╨Ъ╨▓╨░╤А╤В╨╕╨╗╤М╨╜╨░╤П ╤Д╨╛╤А╨╝╤Г╨╗╨░

╨д╨╛╤А╨╝╤Г╨╗╨░ ╨┤╨╗╤П ╤А╨░╤Б╤З╨╡╤В╨░ ╨║╨▓╨░╤А╤В╨╕╨╗╤П ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡

╨д╨╛╤А╨╝╤Г╨╗╨░ ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╣ тАФ ╤Н╤В╨╛ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╨╕╨╣ ╨╕╨╜╤Б╤В╤А╤Г╨╝╨╡╨╜╤В ╨┤╨╗╤П ╤А╨░╤Б╤З╨╡╤В╨░ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╕ ╨╖╨░╨┤╨░╨╜╨╜╤Л╤Е ╨┤╨░╨╜╨╜╤Л╤Е ╨┐╤Г╤В╨╡╨╝ ╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨╕╤Е ╨╜╨░ ╤З╨╡╤В╤Л╤А╨╡ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╜╤Л╤Е ╨╕╨╜╤В╨╡╤А╨▓╨░╨╗╨░, ╤Б╤А╨░╨▓╨╜╨╡╨╜╨╕╤П ╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В╨╛╨▓ ╤Б╨╛ ╨▓╤Б╨╡╨╝ ╨╜╨░╨▒╨╛╤А╨╛╨╝ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣ ╨╕ ╨║╨╛╨╝╨╝╨╡╨╜╤В╨╕╤А╨╛╨▓╨░╨╜╨╕╤П ╤А╨░╨╖╨╗╨╕╤З╨╕╨╣ ╨▓ ╨╜╨░╨▒╨╛╤А╨░╤Е ╨┤╨░╨╜╨╜╤Л╤Е.

╨Ю╨╜ ╤З╨░╤Б╤В╨╛ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡ ╨┤╨╗╤П ╨╕╨╖╨╝╨╡╤А╨╡╨╜╨╕╤П ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╣, ╨║╨╛╤В╨╛╤А╤Л╨╡ ╨╛╨┐╨╕╤Б╤Л╨▓╨░╤О╤В ╤А╨░╨╖╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╨▓╤Б╨╡╤Е ╨┤╨░╨╜╨╜╤Л╤Е ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣ ╨╜╨░ ╤З╨╡╤В╤Л╤А╨╡ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╜╤Л╤Е ╨╕╨╜╤В╨╡╤А╨▓╨░╨╗╨░ ╨╜╨░ ╨╛╤Б╨╜╨╛╨▓╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╣ ╨┤╨░╨╜╨╜╤Л╤Е ╨╕ ╤В╨╛╨│╨╛, ╨│╨┤╨╡ ╨╛╨╜╨╕ ╨╜╨░╤Е╨╛╨┤╤П╤В╤Б╤П ╨┐╨╛ ╤Б╤А╨░╨▓╨╜╨╡╨╜╨╕╤О ╤Б╨╛ ╨▓╤Б╨╡╨╝ ╨╜╨░╨▒╨╛╤А╨╛╨╝ ╨┤╨░╨╜╨╜╤Л╤Е ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣.

