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ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 1
Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ
19
ȼ ɷɥɟɤɬɪɨɧɧɭɸ ɬɚɛɥɢɰɭ ɡɚɧɟɫɥɢ ɪɟɡɭɥɶɬɚɬɵ ɫɞɚɱɢ ɧɨɪɦɚɬɢɜɨɜ ɩɨ ɥɺɝɤɨɣ
ɚɬɥɟɬɢɤɟ ɫɪɟɞɢ ɭɱɚɳɢɯɫɹ 7–11 ɤɥɚɫɫɨɜ. ɇɚ ɪɢɫɭɧɤɟ ɩɪɢɜɟɞɟɧɵ ɩɟɪɜɵɟ ɫɬɪɨɤɢ
ɩɨɥɭɱɢɜɲɟɣɫɹ ɬɚɛɥɢɰɵ.
A
B
C
D
E
Ȼɟɝ
Ƚɨɞ
1 Ɏɚɦɢɥɢɹ
ɂɦɹ
ɉɨɥ
1000 ɦɟɬɪɨɜ,
ɪɨɠɞɟɧɢɹ
ɦɢɧ.
ɉɭɞɨɜɚ
Ʉɫɟɧɢɹ
ɠ
1997
4,47
2
Ƚɭɫɟɜɚ
Ɇɚɪɢɹ
ɠ
1998
4,47
3
1999
5,03
4 Ʌɟɥɶɤɨɜɚ ɇɚɞɟɠɞɚ ɠ
Ɍɢɥɶ
ȿɜɝɟɧɢɣ ɦ
1999
3,32
5
ɠ
1998
5,57
6 Ʌɢɦɚɧɢɧɚ ɇɟɥɥɢ
1997
5,42
7 Ȼɚɫɤɚɤɨɜɚ ɋɜɟɬɥɚɧɚ ɠ
ɠ
1997
5,38
8 ɉɪɨɯɨɪɨɜɚ Ⱥɧɧɚ
ɠ
1999
5,45
9 Ȼɭɠɟɧɢɧɚ Ɉɥɶɝɚ
ɠ
1997
4,58
10 Ɍɪɭɛɚɟɜɚ Ⱥɥɢɧɚ
F
Ȼɟɝ
30 ɦɟɬɪɨɜ,
ɫɟɤ.
4,12
5,82
5,04
5,87
5,32
4,47
5,79
5,08
4,44
G
ɉɪɵɠɨɤ
ɜ ɞɥɢɧɭ
ɫ ɦɟɫɬɚ, ɫɦ
209
205
198
210
182
180
219
222
198
ȼ ɫɬɨɥɛɰɟ A ɭɤɚɡɚɧɚ ɮɚɦɢɥɢɹ; ɜ ɫɬɨɥɛɰɟ B – ɢɦɹ; ɜ ɫɬɨɥɛɰɟ C – ɩɨɥ; ɜ ɫɬɨɥɛɰɟ
D – ɝɨɞ ɪɨɠɞɟɧɢɹ; ɜ ɫɬɨɥɛɰɟ E – ɪɟɡɭɥɶɬɚɬɵ ɜ ɛɟɝɟ ɧɚ 1000 ɦɟɬɪɨɜ; ɜ ɫɬɨɥɛɰɟ
F – ɪɟɡɭɥɶɬɚɬɵ ɜ ɛɟɝɟ ɧɚ 30 ɦɟɬɪɨɜ; ɜ ɫɬɨɥɛɰɟ G – ɪɟɡɭɥɶɬɚɬɵ ɩɨ ɩɪɵɠɤɚɦ
ɜ ɞɥɢɧɭ ɫ ɦɟɫɬɚ.
ȼɫɟɝɨ ɜ ɷɥɟɤɬɪɨɧɧɭɸ ɬɚɛɥɢɰɭ ɛɵɥɢ ɡɚɧɟɫɟɧɵ ɞɚɧɧɵɟ ɩɨ 1000 ɭɱɚɳɢɦɫɹ.
ȼɵɩɨɥɧɢɬɟ ɡɚɞɚɧɢɟ.
Ɉɬɤɪɨɣɬɟ ɮɚɣɥ ɫ ɞɚɧɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɚɛɥɢɰɟɣ (ɪɚɫɩɨɥɨɠɟɧɢɟ ɮɚɣɥɚ ȼɚɦ
ɫɨɨɛɳɚɬ ɨɪɝɚɧɢɡɚɬɨɪɵ ɷɤɡɚɦɟɧɚ). ɇɚ ɨɫɧɨɜɚɧɢɢ ɞɚɧɧɵɯ, ɫɨɞɟɪɠɚɳɢɯɫɹ ɜ ɷɬɨɣ
ɬɚɛɥɢɰɟ, ɨɬɜɟɬɶɬɟ ɧɚ ɞɜɚ ɜɨɩɪɨɫɚ.
1. Ʉɚɤɨɣ ɦɚɤɫɢɦɚɥɶɧɵɣ ɪɟɡɭɥɶɬɚɬ ɩɨ ɩɪɵɠɤɚɦ ɜ ɞɥɢɧɭ ɩɨɤɚɡɚɥɢ ɦɚɥɶɱɢɤɢ
1998 ɝɨɞɚ ɪɨɠɞɟɧɢɹ? Ɉɬɜɟɬ ɧɚ ɷɬɨɬ ɜɨɩɪɨɫ ɡɚɩɢɲɢɬɟ ɜ ɹɱɟɣɤɭ J1 ɬɚɛɥɢɰɵ.
2. ɇɚɣɞɢɬɟ ɫɪɟɞɧɟɟ ɜɪɟɦɹ ɫɪɟɞɢ ɞɟɜɨɱɟɤ ɜ ɛɟɝɟ ɧɚ 30 ɦɟɬɪɨɜ. Ɉɬɜɟɬ ɫ ɬɨɱɧɨɫɬɶɸ
ɞɨ ɨɞɧɨɝɨ ɡɧɚɤɚ ɩɨɫɥɟ ɡɚɩɹɬɨɣ ɡɚɩɢɲɢɬɟ ɜ ɹɱɟɣɤɭ J2 ɬɚɛɥɢɰɵ.
ɉɨɥɭɱɟɧɧɭɸ ɬɚɛɥɢɰɭ ɧɟɨɛɯɨɞɢɦɨ ɫɨɯɪɚɧɢɬɶ ɩɨɞ ɢɦɟɧɟɦ, ɭɤɚɡɚɧɧɵɦ
ɨɪɝɚɧɢɡɚɬɨɪɚɦɢ ɷɤɡɚɦɟɧɚ.
ɉɪɢɦɟɱɚɧɢɟ. ɉɪɢ ɪɟɲɟɧɢɢ ɞɨɩɭɫɤɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɥɸɛɵɯ ɜɨɡɦɨɠɧɨɫɬɟɣ
ɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɤɚɥɶɤɭɥɹɬɨɪɨɜ ɧɟ ɞɨɩɭɫɤɚɟɬɫɹ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
2
Ⱥɥɝɨɪɢɬɦɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɞɥɹ OpenOffice.org Calc ɢ Microsoft Excel ɫɨɜɩɚɞɚɸɬ.
Ɏɨɪɦɭɥɵ ɧɚɩɢɫɚɧɵ ɞɥɹ ɨɛɟɢɯ ɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰ. ȼɬɨɪɨɣ ɜɚɪɢɚɧɬ – ɞɥɹ
OpenOffice.org Calc.
ȼ ɹɱɟɣɤɭ H2 ɡɚɩɢɲɟɦ ɮɨɪɦɭɥɭ:
=ȿɋɅɂ(ɂ(C2="ɦ";D2=1998);G2;0)
=IF(AND(C2="ɦ";D2=1998);G2;0)
ɋɤɨɩɢɪɭɟɦ ɮɨɪɦɭɥɭ ɜɨ ɜɫɟ ɹɱɟɣɤɢ ɞɢɚɩɚɡɨɧɚ H3:H1001.
