢ (ɜɟɥɢɱɢɧɵ ɜɚɪɢaɰɢɢ), ɧɟɠɟɥɢ ɬɚ, ɤɨɬɨɪɚɹ ɧɚɢɛɨɥɟɟ ɯɚɪɚɤɬɟɪɧɚ ɞɥɹ ɢɡɭɱɚɟɦɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ. ȼ ɬɚɤɢɯ ɫɥɭɱɚɹɯɰɟɥɟɫɨɨɛɪɚɡɧɨɜɵɱɢɫɥɹɬɶ¨Q ɢɥɢ¨D, ɜɤɨɬɨɪɵɯɨɬɪɚɠɟɧɞɢɚɩɚɡɨɧ, ɜɤɥɸɱɚɸɳɢɣɜɫɟɛɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ 50% ɢ 80% ɜɫɟɯɧɚɛɥɸɞɟɧɢɣ.
41
ɍɩɪɚɠɧɟɧɢɟ 23. Ʉɚɤɨɣ ɩɪɨɰɟɧɬ ɚɦɟɪɢɤɚɧɫɤɢɯ ɫɟɦɟɣ ɢɦɟɥ ɞɨɯɨɞ ɧɢɠɟ ɩɪɨɠɢɬɨɱɧɨɝɨ ɦɢɧɢɦɭɦɚ (3000 ɞɨɥ.)?
Ⱦɚɥɟɟ ɦɵ ɪɚɫɫɦɨɬɪɢɦ ɩɪɢɦɟɧɟɧɢɟ ɢɡɭɱɟɧɧɵɯ ɜɟɥɢɱɢɧ (Me, Qi, ¨Q) ɤ ɨɞɧɨɣ ɫɨɰɢɨɥɨɝɢɱɟɫɤɨɣɡɚɞɚɱɟ – ɢɡɦɟɪɟɧɢɸɭɫɬɚɧɨɜɤɢɢɧɞɢɜɢɞɨɜ.
ɉɪɢɦɟɪ 10. ɒɤɚɥɚ Ɍɟɪɫɬɨɭɧɚ. ɋ ɩɨɦɨɳɶɸ ɷɬɨɣ ɲɤɚɥɵ ɢɡɦɟɪɹɟɬɫɹ ɨɪɢɟɧɬɚɰɢɹ (ɨɬɧɨɲɟɧɢɟ, ɭɫɬɚɧɨɜɤɚ). Ɍɟɪɫɬɨɭɧ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɢɡɭɱɚɥ ɨɬɧɨɲɟɧɢɟ ɤ ɰɟɪɤɜɢ (ɞɚɥɶɲɟ ɦɵ ɩɨɞɪɨɛɧɨ ɪɚɫɫɦɨɬɪɢɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɩɪɨɰɟɞɭɪɭ), ɨɞɧɚɤɨ ɩɪɟɞɥɨɠɟɧɧɵɣ ɫɩɨɫɨɛ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɞɥɹɢɡɦɟɪɟɧɢɹɪɚɡɥɢɱɧɵɯɭɫɬɚɧɨɜɨɤ. ɂɬɚɤ, ɢɡɭɱɚɟɦɵɣɩɪɢɡɧɚɤ – ɨɬɧɨɲɟɧɢɟ.