╨Ю╨╜ ╨┤╨╡╨╗╨╕╤В╤Б╤П ╨╜╨░ 3 ╤В╨╛╤З╨║╨╕: ╨╜╨╕╨╢╨╜╨╕╨╣ ╨║╨▓╨░╤А╤В╨╕╨╗╤М, ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╨╝╤Л╨╣ Q1, ╨║╨╛╤В╨╛╤А╤Л╨╣ ╨╜╨░╤Е╨╛╨┤╨╕╤В╤Б╤П ╨╝╨╡╨╢╨┤╤Г ╨╜╨░╨╕╨╝╨╡╨╜╤М╤И╨╕╨╝ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡╨╝ ╨╕ ╨╝╨╡╨┤╨╕╨░╨╜╨╛╨╣ ╨┤╨░╨╜╨╜╨╛╨│╨╛ ╨╜╨░╨▒╨╛╤А╨░ ╨┤╨░╨╜╨╜╤Л╤Е. ╨Ь╨╡╨┤╨╕╨░╨╜╨░, ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╨╝╨░╤П Q2, ╤П╨▓╨╗╤П╨╡╤В╤Б╤П ╨╝╨╡╨┤╨╕╨░╨╜╨╛╨╣, ╨░ ╨▓╨╡╤А╤Е╨╜╨╕╨╣ ╨║╨▓╨░╤А╤В╨╕╨╗╤М, ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╨╝╤Л╨╣ Q3, ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤Б╨╛╨▒╨╛╨╣ ╤Б╤А╨╡╨┤╨╜╤О╤О ╤В╨╛╤З╨║╤Г ╨╝╨╡╨╢╨┤╤Г ╨╝╨╡╨┤╨╕╨░╨╜╨╛╨╣. ╨Ь╨╡╨┤╨╕╨░╨╜╨╜╨░╤П ╤Д╨╛╤А╨╝╤Г╨╗╨░ ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П ╨┤╨╗╤П ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╤Б╤А╨╡╨┤╨╜╨╡╨│╨╛ ╤З╨╕╤Б╨╗╨░ ╨▓ ╨╜╨░╨▒╨╛╤А╨╡ ╨┤╨░╨╜╨╜╤Л╤Е, ╤А╨░╤Б╨┐╨╛╨╗╨╛╨╢╨╡╨╜╨╜╨╛╨╝ ╨▓ ╨┐╨╛╤А╤П╨┤╨║╨╡ ╨▓╨╛╨╖╤А╨░╤Б╤В╨░╨╜╨╕╤П. ╨Ь╨╡╨┤╨╕╨░╨╜╨░ = {(n+1)/2}╨┐╨╛╤В╨╛╨║ ╨▒╨╛╨╗╤М╤И╨╡ ╨╕ ╨╜╨░╨╕╨▒╨╛╨╗╤М╤И╨╡╨╡ ╤З╨╕╤Б╨╗╨╛ ╨▓ ╨╖╨░╨┤╨░╨╜╨╜╨╛╨╝ ╨╜╨░╨▒╨╛╤А╨╡ ╨┤╨░╨╜╨╜╤Л╤Е ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П.

╨д╨╛╤А╨╝╤Г╨╗╨░ ╨║╨▓╨░╤А╤В╨╕╨╗╤П ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡ ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╨╡╨╜╨░ тАЛтАЛ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝:

╨д╨╛╤А╨╝╤Г╨╗╨░ ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╣ ╨┤╨╗╤П Q1= ┬╝(n+1)-╨│╨╛ ╤З╨╗╨╡╨╜╨░ ╨д╨╛╤А╨╝╤Г╨╗╨░ ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╣ ╨┤╨╗╤П Q3= ┬╛(n+1)-╨│╨╛ ╤З╨╗╨╡╨╜╨░ ╨д╨╛╤А╨╝╤Г╨╗╨░ ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╣ ╨┤╨╗╤П Q2= Q3тАУQ1 (╤Н╨║╨▓╨╕╨▓╨░╨╗╨╡╨╜╤В╨╜╨╛ ╨╝╨╡╨┤╨╕╨░╨╜╨╡)