Ɉɬɜɟɬ ɧɚ ɩɟɪɜɵɣ ɜɨɩɪɨɫ ɩɨɥɭɱɢɦ ɩɨ ɮɨɪɦɭɥɟ, ɤɨɬɨɪɭɸ ɡɚɩɢɲɟɦ ɜ ɹɱɟɣɤɭ J1:
=ɆȺɄɋ(H2:H1001)
=MAX(H2:H1001)
Ⱦɥɹ ɨɬɜɟɬɚ ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɮɨɪɦɭɥɨɣ, ɡɚɩɢɫɚɜ ɟɟ ɜ ɹɱɟɣɤɭ J2:
=ɋɍɆɆȿɋɅɂ(C2:C1001;"ɠ";F2:F1001)/ɋɑȬɌȿɋɅɂ(C2:C1001;"ɠ")
=SUMIF(C2:C1001;"ɠ";F2:F1001)/COUNTIF(C2:C1001;"ɠ")
ɝɞɟ ɋɍɆɆȿɋɅɂ(C2:C1001;"ɠ";F2:F1001) – ɫɭɦɦɚ ɜɫɟɯ ɪɟɡɭɥɶɬɚɬɨɜ ɩɨ ɛɟɝɭ ɧɚ 30 ɦ
ɫɪɟɞɢ ɞɟɜɨɱɟɤ, ɋɑȬɌȿɋɅɂ(C2:C1001;"ɠ") - ɤɨɥɢɱɟɫɬɜɨ ɞɟɜɨɱɟɤ.
Ɂɚɞɚɞɢɦ ɮɨɪɦɚɬ ɹɱɟɣɤɢ J2 ɱɢɫɥɨɜɨɣ, ɱɢɫɥɨ ɞɟɫɹɬɢɱɧɵɯ ɡɧɚɤɨɜ – 1.
ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɫɩɨɫɨɛɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ.
ȿɫɥɢ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɩɪɚɜɢɥɶɧɨ ɢ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɹ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɮɚɣɥɵ,
ɫɩɟɰɢɚɥɶɧɨ ɩɨɞɝɨɬɨɜɥɟɧɧɵɟ ɞɥɹ ɩɪɨɜɟɪɤɢ ɜɵɩɨɥɧɟɧɢɹ ɞɚɧɧɨɝɨ ɡɚɞɚɧɢɹ, ɬɨ ɞɨɥɠɧɵ
ɩɨɥɭɱɢɬɶɫɹ ɫɥɟɞɭɸɳɢɟ ɨɬɜɟɬɵ:
ɧɚ ɩɟɪɜɵɣ ɜɨɩɪɨɫ – 235;
ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ – 5,2.
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɨɥɭɱɟɧɵ ɩɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɚ ɨɛɚ ɜɨɩɪɨɫɚ. ɋɩɨɫɨɛ ɩɨɥɭɱɟɧɢɹ ɨɬɜɟɬɚ
ɦɨɠɟɬ ɧɟ ɫɨɜɩɚɞɚɬɶ ɫ ɩɪɢɜɟɞɺɧɧɵɦ ɜɵɲɟ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɚ ɜ ɞɪɭɝɢɟ
ɹɱɟɣɤɢ (ɨɬɥɢɱɧɵɟ ɨɬ ɬɟɯ, ɤɨɬɨɪɵɟ ɭɤɚɡɚɧɵ ɜ ɡɚɞɚɧɢɢ) ɩɪɢ ɭɫɥɨɜɢɢ
2
ɩɪɚɜɢɥɶɧɨɫɬɢ ɩɨɥɭɱɟɧɧɵɯ ɨɬɜɟɬɨɜ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɨɜ ɫ ɛɨɥɶɲɟɣ
ɬɨɱɧɨɫɬɶɸ
ɉɨɥɭɱɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɬɨɥɶɤɨ ɧɚ ɨɞɢɧ ɢɡ ɞɜɭɯ ɜɨɩɪɨɫɨɜ
1
0
ɉɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɟ ɩɨɥɭɱɟɧɵ ɧɢ ɧɚ ɨɞɢɧ ɢɡ ɜɨɩɪɨɫɨɜ
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ȼɵɛɟɪɢɬɟ ɬɨɥɶɤɨ ɈȾɇɈ ɢɡ ɩɪɟɞɥɨɠɟɧɧɵɯ ɡɚɞɚɧɢɣ: 20.1 ɢɥɢ 20.2.
20.1 ɂɫɩɨɥɧɢɬɟɥɶ Ɋɨɛɨɬ ɭɦɟɟɬ ɩɟɪɟɦɟɳɚɬɶɫɹ ɩɨ ɥɚɛɢɪɢɧɬɭ, ɧɚɱɟɪɱɟɧɧɨɦɭ
ɧɚ ɩɥɨɫɤɨɫɬɢ, ɪɚɡɛɢɬɨɣ ɧɚ ɤɥɟɬɤɢ. Ɇɟɠɞɭ ɫɨɫɟɞɧɢɦɢ (ɩɨ ɫɬɨɪɨɧɚɦ)
ɤɥɟɬɤɚɦɢ ɦɨɠɟɬ ɫɬɨɹɬɶ ɫɬɟɧɚ, ɱɟɪɟɡ ɤɨɬɨɪɭɸ Ɋɨɛɨɬ ɩɪɨɣɬɢ ɧɟ ɦɨɠɟɬ.
ɍ Ɋɨɛɨɬɚ ɟɫɬɶ ɞɟɜɹɬɶ ɤɨɦɚɧɞ. ɑɟɬɵɪɟ ɤɨɦɚɧɞɵ – ɷɬɨ ɤɨɦɚɧɞɵɩɪɢɤɚɡɵ:
ɜɜɟɪɯ
ɜɧɢɡ
ɜɥɟɜɨ
ɜɩɪɚɜɨ
ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɥɸɛɨɣ ɢɡ ɷɬɢɯ ɤɨɦɚɧɞ Ɋɨɛɨɬ ɩɟɪɟɦɟɳɚɟɬɫɹ ɧɚ ɨɞɧɭ
ɤɥɟɬɤɭ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ: ɜɜɟɪɯ Ĺ, ɜɧɢɡ Ļ, ɜɥɟɜɨ ĸ, ɜɩɪɚɜɨ ĺ. ȿɫɥɢ
Ɋɨɛɨɬ ɩɨɥɭɱɢɬ ɤɨɦɚɧɞɭ ɩɟɪɟɞɜɢɠɟɧɢɹ ɱɟɪɟɡ ɫɬɟɧɭ, ɬɨ ɨɧ ɪɚɡɪɭɲɢɬɫɹ.
ȿɳɺ ɱɟɬɵɪɟ ɤɨɦɚɧɞɵ – ɷɬɨ ɤɨɦɚɧɞɵ ɩɪɨɜɟɪɤɢ ɭɫɥɨɜɢɣ. ɗɬɢ ɤɨɦɚɧɞɵ
ɩɪɨɜɟɪɹɸɬ, ɫɜɨɛɨɞɟɧ ɥɢ ɩɭɬɶ ɞɥɹ Ɋɨɛɨɬɚ ɜ ɤɚɠɞɨɦ ɢɡ ɱɟɬɵɪɺɯ
ɜɨɡɦɨɠɧɵɯ ɧɚɩɪɚɜɥɟɧɢɣ:
ɫɜɟɪɯɭ
ɫɜɨɛɨɞɧɨ
ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ ɫɥɟɜɚ ɫɜɨɛɨɞɧɨ ɫɩɪɚɜɚ
ɫɜɨɛɨɞɧɨ
ɗɬɢ ɤɨɦɚɧɞɵ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɦɟɫɬɟ ɫ ɭɫɥɨɜɢɟɦ «eɫɥɢ»,
ɢɦɟɸɳɢɦ ɫɥɟɞɭɸɳɢɣ ɜɢɞ:
3
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɧɰ ɩɨɤɚ ɭɫɥɨɜɢɟ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ
ɤɰ
ɇɚɩɪɢɦɟɪ, ɞɥɹ ɞɜɢɠɟɧɢɹ ɜɩɪɚɜɨ, ɩɨɤɚ ɷɬɨ ɜɨɡɦɨɠɧɨ, ɦɨɠɧɨ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɣ ɚɥɝɨɪɢɬɦ:
ɧɰ ɩɨɤɚ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ
ɜɩɪɚɜɨ
ɤɰ
Ɍɚɤɠɟ ɭ Ɋɨɛɨɬɚ ɟɫɬɶ ɤɨɦɚɧɞɚ ɡɚɤɪɚɫɢɬɶ, ɩɪɢ ɤɨɬɨɪɨɣ ɡɚɤɪɚɲɢɜɚɟɬɫɹ
ɤɥɟɬɤɚ, ɜ ɤɨɬɨɪɨɣ Ɋɨɛɨɬ ɧɚɯɨɞɢɬɫɹ ɜ ɧɚɫɬɨɹɳɢɣ ɦɨɦɟɧɬ.