ɉɭɧɤɬɵ ɲɤɚɥɵ ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɧɟ ɩɪɨɢɡɜɨɥɶɧɨ, ɚ ɫ ɩɨɦɨɳɶɸ ɨɬɛɨɪɚ ɫɭɠɞɟɧɢɣ, ɨɫɭɳɟɫɬɜɥɹɟɦɨɝɨ ɫɭɞɶɹɦɢ. ɋɩɟɪɜɚ ɩɪɢ ɭɱɚɫɬɢɢ ɩɪɟɞɫɬɚɜɢɬɟɥɟɧ ɨɛɫɥɟɞɭɟɦɨɝɨ ɦɚɫɫɢɜɚ ɛɵɥ ɫɨɫɬɚɜɥɟɧ ɫɩɢɫɨɤ, ɫɨɞɟɪɠɚɜɲɢɣ ɛɨɥɟɟ ɫɬɚ ɜɵɫɤɚɡɵɜɚɧɢɣ, ɨɬɪɚɠɚɸɳɢɯ ɪɚɡɥɢɱɧɨɟ ɨɬɧɨɲɟɧɢɟ ɤ ɢɡɭɱɚɟɦɨɦɭ ɮɟɧɨɦɟɧɭ. Ɂɚɬɟɦ 300 ɫɭɞɶɹɦ, ɩɪɟɞɫɬɚɜɥɹɜɲɢɦ ɦɨɞɟɥɶ ɢɫɫɥɟɞɭɟɦɨɣ ɚɭɞɢɬɨɪɢɢ, ɛɵɥɨ ɩɪɟɞɥɨɠɟɧɨ ɪɚɡɥɨɠɢɬɶ ɤɚɪɬɨɱɤɢ ɫ ɜɵɫɤɚɡɵɜɚɧɢɹɦɢ ɧɚ 11 ɤɭɱɟɤ: ɜ ɩɟɪɜɨɣ ɞɨɥɠɧɵ ɛɵɬɶ ɫɭɠ-
[62]
ɞɟɧɢɹ ɧɚɢɛɨɥɟɟ ɛɥɚɝɨɩɪɢɹɬɧɵɟ ɞɥɹ ɰɟɪɤɜɢ, ɜɨ-ɜɬɨɪɨɣ – ɦɟɧɟɟ ɢ ɬ.ɞ. ɞɨ 11-ɨɣ, ɤɭɞɚ ɩɨɩɚɞɚɸɬ ɧɚɢɦɟɧɟɟɛɥɚɝɨɩɪɢɹɬɧɵɟɫɭɠɞɟɧɢɹ.
ɉɨɫɥɟ ɬɨɝɨ, ɤɚɤ ɫɭɞɶɢ ɡɚɜɟɪɲɢɥɢ ɪɚɛɨɬɭ, ɧɭɠɧɨ ɭɫɬɚɧɨɜɢɬɶ ɰɟɧɭ ɤɚɠɞɨɝɨ ɫɭɠɞɟɧɢɹ, ɦɟɪɭ ɫɨɝɥɚɫɨɜɚɧɧɨɫɬɢ ɫɭɞɟɣɫɤɢɯ ɪɟɲɟɧɢɣ ɩɨ ɤɚɠɞɨɦɭ ɫɭɠɞɟɧɢɸ ɢ ɨɬɨɛɪɚɬɶ ɧɚɛɨɪ ɫɭɠɞɟɧɢɣ, ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɵɯ ɢɫɫɥɟɞɨɜɚɬɟɥɶ ɦɨɠɟɬ ɢɡɭɱɚɬɶ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɟ ɨɬɧɨɲɟɧɢɟ ɢɧɞɢɜɢɞɨɜ ɞɚɧɧɨɣɨɛɳɧɨɫɬɢ.
ɐɟɧɚ ɫɭɠɞɟɧɢɹ ɨɩɪɟɞɟɥɹɥɚɫɶ ɤɚɤ ɦɟɞɢɚɧɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɭɞɟɣɫɤɢɯ ɪɟɲɟɧɢɣ, ɦɟɪɚ ɫɨɝɥɚɫɨɜɚɧɧɨɫɬɢ – ɤɜɚɧɬɢɥɶɧɨɟɨɬɤɥɨɧɟɧɢɟ.