╨Ю╨▒╤К╤П╤Б╨╜╨╡╨╜╨╕╨╡

╨Ъ╨▓╨░╤А╤В╨╕╨╗╨╕ ╨▒╤Г╨┤╤Г╤В ╨┤╨╡╨╗╨╕╤В╤М ╨╕╨╖╨╝╨╡╤А╨╡╨╜╨╕╤П ╨┤╨░╨╜╨╜╨╛╨│╨╛ ╨╜╨░╨▒╨╛╤А╨░ ╨┤╨░╨╜╨╜╤Л╤Е ╨╕╨╗╨╕ ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨╜╨░ ╤З╨╡╤В╤Л╤А╨╡ ╨╛╨┤╨╕╨╜╨░╨║╨╛╨▓╤Л╨╡ ╨╕╨╗╨╕ ╤А╨░╨▓╨╜╤Л╨╡ ╤З╨░╤Б╤В╨╕. ╨Э╨░╨┐╤А╨╕╨╝╨╡╤А, 25% ╨╕╨╖╨╝╨╡╤А╨╡╨╜╨╕╨╣ ╨┤╨░╨╜╨╜╨╛╨│╨╛ ╨╜╨░╨▒╨╛╤А╨░ ╨┤╨░╨╜╨╜╤Л╤Е (╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╨╡╨╜╨╜╤Л╤Е Q1) ╨╜╨╡ ╨┐╤А╨╡╨▓╤Л╤И╨░╤О╤В ╨╜╨╕╨╢╨╜╨╕╨╣ ╨║╨▓╨░╤А╤В╨╕╨╗╤М. 50% ╨╕╨╖╨╝╨╡╤А╨╡╨╜╨╕╨╣ ╨╜╨╡ ╨┐╤А╨╡╨▓╤Л╤И╨░╤О╤В ╨╝╨╡╨┤╨╕╨░╨╜╤Л, ╤В. ╨╡. Q2; ╨╜╨░╨║╨╛╨╜╨╡╤Ж, 75% ╨▒╤Г╨┤╨╡╤В ╨╝╨╡╨╜╤М╤И╨╡, ╤З╨╡╨╝ ╨▓╨╡╤А╤Е╨╜╨╕╨╣ ╨║╨▓╨░╤А╤В╨╕╨╗╤М, ╨║╨╛╤В╨╛╤А╤Л╨╣ ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╤В Q3. ╨б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М╨╜╨╛, 50% ╨╕╨╖╨╝╨╡╤А╨╡╨╜╨╕╨╣ ╨┤╨░╨╜╨╜╨╛╨│╨╛ ╨╜╨░╨▒╨╛╤А╨░ ╨┤╨░╨╜╨╜╤Л╤Е ╨╜╨░╤Е╨╛╨┤╤П╤В╤Б╤П ╨╝╨╡╨╢╨┤╤Г Q1, ╨╜╨╕╨╢╨╜╨╕╨╝ ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╝, ╨╕ Q2, ╨▓╨╡╤А╤Е╨╜╨╕╨╝ ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╝.