ȼɵɩɨɥɧɢɬɟ ɡɚɞɚɧɢɟ.
ɇɚ ɛɟɫɤɨɧɟɱɧɨɦ ɩɨɥɟ ɢɦɟɟɬɫɹ ɝɨɪɢɡɨɧɬɚɥɶɧɚɹ ɫɬɟɧɚ, ɛɟɫɤɨɧɟɱɧɨ
ɩɪɨɞɨɥɠɚɸɳɚɹɫɹ ɜɥɟɜɨ ɢ ɡɚɤɚɧɱɢɜɚɸɳɚɹɫɹ ɥɟɫɬɧɢɰɟɣ, ɤɨɬɨɪɚɹ
ɩɨɞɧɢɦɚɟɬɫɹ ɫɥɟɜɚ ɧɚɩɪɚɜɨ. ȼɵɫɨɬɚ ɤɚɠɞɨɣ ɫɬɭɩɟɧɢ – ɨɞɧɚ ɤɥɟɬɤɚ,
ɲɢɪɢɧɚ – ɬɪɢ ɤɥɟɬɤɢ. Ɋɨɛɨɬ ɧɚɯɨɞɢɬɫɹ ɧɚ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɬɟɧɟ,
ɥɟɜɟɟ ɥɟɫɬɧɢɰɵ.
ɇɚ ɪɢɫɭɧɤɟ ɭɤɚɡɚɧ ɨɞɢɧ ɢɡ ɜɨɡɦɨɠɧɵɯ ɫɩɨɫɨɛɨɜ ɪɚɫɩɨɥɨɠɟɧɢɹ
ɥɟɫɬɧɢɰɵ ɢ Ɋɨɛɨɬɚ (Ɋɨɛɨɬ ɨɛɨɡɧɚɱɟɧ ɛɭɤɜɨɣ «Ɋ») .
ɟɫɥɢ ɭɫɥɨɜɢɟ ɬɨ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ
ɜɫɟ
Ɂɞɟɫɶ ɭɫɥɨɜɢɟ – ɨɞɧɚ ɢɡ ɤɨɦɚɧɞ ɩɪɨɜɟɪɤɢ ɭɫɥɨɜɢɹ.
ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ – ɷɬɨ ɨɞɧɚ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɥɸɛɵɯ
ɤɨɦɚɧɞ-ɩɪɢɤɚɡɨɜ.
ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɟɪɟɞɜɢɠɟɧɢɹ ɧɚ ɨɞɧɭ ɤɥɟɬɤɭ ɜɩɪɚɜɨ, ɟɫɥɢ ɫɩɪɚɜɚ ɧɟɬ
ɫɬɟɧɤɢ, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɚɤɨɣ ɚɥɝɨɪɢɬɦ:
ɟɫɥɢ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɬɨ
ɜɩɪɚɜɨ
ɜɫɟ
ɇɚɩɢɲɢɬɟ ɞɥɹ Ɋɨɛɨɬɚ ɚɥɝɨɪɢɬɦ, ɡɚɤɪɚɲɢɜɚɸɳɢɣ ɜɫɟ ɤɥɟɬɤɢ,
ɪɚɫɩɨɥɨɠɟɧɧɵɟ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɧɚɞ ɫɬɭɩɟɧɹɦɢ ɥɟɫɬɧɢɰɵ.
Ɍɪɟɛɭɟɬɫɹ ɡɚɤɪɚɫɢɬɶ ɬɨɥɶɤɨ ɤɥɟɬɤɢ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɞɚɧɧɨɦɭ
ɭɫɥɨɜɢɸ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɪɢɜɟɞɺɧɧɨɝɨ ɜɵɲɟ ɪɢɫɭɧɤɚ Ɋɨɛɨɬ ɞɨɥɠɟɧ
ɡɚɤɪɚɫɢɬɶ ɫɥɟɞɭɸɳɢɟ ɤɥɟɬɤɢ (ɫɦ. ɪɢɫɭɧɨɤ) :
ȼ ɨɞɧɨɦ ɭɫɥɨɜɢɢ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɟɫɤɨɥɶɤɨ ɤɨɦɚɧɞ ɩɪɨɜɟɪɤɢ
ɭɫɥɨɜɢɣ, ɩɪɢɦɟɧɹɹ ɥɨɝɢɱɟɫɤɢɟ ɫɜɹɡɤɢ ɢ, ɢɥɢ, ɧɟ, ɧɚɩɪɢɦɟɪ:
ɟɫɥɢ (ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ) ɢ (ɧɟ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ) ɬɨ
ɜɩɪɚɜɨ
ɜɫɟ
Ⱦɥɹ ɩɨɜɬɨɪɟɧɢɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɤɨɦɚɧɞ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ
ɰɢɤɥ «ɩɨɤɚ», ɢɦɟɸɳɢɣ ɫɥɟɞɭɸɳɢɣ ɜɢɞ:
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
4
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
5
Ʉɨɧɟɱɧɨɟ ɪɚɫɩɨɥɨɠɟɧɢɟ Ɋɨɛɨɬɚ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɢɡɜɨɥɶɧɵɦ.
Ⱥɥɝɨɪɢɬɦ ɞɨɥɠɟɧ ɪɟɲɚɬɶ ɡɚɞɚɱɭ ɞɥɹ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɪɚɡɦɟɪɚ ɩɨɥɹ ɢ
ɥɸɛɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɫɬɭɩɟɧɟɣ.
ɉɪɢ ɢɫɩɨɥɧɟɧɢɢ ɚɥɝɨɪɢɬɦɚ Ɋɨɛɨɬ ɧɟ ɞɨɥɠɟɧ ɪɚɡɪɭɲɢɬɶɫɹ,
ɜɵɩɨɥɧɟɧɢɟ ɚɥɝɨɪɢɬɦɚ ɞɨɥɠɧɨ ɡɚɜɟɪɲɢɬɶɫɹ.
Ⱥɥɝɨɪɢɬɦ ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧ ɜ ɫɪɟɞɟ ɮɨɪɦɚɥɶɧɨɝɨ ɢɫɩɨɥɧɢɬɟɥɹ
ɢɥɢ ɡɚɩɢɫɚɧ ɜ ɬɟɤɫɬɨɜɨɦ ɪɟɞɚɤɬɨɪɟ.
ɋɨɯɪɚɧɢɬɟ ɚɥɝɨɪɢɬɦ ɜ ɬɟɤɫɬɨɜɨɦ ɮɚɣɥɟ. ɇɚɡɜɚɧɢɟ ɮɚɣɥɚ ɢ ɤɚɬɚɥɨɝ
ɞɥɹ ɫɨɯɪɚɧɟɧɢɹ ȼɚɦ ɫɨɨɛɳɚɬ ɨɪɝɚɧɢɡɚɬɨɪɵ ɷɤɡɚɦɟɧɚ.
20.2
ɇɚɩɢɲɢɬɟ ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɧɚɬɭɪɚɥɶɧɵɯ
ɱɢɫɟɥ ɨɩɪɟɞɟɥɹɟɬ ɫɭɦɦɭ ɞɜɭɯɡɧɚɱɧɵɯ ɱɢɫɟɥ, ɤɪɚɬɧɵɯ 5. ɉɪɨɝɪɚɦɦɚ
ɩɨɥɭɱɚɟɬ ɧɚ ɜɯɨɞ ɧɚɬɭɪɚɥɶɧɵɟ ɱɢɫɥɚ, ɤɨɥɢɱɟɫɬɜɨ ɜɜɟɞɺɧɧɵɯ ɱɢɫɟɥ
ɧɟɢɡɜɟɫɬɧɨ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɱɢɫɟɥ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɱɢɫɥɨɦ 0 (0 –
ɩɪɢɡɧɚɤ ɨɤɨɧɱɚɧɢɹ ɜɜɨɞɚ, ɧɟ ɜɯɨɞɢɬ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ) .
Ʉɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ ɧɟ ɩɪɟɜɵɲɚɟɬ 100. ȼɜɟɞɺɧɧɵɟ ɱɢɫɥɚ ɧɟ ɩɪɟɜɵɲɚɸɬ 30000.
ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ: ɫɭɦɦɭ ɞɜɭɯɡɧɚɱɧɵɯ ɱɢɫɟɥ,
ɤɪɚɬɧɵɯ 5.
22
45
120
0
ɉɪɢɦɟɪ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɵ:
ȼɯɨɞɧɵɟ ɞɚɧɧɵɟ
ȼɵɯɨɞɧɵɟ ɞɚɧɧɵɟ
45
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
6
Ɋɟɲɟɧɢɟ ɡɚɞɚɧɢɹ 20.1
Ʉɨɦɚɧɞɵ ɢɫɩɨɥɧɢɬɟɥɹ ɛɭɞɟɦ ɡɚɩɢɫɵɜɚɬɶ ɠɢɪɧɵɦ ɲɪɢɮɬɨɦ, ɚ ɤɨɦɦɟɧɬɚɪɢɢ,
ɩɨɹɫɧɹɸɳɢɟ ɚɥɝɨɪɢɬɦ ɢ ɧɟ ɹɜɥɹɸɳɢɟɫɹ ɟɝɨ ɱɚɫɬɶɸ, – ɤɭɪɫɢɜɨɦ. ɇɚɱɚɥɨ ɤɨɦɦɟɧɬɚɪɢɹ
ɛɭɞɟɦ ɨɛɨɡɧɚɱɚɬɶ ɫɢɦɜɨɥɨɦ «|».
| Ⱦɜɢɝɚɟɦɫɹ ɜɩɪɚɜɨ, ɩɨɤɚ ɧɟ ɞɨɣɞɺɦ ɞɨ ɧɚɱɚɥɚ ɥɟɫɬɧɢɰɵ,
ɧɰ ɩɨɤɚ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ
ɜɩɪɚɜɨ
ɤɰ
| ɉɨɞɧɢɦɚɟɦɫɹ ɩɨ ɫɬɭɩɟɧɶɤɚɦ, ɡɚɤɪɚɲɢɜɚɹ ɧɭɠɧɵɟ ɤɥɟɬɤɢ
ɧɰ ɩɨɤɚ ɧɟ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ
ɜɜɟɪɯ
ɜɩɪɚɜɨ
ɡɚɤɪɚɫɢɬɶ
ɜɩɪɚɜɨ
ɡɚɤɪɚɫɢɬɶ
ɜɩɪɚɜɨ
ɡɚɤɪɚɫɢɬɶ
ɤɰ
ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɜɚɪɢɚɧɬɵ ɪɟɲɟɧɢɹ
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
Ⱥɥɝɨɪɢɬɦ ɩɪɚɜɢɥɶɧɨ ɪɚɛɨɬɚɟɬ ɩɪɢ ɜɫɟɯ ɞɨɩɭɫɬɢɦɵɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ
2
ɉɪɢ ɜɫɟɯ ɞɨɩɭɫɬɢɦɵɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɜɟɪɧɨ ɫɥɟɞɭɸɳɟɟ:
1) ɜɵɩɨɥɧɟɧɢɟ ɚɥɝɨɪɢɬɦɚ ɡɚɜɟɪɲɚɟɬɫɹ, ɢ ɩɪɢ ɷɬɨɦ Ɋɨɛɨɬ ɧɟ ɪɚɡɛɢɜɚɟɬɫɹ;
1
2) ɡɚɤɪɚɲɟɧɨ ɧɟ ɛɨɥɟɟ 10 ɥɢɲɧɢɯ ɤɥɟɬɨɤ;
3) ɨɫɬɚɥɢɫɶ ɧɟɡɚɤɪɚɲɟɧɧɵɦɢ ɧɟ ɛɨɥɟɟ 10 ɤɥɟɬɨɤ ɢɡ ɱɢɫɥɚ ɬɟɯ, ɤɨɬɨɪɵɟ
ɞɨɥɠɧɵ ɛɵɥɢ ɛɵɬɶ ɡɚɤɪɚɲɟɧɵ
Ɂɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɧɟɜɟɪɧɨ, ɬɨ ɟɫɬɶ ɧɟ ɜɵɩɨɥɧɟɧɵ ɭɫɥɨɜɢɹ, ɩɨɡɜɨɥɹɸɳɢɟ
0
ɩɨɫɬɚɜɢɬɶ 1 ɢɥɢ 2 ɛɚɥɥɚ
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
2
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
7
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
Ɋɟɲɟɧɢɟ ɡɚɞɚɧɢɹ 20.2
Ɋɟɲɟɧɢɟɦ ɹɜɥɹɟɬɫɹ ɩɪɨɝɪɚɦɦɚ, ɡɚɩɢɫɚɧɧɚɹ ɧɚ ɥɸɛɨɦ ɹɡɵɤɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ.
ɉɪɢɦɟɪ ɜɟɪɧɨɝɨ ɪɟɲɟɧɢɹ, ɡɚɩɢɫɚɧɧɨɝɨ ɧɚ ɹɡɵɤɟ ɉɚɫɤɚɥɶ:
var a, sum: integer;
begin
sum:= 0;
readln(a);
while a<>0 do begin
if (a > 9) and (a <100) and (a mod 5 = 0) then
sum := sum + a;
readln(a);
end;
writeln(sum);
end.
Ⱦɥɹ ɩɪɨɜɟɪɤɢ ɩɪɚɜɢɥɶɧɨɫɬɢ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɵ ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɟ
ɬɟɫɬɵ:
ʋ
1
2
3
ȼɯɨɞɧɵɟ ɞɚɧɧɵɟ
5
15
100
0
25
15
0
45
46
0
ȼɵɯɨɞɧɵɟ ɞɚɧɧɵɟ
15
40
45
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɪɟɞɥɨɠɟɧɨ ɜɟɪɧɨɟ ɪɟɲɟɧɢɟ. ɉɪɨɝɪɚɦɦɚ ɩɪɚɜɢɥɶɧɨ ɪɚɛɨɬɚɟɬ ɧɚ ɜɫɟɯ
ɩɪɢɜɟɞɺɧɧɵɯ ɜɵɲɟ ɬɟɫɬɚɯ.
2
ɉɪɨɝɪɚɦɦɚ ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɚ ɧɚ ɥɸɛɨɦ ɹɡɵɤɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ
ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɟɜɟɪɧɵɣ ɨɬɜɟɬ ɧɚ ɨɞɧɨɦ ɢɡ ɬɟɫɬɨɜ, ɩɪɢɜɟɞɺɧɧɵɯ ɜɵɲɟ.
1
ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɚ ɬɟɫɬɚɯ ɧɟɜɟɪɧɵɟ ɨɬɜɟɬɵ, ɨɬɥɢɱɧɵɟ ɨɬ ɨɩɢɫɚɧɧɵɯ
0
ɜ ɤɪɢɬɟɪɢɢ ɧɚ 1 ɛɚɥɥ
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
2
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
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1
Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ
19
ȼ ɷɥɟɤɬɪɨɧɧɭɸ ɬɚɛɥɢɰɭ ɡɚɧɟɫɥɢ ɪɟɡɭɥɶɬɚɬɵ ɫɞɚɱɢ ɧɨɪɦɚɬɢɜɨɜ ɩɨ ɥɺɝɤɨɣ
ɚɬɥɟɬɢɤɟ ɫɪɟɞɢ ɭɱɚɳɢɯɫɹ 7–11 ɤɥɚɫɫɨɜ. ɇɚ ɪɢɫɭɧɤɟ ɩɪɢɜɟɞɟɧɵ ɩɟɪɜɵɟ ɫɬɪɨɤɢ
ɩɨɥɭɱɢɜɲɟɣɫɹ ɬɚɛɥɢɰɵ.