ɑɬɨɛɵ ɨɛɪɚɛɨɬɚɬɶ ɪɟɡɭɥɶɬɚɬɵ ɪɚɛɨɬɵ ɫɭɞɟɣ, ɞɥɹ ɤɚɠɞɨɝɨ ɢɡ ɫɭɠɞɟɧɢɣ ɩɟɪɜɨɧɚɱɚɥɶɧɨɝɨ ɫɩɢɫɤɚɫɨɫɬɚɜɥɹɟɬɫɹɬɚɤɚɹɬɚɛɥɢɰɚ:
|
Ni(ɱɢɫɥɨ |
ɫɭɞɟɣ, |
vi (% ɤ ɨɛɳɟɦɭ |
fi (ɤɭɦɭɥɹɬɢɜɧɵɣ %) |
|
ɩɨɦɟɫɬɢɜɲɢɯ |
|
ɱɢɫɥɭɫɭɞɟɣ) |
|
ɉɭɧɤɬɵɲɤɚɥɵ |
|
|
|
|
|
ɞɚɧɧɨɟ ɫɭɠɞɟɧɢɟ ɜ |
|
|
|
|
ɷɬɨɬɩɭɧɤɬ) |
|
|
|
1 |
2 |
|
3 |
4 |
1 |
0 |
|
0 |
0 |
2 |
0 |
|
0 |
0 |
3 |
0 |
|
0 |
0 |
4 |
0 |
|
0 |
0 |
5 |
0 |
|
0 |
0 |
6 |
12 |
|
4% |
4% |
7 |
12 |
|
4% |
8% |
8 |
60 |
|
20% |
28% |
9 |
66 |
|
22% |
50% |
10 |
90 |
|
30% |
80% |
11 |
60 |
|
20% |
100% |
|
|
|
|
|
|
300 |
|
100% |
|
42
Ɂɚɬɟɦ ɫɬɪɨɢɬɫɹ ɤɭɦɭɥɹɬɚ (ɪɢɫ. 18). ɉɪɢ ɷɬɨɦ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɨɬɧɨɲɟɧɢɟ ɢɡɦɟɧɹɟɬɫɹ ɤɨɧɬɢɧɭɚɥɶɧɨ, ɩɭɧɤɬɵ 1, 2, ..., 11 – ɨɬɞɟɥɶɧɵɟ ɬɨɱɤɢ, ɤɨɬɨɪɵɟ ɜɵɞɟɥɹɸɬ ɜ ɞɚɧɧɨɦ ɤɨɧɬɢɧɭɭɦɟ ɢɧɬɟɪɜɚɥɵ; ɨɪɞɢɧɚɬɵɤɭɦɭɥɹɬɵɫɨɨɬɜɟɬɫɬɜɭɸɬɫɟɪɟɞɢɧɚɦɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯɢɧɬɟɪɜɚɥɨɜ.
Ⱦɥɹ ɩɪɟɞɫɬɚɜɥɟɧɧɨɝɨ ɧɚ ɝɪɚɮɢɤɟ ɫɭɠɞɟɧɢɹ, ɤɚɤ ɜɢɞɧɨ ɢɡ ɱɟɪɬɟɠɚ, Ɇɟ = 8,5; Q1=7,3, Q3=9,3, ¨Q=2,0. ɉɪɨɞɟɥɚɜ ɬɚɤɭɸ ɩɪɨɰɟɞɭɪɭ ɫɨ ɜɫɟɦɢ ɫɭɠɞɟɧɢɹɦɢ, ɜ ɢɬɨɝɨɜɭɸ ɲɤɚɥɭ ɨɬɛɢɪɚɸɬ ɬɟ, ɤɨɬɨɪɵɟ: 1) ɩɨɤɪɵɜɚɸɬ ɛɨɥɟɟ ɢɥɢ ɦɟɧɟɟ ɪɚɜɧɨɦɟɪɧɨ ɜɫɸ ɲɤɚɥɭ; 2) ɢɦɟɸɬ ɧɚɢɛɨɥɟɟ ɫɨɝɥɚɫɨɜɚɧɧɵɟ
[63]
ɨɰɟɧɤɢ, ɬ.ɟ. ɢɡ ɧɟɫɤɨɥɶɤɢɯ ɫɭɠɞɟɧɢɣ ɫ ɛɥɢɡɤɢɦɢ Ɇe ɩɪɟɞɩɨɱɬɟɧɢɟ ɨɬɞɚɟɬɫɹ ɫɭɠɞɟɧɢɸ ɫ ɦɢɧɢɦɚɥɶɧɵɦɤɜɚɪɬɢɥɶɧɵɦɨɬɤɥɨɧɟɧɢɟɦ¨Q.