╨Я╤А╨╕╨╝╨╡╤А╤Л

╨Ф╨░╨▓╨░╨╣╤В╨╡ ╤А╨░╤Б╤Б╨╝╨╛╤В╤А╨╕╨╝ ╨╜╨╡╤Б╨║╨╛╨╗╤М╨║╨╛ ╨┐╤А╨╛╤Б╤В╤Л╤Е ╨╕ ╤Б╨╗╨╛╨╢╨╜╤Л╤Е ╨┐╤А╨╕╨╝╨╡╤А╨╛╨▓ ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╣ ╨▓ excelQuartile. ╨Т ╤Д╤Г╨╜╨║╤Ж╨╕╤П╤Е ExcelQuartile ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╤О╤В╤Б╤П ╨┤╨╗╤П ╨┐╨╛╨╕╤Б╨║╨░ ╤А╨░╨╖╨╗╨╕╤З╨╜╤Л╤Е ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╣ ╨▓ ╨╜╨░╨▒╨╛╤А╨╡ ╨┤╨░╨╜╨╜╤Л╤Е ╨╕ ╨╛╨╜╨╕ ╤П╨▓╨╗╤П╤О╤В╤Б╤П ╤З╨░╤Б╤В╤М╤О ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╨╕╤Е ╤Д╤Г╨╜╨║╤Ж╨╕╨╣ Excel. ╨Х╤Б╤В╤М ╤В╤А╨╕ ╨║╨▓╨░╤А╤В╨╕╨╗╨╕; ╨┐╨╡╤А╨▓╤Л╨╣ ╨║╨▓╨░╤А╤В╨╕╨╗╤М (Q1) тАФ ╤Н╤В╨╛ ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╤З╨╕╤Б╨╗╨╛ ╨╝╨╡╨╢╨┤╤Г ╨╜╨░╨╕╨╝╨╡╨╜╤М╤И╨╕╨╝ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡╨╝ ╨╕ ╨╝╨╡╨┤╨╕╨░╨╜╨╜╤Л╨╝ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡╨╝ ╨╜╨░╨▒╨╛╤А╨░ ╨┤╨░╨╜╨╜╤Л╤Е. ╨Т╤В╨╛╤А╨╛╨╣ ╨║╨▓╨░╤А╤В╨╕╨╗╤М (Q2) ╤П╨▓╨╗╤П╨╡╤В╤Б╤П ╨╝╨╡╨┤╨╕╨░╨╜╨╛╨╣ ╨┤╨░╨╜╨╜╤Л╤Е. ╨в╤А╨╡╤В╨╕╨╣ ╨║╨▓╨░╤А╤В╨╕╨╗╤М (Q3) тАФ ╤Н╤В╨╛ ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨╝╨╡╨╢╨┤╤Г ╨╝╨╡╨┤╨╕╨░╨╜╨╛╨╣ ╨╜╨░╨▒╨╛╤А╨░ ╨┤╨░╨╜╨╜╤Л╤Е ╨╕ ╨╝╨░╨║╤Б╨╕╨╝╨░╨╗╤М╨╜╤Л╨╝ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡╨╝. ╨з╤В╨╛╨▒╤Л ╨╗╤Г╤З╤И╨╡ ╨┐╨╛╨╜╤П╤В╤М ╨╡╨│╨╛, ╨┐╤А╨╛╤З╨╕╤В╨░╨╣╤В╨╡ ╨▒╨╛╨╗╤М╤И╨╡.
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╨Т╤Л ╨╝╨╛╨╢╨╡╤В╨╡ ╤Б╨║╨░╤З╨░╤В╤М ╤Н╤В╨╛╤В ╤И╨░╨▒╨╗╨╛╨╜ ╤Д╨╛╤А╨╝╤Г╨╗╤Л ╨║╨▓╨░╤А╤В╨╕╨╗╤П Excel ╨╖╨┤╨╡╤Б╤М — ╨д╨╛╤А╨╝╤Г╨╗╨░ ╨║╨▓╨░╤А╤В╨╕╨╗╤П Excel ╨и╨░╨▒╨╗╨╛╨╜

╨Я╤А╨╕╨╝╨╡╤А тДЦ1

╨а╨░╤Б╤Б╨╝╨╛╤В╤А╨╕╨╝ ╨╜╨░╨▒╨╛╤А ╨┤╨░╨╜╨╜╤Л╤Е ╨╕╨╖ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╤Е ╤З╨╕╤Б╨╡╨╗: 10, 2, 4, 7, 8, 5, 11, 3, 12. ╨Т╨░╨╝ ╨╜╨╡╨╛╨▒╤Е╨╛╨┤╨╕╨╝╨╛ ╨▓╤Л╤З╨╕╤Б╨╗╨╕╤В╤М ╨▓╤Б╨╡ 3 ╨║╨▓╨░╤А╤В╨╕╨╗╨╕.

╨а╨╡╤И╨╡╨╜╨╕╨╡:

╨Ш╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╣╤В╨╡ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╡ ╨┤╨░╨╜╨╜╤Л╨╡ ╨┤╨╗╤П ╤А╨░╤Б╤З╨╡╤В╨░ ╨║╨▓╨░╤А╤В╨╕╨╗╤П.