A
B
C
D
E
Ȼɟɝ
Ƚɨɞ
1 Ɏɚɦɢɥɢɹ
ɂɦɹ
ɉɨɥ
1000 ɦɟɬɪɨɜ,
ɪɨɠɞɟɧɢɹ
ɦɢɧ.
ɉɭɞɨɜɚ
Ʉɫɟɧɢɹ
ɠ
1997
4,47
2
Ƚɭɫɟɜɚ
Ɇɚɪɢɹ
ɠ
1998
4,47
3
1999
5,03
4 Ʌɟɥɶɤɨɜɚ ɇɚɞɟɠɞɚ ɠ
Ɍɢɥɶ
ȿɜɝɟɧɢɣ ɦ
1999
3,32
5
ɠ
1998
5,57
6 Ʌɢɦɚɧɢɧɚ ɇɟɥɥɢ
1997
5,42
7 Ȼɚɫɤɚɤɨɜɚ ɋɜɟɬɥɚɧɚ ɠ
ɠ
1997
5,38
8 ɉɪɨɯɨɪɨɜɚ Ⱥɧɧɚ
ɠ
1999
5,45
9 Ȼɭɠɟɧɢɧɚ Ɉɥɶɝɚ
ɠ
1997
4,58
10 Ɍɪɭɛɚɟɜɚ Ⱥɥɢɧɚ
F
Ȼɟɝ
30 ɦɟɬɪɨɜ,
ɫɟɤ.
4,12
5,82
5,04
5,87
5,32
4,47
5,79
5,08
4,44
G
ɉɪɵɠɨɤ
ɜ ɞɥɢɧɭ
ɫ ɦɟɫɬɚ, ɫɦ
209
205
198
210
182
180
219
222
198
ȼ ɫɬɨɥɛɰɟ A ɭɤɚɡɚɧɚ ɮɚɦɢɥɢɹ; ɜ ɫɬɨɥɛɰɟ B – ɢɦɹ; ɜ ɫɬɨɥɛɰɟ C – ɩɨɥ; ɜ ɫɬɨɥɛɰɟ
D – ɝɨɞ ɪɨɠɞɟɧɢɹ; ɜ ɫɬɨɥɛɰɟ E – ɪɟɡɭɥɶɬɚɬɵ ɜ ɛɟɝɟ ɧɚ 1000 ɦɟɬɪɨɜ; ɜ ɫɬɨɥɛɰɟ F –
ɪɟɡɭɥɶɬɚɬɵ ɜ ɛɟɝɟ ɧɚ 30 ɦɟɬɪɨɜ; ɜ ɫɬɨɥɛɰɟ G – ɪɟɡɭɥɶɬɚɬɵ ɩɨ ɩɪɵɠɤɚɦ ɜ ɞɥɢɧɭ
ɫ ɦɟɫɬɚ.
ȼɫɟɝɨ ɜ ɷɥɟɤɬɪɨɧɧɭɸ ɬɚɛɥɢɰɭ ɛɵɥɢ ɡɚɧɟɫɟɧɵ ɞɚɧɧɵɟ ɩɨ 1000 ɭɱɚɳɢɦɫɹ.
ȼɵɩɨɥɧɢɬɟ ɡɚɞɚɧɢɟ.
Ɉɬɤɪɨɣɬɟ ɮɚɣɥ ɫ ɞɚɧɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɚɛɥɢɰɟɣ (ɪɚɫɩɨɥɨɠɟɧɢɟ ɮɚɣɥɚ ȼɚɦ
ɫɨɨɛɳɚɬ ɨɪɝɚɧɢɡɚɬɨɪɵ ɷɤɡɚɦɟɧɚ). ɇɚ ɨɫɧɨɜɚɧɢɢ ɞɚɧɧɵɯ, ɫɨɞɟɪɠɚɳɢɯɫɹ ɜ ɷɬɨɣ
ɬɚɛɥɢɰɟ, ɨɬɜɟɬɶɬɟ ɧɚ ɞɜɚ ɜɨɩɪɨɫɚ.
1. Ʉɚɤɨɣ ɦɢɧɢɦɚɥɶɧɵɣ ɪɟɡɭɥɶɬɚɬ ɩɨ ɩɪɵɠɤɚɦ ɜ ɞɥɢɧɭ ɩɨɤɚɡɚɥɢ ɞɟɜɨɱɤɢ
1997 ɝɨɞɚ ɪɨɠɞɟɧɢɹ? Ɉɬɜɟɬ ɧɚ ɷɬɨɬ ɜɨɩɪɨɫ ɡɚɩɢɲɢɬɟ ɜ ɹɱɟɣɤɭ J1 ɬɚɛɥɢɰɵ.
2. ɇɚɣɞɢɬɟ ɫɪɟɞɧɟɟ ɜɪɟɦɹ ɫɪɟɞɢ ɦɚɥɶɱɢɤɨɜ ɜ ɛɟɝɟ ɧɚ 1000 ɦɟɬɪɨɜ. Ɉɬɜɟɬ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɞɜɭɯ ɡɧɚɤɨɜ ɩɨɫɥɟ ɡɚɩɹɬɨɣ ɡɚɩɢɲɢɬɟ ɜ ɹɱɟɣɤɭ J2 ɬɚɛɥɢɰɵ.
ɉɨɥɭɱɟɧɧɭɸ ɬɚɛɥɢɰɭ ɧɟɨɛɯɨɞɢɦɨ ɫɨɯɪɚɧɢɬɶ ɩɨɞ ɢɦɟɧɟɦ, ɭɤɚɡɚɧɧɵɦ
ɨɪɝɚɧɢɡɚɬɨɪɚɦɢ ɷɤɡɚɦɟɧɚ.
ɉɪɢɦɟɱɚɧɢɟ. ɉɪɢ ɪɟɲɟɧɢɢ ɞɨɩɭɫɤɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɥɸɛɵɯ ɜɨɡɦɨɠɧɨɫɬɟɣ
ɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɤɚɥɶɤɭɥɹɬɨɪɨɜ ɧɟ ɞɨɩɭɫɤɚɟɬɫɹ.
Ⱥɥɝɨɪɢɬɦɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɞɥɹ OpenOffice.org Calc ɢ Microsoft Excel ɫɨɜɩɚɞɚɸɬ.
Ɏɨɪɦɭɥɵ ɧɚɩɢɫɚɧɵ ɞɥɹ ɨɛɟɢɯ ɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰ. ȼɬɨɪɨɣ ɜɚɪɢɚɧɬ – ɞɥɹ
OpenOffice.org Calc.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
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2
ȼ ɹɱɟɣɤɭ H2 ɡɚɩɢɲɟɦ ɮɨɪɦɭɥɭ:
=ȿɋɅɂ(ɂ(C2="ɠ";D2=1997);G2;" ")
=IF(AND(C2="ɠ";D2=1997);G2;" ")
ɋɤɨɩɢɪɭɟɦ ɮɨɪɦɭɥɭ ɜɨ ɜɫɟ ɹɱɟɣɤɢ ɞɢɚɩɚɡɨɧɚ H3:H1001.
Ɉɬɜɟɬ ɧɚ ɩɟɪɜɵɣ ɜɨɩɪɨɫ ɩɨɥɭɱɢɦ ɩɨ ɮɨɪɦɭɥɟ, ɤɨɬɨɪɭɸ ɡɚɩɢɲɟɦ ɜ ɹɱɟɣɤɭ J1:
=Ɇɂɇ(H2:H1001)
=MIN(H2:H1001)
Ⱦɥɹ ɨɬɜɟɬɚ ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ ɫɧɚɱɚɥɚ ɧɚɣɞɺɦ ɤɨɥɢɱɟɫɬɜɨ ɦɚɥɶɱɢɤɨɜ. ɗɬɨ ɦɨɠɧɨ ɫɞɟɥɚɬɶ
ɪɚɡɥɢɱɧɵɦɢ ɫɩɨɫɨɛɚɦɢ, ɜ ɬɨɦ ɱɢɫɥɟ ɩɪɢ ɩɨɦɨɳɢ ɮɨɪɦɭɥɵ:
=ɋɑȬɌȿɋɅɂ(C2:C1001;"ɦ")
=COUNTIF(C2:C1001;"ɦ"),
ɤɨɬɨɪɭɸ ɡɚɩɢɲɟɦ, ɧɚɩɪɢɦɟɪ, ɜ ɹɱɟɣɤɭ ɋ1002. (Ɇɨɠɧɨ ɨɬɫɨɪɬɢɪɨɜɚɬɶ ɬɚɛɥɢɰɭ ɩɨ
ɫɬɨɥɛɰɭ C, ɢ ɡɚɬɟɦ ɩɨɫɱɢɬɚɬɶ ɤɨɥɢɱɟɫɬɜɨ ɫɬɪɨɤ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɞɢɚɩɚɡɨɧɟ.)