Ɉɤɨɧɱɚɬɟɥɶɧɚɹ ɲɤɚɥɚ ɫɨɞɟɪɠɢɬ 10–15 ɫɭɠɞɟɧɢɣ, ɤɚɠɞɨɟ ɢɡ ɤɨɬɨɪɵɯ ɢɦɟɟɬ ɫɜɨɣ «ɜɟɫ» (ɰɟɧɭ) – ɦɟɞɢɚɧɭɫɭɞɟɣɫɤɢɯɪɟɲɟɧɢɣ. Ɉɬɨɛɪɚɧɧɵɟɫɭɠɞɟɧɢɹɩɪɟɞɥɚɝɚɸɬɫɹɪɟɫɩɨɧ-
Ɋɢɫ. 18. ɄɭɦɭɥɹɬɚɞɥɹɩɨɫɬɪɨɟɧɢɹɲɤɚɥɵɌɟɪɫɬɨɭɧɚ
ɞɟɧɬɭ. ȿɝɨ ɪɚɧɝ ɩɨ ɞɚɧɧɨɣ ɲɤɚɥɟ – ɦɟɞɢɚɧɚ «ɜɟɫɨɜ» ɩɪɢɧɹɬɵɯ ɢɦ ɫɭɠɞɟɧɢɣ, ɬ.ɟ. ɫɭɠɞɟɧɢɣ, ɫ ɤɨɬɨɪɵɦɢ ɨɧ ɫɨɝɥɚɫɟɧ. ȿɫɥɢ ɪɟɫɩɨɧɞɟɧɬ Ⱥ ɫɨɝɥɚɫɟɧ ɫ ɬɚɤɢɦɢ ɩɹɬɶɸ ɫɭɠɞɟɧɢɹɦɢ, ɭ ɤɨɬɨɪɵɯ «ɜɟɫɚ»: 4,4; 4,8; 5,1; 5,6; 6,1, ɬɨ ɟɝɨ ɪɚɧɝ 5,1. ȿɫɥɢ ɪɟɫɩɨɧɞɟɧɬ ȼ ɜɵɛɪɚɥ ɱɟɬɵɪɟ ɫɭɠɞɟɧɢɹ ɫ «ɜɟɫɚɦɢ»: 7,6; 8,1; 8,5; 8,7, ɬɨ ɟɝɨ ɪɚɧɝ 8,3 (ɦɟɞɢɚɧɚ «ɜɟɫɨɜ» ɜ ɫɥɭɱɚɟ ɱɟɬɧɨɝɨ ɱɢɫɥɚ ɫɭɠɞɟɧɢɣ,
ɩɨɨɩɪɟɞɟɥɟɧɢɸ, 8,1 8,5 8,3 ). 2
Ɉɬɦɟɬɢɦ, ɱɬɨ ɲɤɚɥɚ Ɍɟɪɫɬɨɭɧɚ ɨɛɥɚɞɚɟɬ ɪɹɞɨɦ ɧɟɞɨɫɬɚɬɤɨɜ, ɭɫɬɪɚɧɟɧɧɵɯ ɜ ɛɨɥɟɟ ɫɨɜɟɪɲɟɧɧɵɯɦɟɬɨɞɚɯ30.
[64]
30 Ʉɥɢɝɟɪ ɋ. Ⱥ., Ʉɨɫɨɥɚɩɨɜ Ɇ. ɋ., Ɍɨɥɫɬɨɜɚ ɘ. ɇ. ɒɤɚɥɢɪɨɜɚɧɢɟ ɩɪɢ ɫɛɨɪɟ ɢ ɚɧɚɥɢɡɟ ɫɨɰɢɨɥɨɝɢɱɟɫɤɨɣ ɢɧɮɨɪɦɚɰɢɢ. Ɇ., 1978, ɫ. 71—81.
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