╨а╨░╤Б╤З╨╡╤В ╨╝╨╡╨┤╨╕╨░╨╜╤Л ╨╕╨╗╨╕ Q2 ╨╝╨╛╨╢╨╜╨╛ ╨▓╤Л╨┐╨╛╨╗╨╜╨╕╤В╤М ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝:

╨Ь╨╡╨┤╨╕╨░╨╜╨░ ╨╕╨╗╨╕ Q2 = ╨б╤Г╨╝╨╝╨░ (2+3+4+5+7+8+10+11+12)/9

╨Ь╨╡╨┤╨╕╨░╨╜╨░ ╨╕╨╗╨╕ Q2 ╨▒╤Г╨┤╨╡╤В тАУ

╨Ь╨╡╨┤╨╕╨░╨╜╨░ ╨╕╨╗╨╕ Q2 «=» 7

╨Я╨╛╤Б╨║╨╛╨╗╤М╨║╤Г ╨║╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣ ╨╜╨╡╤З╨╡╤В╨╜╨╛╨╡, ╤В╨╛ ╨╡╤Б╤В╤М 9, ╨╝╨╡╨┤╨╕╨░╨╜╨░ ╨▒╤Г╨┤╨╡╤В ╨╗╨╡╨╢╨░╤В╤М ╨╜╨░ 5-╨╣ ╨┐╨╛╨╖╨╕╤Ж╨╕╨╕, ╤В╨╛ ╨╡╤Б╤В╤М 7, ╨╕ ╤В╨╛ ╨╢╨╡ ╤Б╨░╨╝╨╛╨╡ ╨▒╤Г╨┤╨╡╤В Q2 ╨┤╨╗╤П ╤Н╤В╨╛╨│╨╛ ╨┐╤А╨╕╨╝╨╡╤А╨░.

╨а╨░╤Б╤З╨╡╤В Q1 ╨╝╨╛╨╢╨╜╨╛ ╨▓╤Л╨┐╨╛╨╗╨╜╨╕╤В╤М ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝:

Q1= ┬╝ (9 + 1)

= ┬╝ (10)

Q1 ╨▒╤Г╨┤╨╡╤В тАУ

Q1 «=» 2,5

╨н╤В╨╛ ╨╛╨╖╨╜╨░╤З╨░╨╡╤В, ╤З╤В╨╛ Q1 ╤П╨▓╨╗╤П╨╡╤В╤Б╤П ╤Б╤А╨╡╨┤╨╜╨╕╨╝ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡╨╝ 2-╨╣ ╨╕ 3-╨╣ ╨┐╨╛╨╖╨╕╤Ж╨╕╨╣ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣, ╨║╨╛╤В╨╛╤А╤Л╨╡ ╨╖╨┤╨╡╤Б╤М ╤А╨░╨▓╨╜╤Л 3 ╨╕ 4, ╨░ ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╤В╨╛╨│╨╛ ╨╢╨╡ ╤А╨░╨▓╨╜╨╛ (3 + 4)/2 = 3,5.

╨а╨░╤Б╤З╨╡╤В Q3 ╨╝╨╛╨╢╨╜╨╛ ╨▓╤Л╨┐╨╛╨╗╨╜╨╕╤В╤М ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝:

Q3 = ┬╛ (9 + 1)

= ┬╛ (10)

Q3 ╨▒╤Г╨┤╨╡╤В тАУ

Q3 «=» 7.5 ╨б╤А╨╛╨║

╨н╤В╨╛ ╨╛╨╖╨╜╨░╤З╨░╨╡╤В, ╤З╤В╨╛ Q3 ╤П╨▓╨╗╤П╨╡╤В╤Б╤П ╤Б╤А╨╡╨┤╨╜╨╕╨╝ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡╨╝ 8-╨╣ ╨╕ 9-╨╣ ╨┐╨╛╨╖╨╕╤Ж╨╕╨╣ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣, ╨║╨╛╤В╨╛╤А╤Л╨╡ ╨╖╨┤╨╡╤Б╤М ╤А╨░╨▓╨╜╤Л 10 ╨╕ 11. ╨в╨╛ ╨╢╨╡ ╤Б╨░╨╝╨╛╨╡ ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╤А╨░╨▓╨╜╨╛ (10+11)/2 = 10,5.