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ȼɵɛɟɪɢɬɟ ɬɨɥɶɤɨ ɈȾɇɈ ɢɡ ɩɪɟɞɥɨɠɟɧɧɵɯ ɡɚɞɚɧɢɣ: 20.1 ɢɥɢ 20.2.
20.1 ɂɫɩɨɥɧɢɬɟɥɶ Ɋɨɛɨɬ ɭɦɟɟɬ ɩɟɪɟɦɟɳɚɬɶɫɹ ɩɨ ɥɚɛɢɪɢɧɬɭ, ɧɚɱɟɪɱɟɧɧɨɦɭ
ɧɚ ɩɥɨɫɤɨɫɬɢ, ɪɚɡɛɢɬɨɣ ɧɚ ɤɥɟɬɤɢ. Ɇɟɠɞɭ ɫɨɫɟɞɧɢɦɢ (ɩɨ ɫɬɨɪɨɧɚɦ)
ɤɥɟɬɤɚɦɢ ɦɨɠɟɬ ɫɬɨɹɬɶ ɫɬɟɧɚ, ɱɟɪɟɡ ɤɨɬɨɪɭɸ Ɋɨɛɨɬ ɩɪɨɣɬɢ ɧɟ ɦɨɠɟɬ.
ɍ Ɋɨɛɨɬɚ ɟɫɬɶ ɞɟɜɹɬɶ ɤɨɦɚɧɞ. ɑɟɬɵɪɟ ɤɨɦɚɧɞɵ – ɷɬɨ ɤɨɦɚɧɞɵɩɪɢɤɚɡɵ:
ɜɜɟɪɯ
ɜɧɢɡ
ɜɥɟɜɨ
ɜɩɪɚɜɨ
ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɥɸɛɨɣ ɢɡ ɷɬɢɯ ɤɨɦɚɧɞ Ɋɨɛɨɬ ɩɟɪɟɦɟɳɚɟɬɫɹ ɧɚ ɨɞɧɭ
ɤɥɟɬɤɭ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ: ɜɜɟɪɯ Ĺ, ɜɧɢɡ Ļ, ɜɥɟɜɨ ĸ, ɜɩɪɚɜɨ ĺ. ȿɫɥɢ
Ɋɨɛɨɬ ɩɨɥɭɱɢɬ ɤɨɦɚɧɞɭ ɩɟɪɟɞɜɢɠɟɧɢɹ ɱɟɪɟɡ ɫɬɟɧɭ, ɬɨ ɨɧ ɪɚɡɪɭɲɢɬɫɹ.
ȿɳɺ ɱɟɬɵɪɟ ɤɨɦɚɧɞɵ – ɷɬɨ ɤɨɦɚɧɞɵ ɩɪɨɜɟɪɤɢ ɭɫɥɨɜɢɣ. ɗɬɢ ɤɨɦɚɧɞɵ
ɩɪɨɜɟɪɹɸɬ, ɫɜɨɛɨɞɟɧ ɥɢ ɩɭɬɶ ɞɥɹ Ɋɨɛɨɬɚ ɜ ɤɚɠɞɨɦ ɢɡ ɱɟɬɵɪɺɯ
ɜɨɡɦɨɠɧɵɯ ɧɚɩɪɚɜɥɟɧɢɣ:
Ɂɚɬɟɦ ɜ ɹɱɟɣɤɭ I2 ɡɚɩɢɲɟɦ ɮɨɪɦɭɥɭ:
ɫɜɟɪɯɭ ɫɜɨɛɨɞɧɨ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ ɫɥɟɜɚ ɫɜɨɛɨɞɧɨ ɫɩɪɚɜɚ
ɫɜɨɛɨɞɧɨ
=ȿɋɅɂ(C2="ɦ";E2;0)
=IF(C2="ɦ";E2;0)
ɗɬɢ ɤɨɦɚɧɞɵ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɦɟɫɬɟ ɫ ɭɫɥɨɜɢɟɦ «eɫɥɢ»,
ɢɦɟɸɳɢɦ ɫɥɟɞɭɸɳɢɣ ɜɢɞ:
ɋɤɨɩɢɪɭɟɦ ɮɨɪɦɭɥɭ ɜɨ ɜɫɟ ɹɱɟɣɤɢ ɞɢɚɩɚɡɨɧɚ I3:I1001. Ɉɬɜɟɬ ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ
ɩɨɥɭɱɢɦ ɩɨ ɮɨɪɦɭɥɟ, ɤɨɬɨɪɭɸ ɡɚɩɢɲɟɦ ɜ ɹɱɟɣɤɭ J2:
=ɋɍɆɆ(I2:I1001)/C1002
=SUM(I2:I1001)/C1002
Ɂɚɞɚɞɢɦ ɮɨɪɦɚɬ ɹɱɟɣɤɢ J2 ɱɢɫɥɨɜɨɣ, ɱɢɫɥɨ ɞɟɫɹɬɢɱɧɵɯ ɡɧɚɤɨɜ – 2.
ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɫɩɨɫɨɛɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ.
ȿɫɥɢ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɩɪɚɜɢɥɶɧɨ ɢ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɹ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɮɚɣɥɵ,
ɫɩɟɰɢɚɥɶɧɨ ɩɨɞɝɨɬɨɜɥɟɧɧɵɟ ɞɥɹ ɩɪɨɜɟɪɤɢ ɜɵɩɨɥɧɟɧɢɹ ɞɚɧɧɨɝɨ ɡɚɞɚɧɢɹ, ɬɨ ɞɨɥɠɧɵ
ɩɨɥɭɱɢɬɶɫɹ ɫɥɟɞɭɸɳɢɟ ɨɬɜɟɬɵ:
ɧɚ ɩɟɪɜɵɣ ɜɨɩɪɨɫ – 177;
ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ – 4,61.
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɨɥɭɱɟɧɵ ɩɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɚ ɨɛɚ ɜɨɩɪɨɫɚ. ɋɩɨɫɨɛ ɩɨɥɭɱɟɧɢɹ ɨɬɜɟɬɚ
ɦɨɠɟɬ ɧɟ ɫɨɜɩɚɞɚɬɶ ɫ ɩɪɢɜɟɞɺɧɧɵɦ ɜɵɲɟ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɚ ɜ ɞɪɭɝɢɟ
ɹɱɟɣɤɢ (ɨɬɥɢɱɧɵɟ ɨɬ ɬɟɯ, ɤɨɬɨɪɵɟ ɭɤɚɡɚɧɵ ɜ ɡɚɞɚɧɢɢ) ɩɪɢ ɭɫɥɨɜɢɢ
2
ɩɪɚɜɢɥɶɧɨɫɬɢ ɩɨɥɭɱɟɧɧɵɯ ɨɬɜɟɬɨɜ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɨɜ ɫ ɛɨɥɶɲɟɣ
ɬɨɱɧɨɫɬɶɸ
ɉɨɥɭɱɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɬɨɥɶɤɨ ɧɚ ɨɞɢɧ ɢɡ ɞɜɭɯ ɜɨɩɪɨɫɨɜ
1
ɉɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɟ ɩɨɥɭɱɟɧɵ ɧɢ ɧɚ ɨɞɢɧ ɢɡ ɜɨɩɪɨɫɨɜ
0
2
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɟɫɥɢ ɭɫɥɨɜɢɟ ɬɨ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ
ɜɫɟ
Ɂɞɟɫɶ ɭɫɥɨɜɢɟ –
ɨɞɧɚ ɢɡ
ɤɨɦɚɧɞ ɩɪɨɜɟɪɤɢ ɭɫɥɨɜɢɹ.
ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ – ɷɬɨ ɨɞɧɚ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɥɸɛɵɯ
ɤɨɦɚɧɞ-ɩɪɢɤɚɡɨɜ.
ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɟɪɟɞɜɢɠɟɧɢɹ ɧɚ ɨɞɧɭ ɤɥɟɬɤɭ ɜɩɪɚɜɨ, ɟɫɥɢ ɫɩɪɚɜɚ ɧɟɬ
ɫɬɟɧɤɢ, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɚɤɨɣ ɚɥɝɨɪɢɬɦ:
ɟɫɥɢ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɬɨ
ɜɩɪɚɜɨ
ɜɫɟ
ȼ ɨɞɧɨɦ ɭɫɥɨɜɢɢ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɟɫɤɨɥɶɤɨ ɤɨɦɚɧɞ ɩɪɨɜɟɪɤɢ
ɭɫɥɨɜɢɣ, ɩɪɢɦɟɧɹɹ ɥɨɝɢɱɟɫɤɢɟ ɫɜɹɡɤɢ ɢ, ɢɥɢ, ɧɟ, ɧɚɩɪɢɦɟɪ:
ɟɫɥɢ (ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ) ɢ (ɧɟ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ) ɬɨ
ɜɩɪɚɜɨ
ɜɫɟ
Ⱦɥɹ ɩɨɜɬɨɪɟɧɢɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɤɨɦɚɧɞ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ
ɰɢɤɥ «ɩɨɤɚ», ɢɦɟɸɳɢɣ ɫɥɟɞɭɸɳɢɣ ɜɢɞ:
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
3
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɧɰ ɩɨɤɚ ɭɫɥɨɜɢɟ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ
ɤɰ
ɇɚɩɪɢɦɟɪ, ɞɥɹ ɞɜɢɠɟɧɢɹ ɜɩɪɚɜɨ, ɩɨɤɚ ɷɬɨ ɜɨɡɦɨɠɧɨ, ɦɨɠɧɨ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɣ ɚɥɝɨɪɢɬɦ:
ɧɰ ɩɨɤɚ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ
ɜɩɪɚɜɨ
ɤɰ
Ɍɚɤɠɟ ɭ Ɋɨɛɨɬɚ ɟɫɬɶ ɤɨɦɚɧɞɚ ɡɚɤɪɚɫɢɬɶ, ɩɪɢ ɤɨɬɨɪɨɣ ɡɚɤɪɚɲɢɜɚɟɬɫɹ
ɤɥɟɬɤɚ, ɜ ɤɨɬɨɪɨɣ Ɋɨɛɨɬ ɧɚɯɨɞɢɬɫɹ ɜ ɧɚɫɬɨɹɳɢɣ ɦɨɦɟɧɬ.
ȼɵɩɨɥɧɢɬɟ ɡɚɞɚɧɢɟ.
ɇɚ ɛɟɫɤɨɧɟɱɧɨɦ ɩɨɥɟ ɢɦɟɸɬɫɹ ɞɜɟ ɝɨɪɢɡɨɧɬɚɥɶɧɵɟ ɫɬɟɧɵ,
ɫɨɟɞɢɧɟɧɧɵɟ ɥɟɫɬɧɢɰɟɣ. ȼɟɪɯɧɹɹ ɫɬɟɧɚ ɛɟɫɤɨɧɟɱɧɨ ɩɪɨɞɨɥɠɚɟɬɫɹ
ɜɥɟɜɨ, ɧɢɠɧɹɹ – ɜɩɪɚɜɨ. Ʉɨɥɢɱɟɫɬɜɨ ɫɬɭɩɟɧɟɣ ɥɟɫɬɧɢɰɵ ɧɟɢɡɜɟɫɬɧɨ.
ȼɵɫɨɬɚ ɤɚɠɞɨɣ ɫɬɭɩɟɧɢ 2 ɤɥɟɬɤɢ, ɲɢɪɢɧɚ – 3 ɤɥɟɬɤɢ. Ɋɨɛɨɬ
ɧɚɯɨɞɢɬɫɹ ɧɚ ɧɢɠɧɟɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɬɟɧɟ, ɩɪɚɜɟɟ ɥɟɫɬɧɢɰɵ.
ɇɚ ɪɢɫɭɧɤɟ ɭɤɚɡɚɧ ɨɞɢɧ ɢɡ ɜɨɡɦɨɠɧɵɯ ɫɩɨɫɨɛɨɜ ɪɚɫɩɨɥɨɠɟɧɢɹ
ɥɟɫɬɧɢɰɵ, ɫɬɟɧ ɢ Ɋɨɛɨɬɚ (Ɋɨɛɨɬ ɨɛɨɡɧɚɱɟɧ ɛɭɤɜɨɣ «Ɋ») .
4
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
Ʉɨɧɟɱɧɨɟ ɪɚɫɩɨɥɨɠɟɧɢɟ Ɋɨɛɨɬɚ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɢɡɜɨɥɶɧɵɦ. Ⱥɥɝɨɪɢɬɦ
ɞɨɥɠɟɧ ɪɟɲɚɬɶ ɡɚɞɚɱɭ ɞɥɹ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɪɚɡɦɟɪɚ ɩɨɥɹ ɢ ɥɸɛɨɝɨ
ɤɨɥɢɱɟɫɬɜɚ ɫɬɭɩɟɧɟɣ.
ɉɪɢ ɢɫɩɨɥɧɟɧɢɢ ɚɥɝɨɪɢɬɦɚ Ɋɨɛɨɬ ɧɟ ɞɨɥɠɟɧ ɪɚɡɪɭɲɢɬɶɫɹ,
ɜɵɩɨɥɧɟɧɢɟ ɚɥɝɨɪɢɬɦɚ ɞɨɥɠɧɨ ɡɚɜɟɪɲɢɬɶɫɹ.
Ⱥɥɝɨɪɢɬɦ ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧ ɜ ɫɪɟɞɟ ɮɨɪɦɚɥɶɧɨɝɨ ɢɫɩɨɥɧɢɬɟɥɹ
ɢɥɢ ɡɚɩɢɫɚɧ ɜ ɬɟɤɫɬɨɜɨɦ ɪɟɞɚɤɬɨɪɟ.
ɋɨɯɪɚɧɢɬɟ ɚɥɝɨɪɢɬɦ ɜ ɬɟɤɫɬɨɜɨɦ ɮɚɣɥɟ. ɇɚɡɜɚɧɢɟ ɮɚɣɥɚ ɢ ɤɚɬɚɥɨɝ ɞɥɹ
ɫɨɯɪɚɧɟɧɢɹ ȼɚɦ ɫɨɨɛɳɚɬ ɨɪɝɚɧɢɡɚɬɨɪɵ ɷɤɡɚɦɟɧɚ.
20.2 ɇɚɩɢɲɢɬɟ ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɧɚɬɭɪɚɥɶɧɵɯ
ɱɢɫɟɥ ɨɩɪɟɞɟɥɹɟɬ ɤɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ, ɦɟɧɶɲɢɯ 500 ɢ ɤɪɚɬɧɵɯ 3.
ɉɪɨɝɪɚɦɦɚ ɩɨɥɭɱɚɟɬ ɧɚ ɜɯɨɞ ɧɚɬɭɪɚɥɶɧɵɟ ɱɢɫɥɚ, ɤɨɥɢɱɟɫɬɜɨ
ɜɜɟɞɺɧɧɵɯ
ɱɢɫɟɥ
ɧɟɢɡɜɟɫɬɧɨ,
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ
ɱɢɫɟɥ
ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɱɢɫɥɨɦ 0 (0 – ɩɪɢɡɧɚɤ ɨɤɨɧɱɚɧɢɹ ɜɜɨɞɚ, ɧɟ ɜɯɨɞɢɬ
ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ) .
Ʉɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ ɧɟ ɩɪɟɜɵɲɚɟɬ 1000. ȼɜɟɞɺɧɧɵɟ ɱɢɫɥɚ ɧɟ
ɩɪɟɜɵɲɚɸɬ 30000.
ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ: ɤɨɥɢɱɟɫɬɜɨ ɧɚɬɭɪɚɥɶɧɵɯ
ɱɢɫɟɥ, ɦɟɧɶɲɢɯ 500 ɢ ɤɪɚɬɧɵɯ 3.
45
20
600
0
ɉɪɢɦɟɪ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɵ:
ȼɯɨɞɧɵɟ ɞɚɧɧɵɟ
ȼɵɯɨɞɧɵɟ ɞɚɧɧɵɟ
1
ɇɚɩɢɲɢɬɟ ɞɥɹ Ɋɨɛɨɬɚ ɚɥɝɨɪɢɬɦ, ɡɚɤɪɚɲɢɜɚɸɳɢɣ ɤɥɟɬɤɢ,
ɪɚɫɩɨɥɨɠɟɧɧɵɟ ɪɹɞɨɦ ɫ ɜɟɪɬɢɤɚɥɶɧɨɣ ɱɚɫɬɶɸ ɤɚɠɞɨɣ ɫɬɭɩɟɧɢ.
Ɍɪɟɛɭɟɬɫɹ ɡɚɤɪɚɫɢɬɶ ɬɨɥɶɤɨ ɤɥɟɬɤɢ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɞɚɧɧɨɦɭ
ɭɫɥɨɜɢɸ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɪɢɜɟɞɺɧɧɨɝɨ ɜɵɲɟ ɪɢɫɭɧɤɚ Ɋɨɛɨɬ ɞɨɥɠɟɧ
ɡɚɤɪɚɫɢɬɶ ɫɥɟɞɭɸɳɢɟ ɤɥɟɬɤɢ (ɫɦ. ɪɢɫɭɧɨɤ) :
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
5
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
6
Ɋɟɲɟɧɢɟ ɡɚɞɚɧɢɹ 20.1
Ʉɨɦɚɧɞɵ ɢɫɩɨɥɧɢɬɟɥɹ ɛɭɞɟɦ ɡɚɩɢɫɵɜɚɬɶ ɠɢɪɧɵɦ ɲɪɢɮɬɨɦ, ɚ ɤɨɦɦɟɧɬɚɪɢɢ,
ɩɨɹɫɧɹɸɳɢɟ ɚɥɝɨɪɢɬɦ ɢ ɧɟ ɹɜɥɹɸɳɢɟɫɹ ɟɝɨ ɱɚɫɬɶɸ, – ɤɭɪɫɢɜɨɦ. ɇɚɱɚɥɨ ɤɨɦɦɟɧɬɚɪɢɹ
ɛɭɞɟɦ ɨɛɨɡɧɚɱɚɬɶ ɫɢɦɜɨɥɨɦ «|».
| Ⱦɜɢɝɚɟɦɫɹ ɜɥɟɜɨ, ɩɨɤɚ ɧɟ ɞɨɣɞɺɦ ɞɨ ɧɚɱɚɥɚ ɥɟɫɬɧɢɰɵ,
ɧɰ ɩɨɤɚ ɫɥɟɜɚ ɫɜɨɛɨɞɧɨ
ɜɥɟɜɨ
ɤɰ
| ɉɨɞɧɢɦɚɟɦɫɹ ɩɨ ɫɬɭɩɟɧɶɤɚɦ, ɡɚɤɪɚɲɢɜɚɹ ɧɭɠɧɵɟ ɤɥɟɬɤɢ
ɧɰ ɩɨɤɚ ɧɟ ɫɥɟɜɚ ɫɜɨɛɨɞɧɨ
ɡɚɤɪɚɫɢɬɶ
ɜɜɟɪɯ
ɡɚɤɪɚɫɢɬɶ
ɜɜɟɪɯ
ɜɥɟɜɨ
ɜɥɟɜɨ
ɜɥɟɜɨ
ɤɰ
ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɜɚɪɢɚɧɬɵ ɪɟɲɟɧɢɹ.
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
Ⱥɥɝɨɪɢɬɦ ɩɪɚɜɢɥɶɧɨ ɪɚɛɨɬɚɟɬ ɩɪɢ ɜɫɟɯ ɞɨɩɭɫɬɢɦɵɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ
2
ɉɪɢ ɜɫɟɯ ɞɨɩɭɫɬɢɦɵɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɜɟɪɧɨ ɫɥɟɞɭɸɳɟɟ:
1) ɜɵɩɨɥɧɟɧɢɟ ɚɥɝɨɪɢɬɦɚ ɡɚɜɟɪɲɚɟɬɫɹ, ɢ ɩɪɢ ɷɬɨɦ Ɋɨɛɨɬ ɧɟ ɪɚɡɛɢɜɚɟɬɫɹ;
1
2) ɡɚɤɪɚɲɟɧɨ ɧɟ ɛɨɥɟɟ 10 ɥɢɲɧɢɯ ɤɥɟɬɨɤ;
3) ɨɫɬɚɥɢɫɶ ɧɟɡɚɤɪɚɲɟɧɧɵɦɢ ɧɟ ɛɨɥɟɟ 10 ɤɥɟɬɨɤ ɢɡ ɱɢɫɥɚ ɬɟɯ, ɤɨɬɨɪɵɟ
ɞɨɥɠɧɵ ɛɵɥɢ ɛɵɬɶ ɡɚɤɪɚɲɟɧɵ
Ɂɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɧɟɜɟɪɧɨ, ɬɨ ɟɫɬɶ ɧɟ ɜɵɩɨɥɧɟɧɵ ɭɫɥɨɜɢɹ, ɩɨɡɜɨɥɹɸɳɢɟ
0
ɩɨɫɬɚɜɢɬɶ 1 ɢɥɢ 2 ɛɚɥɥɚ
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
2
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
7
Ɋɟɲɟɧɢɟ ɡɚɞɚɧɢɹ 20.2
Ɋɟɲɟɧɢɟɦ ɹɜɥɹɟɬɫɹ ɩɪɨɝɪɚɦɦɚ, ɡɚɩɢɫɚɧɧɚɹ ɧɚ ɥɸɛɨɦ ɹɡɵɤɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ.
ɉɪɢɦɟɪ ɜɟɪɧɨɝɨ ɪɟɲɟɧɢɹ, ɡɚɩɢɫɚɧɧɨɝɨ ɧɚ ɹɡɵɤɟ ɉɚɫɤɚɥɶ:
var a, n: integer;
begin
n := 0;
readln(a);
while a<>0 do begin
if (a mod 3 = 0) and (a<500) then
n := n + 1;
readln(a);
end;
writeln(n);
end.
Ⱦɥɹ ɩɪɨɜɟɪɤɢ ɩɪɚɜɢɥɶɧɨɫɬɢ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɵ ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɟ
ɬɟɫɬɵ:
ʋ
1
2
3
ȼɯɨɞɧɵɟ ɞɚɧɧɵɟ
12
0
122
600
0
45
105
0
ȼɵɯɨɞɧɵɟ ɞɚɧɧɵɟ
1
0
2
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɪɟɞɥɨɠɟɧɨ ɜɟɪɧɨɟ ɪɟɲɟɧɢɟ. ɉɪɨɝɪɚɦɦɚ ɩɪɚɜɢɥɶɧɨ ɪɚɛɨɬɚɟɬ ɧɚ ɜɫɟɯ
ɩɪɢɜɟɞɺɧɧɵɯ ɜɵɲɟ ɬɟɫɬɚɯ.
2
ɉɪɨɝɪɚɦɦɚ ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɚ ɧɚ ɥɸɛɨɦ ɹɡɵɤɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ
ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɟɜɟɪɧɵɣ ɨɬɜɟɬ ɧɚ ɨɞɧɨɦ ɢɡ ɬɟɫɬɨɜ, ɩɪɢɜɟɞɺɧɧɵɯ ɜɵɲɟ.
1
ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɚ ɬɟɫɬɚɯ ɧɟɜɟɪɧɵɟ ɨɬɜɟɬɵ, ɨɬɥɢɱɧɵɟ ɨɬ ɨɩɢɫɚɧɧɵɯ
0
ɜ ɤɪɢɬɟɪɢɢ ɧɚ 1 ɛɚɥɥ
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
2
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
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megrebin
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