╨Я╤А╨╕╨╝╨╡╤А #2

Simple Ltd. тАФ ╨┐╤А╨╛╨╕╨╖╨▓╨╛╨┤╨╕╤В╨╡╨╗╤М ╨╛╨┤╨╡╨╢╨┤╤Л, ╤А╨░╨▒╨╛╤В╨░╤О╤Й╨╕╨╣ ╨┐╨╛ ╤Б╤Е╨╡╨╝╨╡, ╤З╤В╨╛╨▒╤Л ╨┐╨╛╤А╨░╨┤╨╛╨▓╨░╤В╤М ╤Б╨▓╨╛╨╕╤Е ╤Б╨╛╤В╤А╤Г╨┤╨╜╨╕╨║╨╛╨▓ ╨╖╨░ ╨╕╤Е ╤Г╤Б╨╕╨╗╨╕╤П. ╨а╤Г╨║╨╛╨▓╨╛╨┤╤Б╤В╨▓╨╛ ╨╛╨▒╤Б╤Г╨╢╨┤╨░╨╡╤В ╨╖╨░╨┐╤Г╤Б╨║ ╨╜╨╛╨▓╨╛╨╣ ╨╕╨╜╨╕╤Ж╨╕╨░╤В╨╕╨▓╤Л, ╨▓ ╨║╨╛╤В╨╛╤А╨╛╨╣ ╨│╨╛╨▓╨╛╤А╨╕╤В╤Б╤П, ╤З╤В╨╛ ╨╛╨╜╨╕ ╤Е╨╛╤В╤П╤В ╤А╨░╨╖╨┤╨╡╨╗╨╕╤В╤М ╤Б╨▓╨╛╨╕╤Е ╤Б╨╛╤В╤А╤Г╨┤╨╜╨╕╨║╨╛╨▓ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝:

• ╨Т╨╡╤А╤Е╨╜╨╕╨╡ 25%, ╨╗╨╡╨╢╨░╤Й╨╕╨╡ ╨▓╤Л╤И╨╡ Q3 — 25 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓ ╨╖╨░ ╤В╨║╨░╨╜╤М
• ╨С╨╛╨╗╤М╤И╨╡, ╤З╨╡╨╝ ╤Б╤А╨╡╨┤╨╜╨╕╨╣, ╨╜╨╛ ╨╝╨╡╨╜╤М╤И╨╡, ╤З╨╡╨╝ Q3 тАФ 20 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓ ╨╖╨░ ╤В╨║╨░╨╜╤М.
• ╨С╨╛╨╗╤М╤И╨╡, ╤З╨╡╨╝ Q1, ╨╜╨╛ ╨╝╨╡╨╜╤М╤И╨╡, ╤З╨╡╨╝ Q2 тАФ 18 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓ ╨╖╨░ ╤В╨║╨░╨╜╤М.
• ╨а╤Г╨║╨╛╨▓╨╛╨┤╤Б╤В╨▓╨╛ ╤Б╨╛╨▒╤А╨░╨╗╨╛ ╤Б╤А╨╡╨┤╨╜╨╡╤Б╤Г╤В╨╛╤З╨╜╤Л╨╡ ╨┤╨░╨╜╨╜╤Л╨╡ ╨╛ ╨┐╤А╨╛╨╕╨╖╨▓╨╛╨┤╨╕╤В╨╡╨╗╤М╨╜╨╛╤Б╤В╨╕ ╨╖╨░ ╨┐╨╛╤Б╨╗╨╡╨┤╨╜╨╕╨╡ 10 ╨┤╨╜╨╡╨╣ ╨▓ ╤А╨░╤Б╤З╨╡╤В╨╡ ╨╜╨░ ╨╛╨┤╨╜╨╛╨│╨╛ (╤Б╤А╨╡╨┤╨╜╨╡╨│╨╛) ╤А╨░╨▒╨╛╤В╨╜╨╕╨║╨░.
• 55, 69, 88, 50, 77, 45, 40, 90, 75, 56.
• ╨Ш╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╣╤В╨╡ ╤Д╨╛╤А╨╝╤Г╨╗╤Г ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╣ ╨┤╨╗╤П ╨┐╨╛╤Б╤В╤А╨╛╨╡╨╜╨╕╤П ╤Б╤В╤А╤Г╨║╤В╤Г╤А╤Л ╨▓╨╛╨╖╨╜╨░╨│╤А╨░╨╢╨┤╨╡╨╜╨╕╤П.
• ╨Ъ╨░╨║╨╛╨╡ ╨▓╨╛╨╖╨╜╨░╨│╤А╨░╨╢╨┤╨╡╨╜╨╕╨╡ ╨┐╨╛╨╗╤Г╤З╨╕╤В ╤Б╨╛╤В╤А╤Г╨┤╨╜╨╕╨║, ╨╡╤Б╨╗╨╕ ╨╛╨╜ ╨┐╤А╨╛╨╕╨╖╨▓╨╡╨┤╨╡╤В 76 ╨│╨╛╤В╨╛╨▓╤Л╤Е ╨▓╨╡╤Й╨╡╨╣?

╨а╨╡╤И╨╡╨╜╨╕╨╡:

╨Ш╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╣╤В╨╡ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╡ ╨┤╨░╨╜╨╜╤Л╨╡ ╨┤╨╗╤П ╤А╨░╤Б╤З╨╡╤В╨░ ╨║╨▓╨░╤А╤В╨╕╨╗╤П.

╨Ъ╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣ ╨╖╨┤╨╡╤Б╤М ╤А╨░╨▓╨╜╨╛ 10, ╨╕ ╨╜╨░╤И╨╕╨╝ ╨┐╨╡╤А╨▓╤Л╨╝ ╤И╨░╨│╨╛╨╝ ╨▒╤Г╨┤╨╡╤В ╨┐╤А╨╡╨╛╨▒╤А╨░╨╖╨╛╨▓╨░╨╜╨╕╨╡ ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╜╨╜╤Л╤Е ╨▓╤Л╤И╨╡ ╨╜╨╡╨╛╨▒╤А╨░╨▒╨╛╤В╨░╨╜╨╜╤Л╤Е ╨┤╨░╨╜╨╜╤Л╤Е ╨▓ ╨┐╨╛╤А╤П╨┤╨║╨╡ ╨▓╨╛╨╖╤А╨░╤Б╤В╨░╨╜╨╕╤П.
40, 45, 50, 55, 56, 69, 75, 77, 88, 90
╨а╨░╤Б╤З╨╡╤В ╨║╨▓╨░╤А╤В╨╕╨╗╤П Q1 ╨╝╨╛╨╢╨╡╤В ╨▒╤Л╤В╤М ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝:

Q1 = ┬╝ (n+1)-╨╣ ╤З╨╗╨╡╨╜

= ┬╝ (10+1)

= ┬╝ (11)

Q1 ╨▒╤Г╨┤╨╡╤В тАУ

Q1 «=» 2.75 ╨б╤А╨╛╨║

╨Ч╨┤╨╡╤Б╤М ╨╜╨╡╨╛╨▒╤Е╨╛╨┤╨╕╨╝╨╛ ╨▓╨╖╤П╤В╤М ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡, ╤Б╨╛╤Б╤В╨╛╤П╤Й╨╡╨╡ ╨╕╨╖ 2-╨│╨╛ ╨╕ 3-╨│╨╛ ╤З╨╗╨╡╨╜╨╛╨▓, ╨║╨╛╤В╨╛╤А╤Л╨╡ ╤А╨░╨▓╨╜╤Л 45 ╨╕ 50. ╨д╨╛╤А╨╝╤Г╨╗╨░ ╤А╨░╤Б╤Б╤З╨╕╤В╤Л╨▓╨░╨╡╤В╤Б╤П ╨┐╤Г╤В╨╡╨╝ ╤Б╨╗╨╛╨╢╨╡╨╜╨╕╤П ╨▓╤Б╨╡╤Е ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╣ ╨╖╨░╨┤╨░╨╜╨╜╨╛╨│╨╛ ╨╜╨░╨▒╨╛╤А╨░, ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╨╝╨╛╨│╨╛ ╤Б╤Г╨╝╨╝╨╕╤А╨╛╨▓╨░╨╜╨╕╨╡╨╝ X, ╨╕ ╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨╡╨│╨╛ ╨╜╨░ ╨║╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╣, ╨╖╨░╨┤╨░╨╜╨╜╤Л╤Е ╨▓ ╨╜╨░╨▒╨╛╤А╨╡, ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╨╝╨╛╨╝ N. ╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡ ╨╛ ╤В╨╛╨╝ ╨╢╨╡: (45 + 50) / 2 = 47,50

Q1 ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 47,50, ╤З╤В╨╛ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 25% ╨╝╨╕╨╜╨╕╨╝╤Г╨╝╨░.

╨а╨░╤Б╤З╨╡╤В ╨║╨▓╨░╤А╤В╨╕╨╗╤П Q3 ╨╝╨╛╨╢╨╜╨╛ ╨▓╤Л╨┐╨╛╨╗╨╜╨╕╤В╤М ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝:

Q3 = ┬╛ (n+1)-╨╣ ╤З╨╗╨╡╨╜

= ┬╛ (11)

Q3 ╨▒╤Г╨┤╨╡╤В тАУ

Q3 «=» 8.25 ╨б╤А╨╛╨║

╨Ч╨┤╨╡╤Б╤М ╨╜╨╡╨╛╨▒╤Е╨╛╨┤╨╕╨╝╨╛ ╨▓╨╖╤П╤В╤М ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ 8-╨│╨╛ ╨╕ 9-╨│╨╛ ╤З╨╗╨╡╨╜╨╛╨▓, ╤В╨╛ ╨╡╤Б╤В╤М 88 ╨╕ 90. ╨б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╤А╨░╨▓╨╜╨╛ (88 + 90) / 2 = 89,00.

Q3 тАФ 89, ╤З╤В╨╛ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 25% ╨╗╤Г╤З╤И╨╕╤Е.

╨а╨░╤Б╤З╨╡╤В ╨╝╨╡╨┤╨╕╨░╨╜╤Л ╨╕╨╗╨╕ Q2 ╨╝╨╛╨╢╨╡╤В ╨▒╤Л╤В╤М ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝:

╨б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ (Q2) = 8,25 тАУ 2,75.

╨Ь╨╡╨┤╨╕╨░╨╜╨░ ╨╕╨╗╨╕ Q2 ╨▒╤Г╨┤╨╡╤В тАУ

╨Ь╨╡╨┤╨╕╨░╨╜╨░ ╨╕╨╗╨╕ Q2«=» 5.5 ╨б╤А╨╛╨║

╨Ч╨┤╨╡╤Б╤М ╨╜╨╡╨╛╨▒╤Е╨╛╨┤╨╕╨╝╨╛ ╨▓╨╖╤П╤В╤М ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡, ╨║╨╛╤В╨╛╤А╨╛╨╡ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 5 ╨╕ 6 56 ╨╕ 69. ╨б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╤А╨░╨▓╨╜╨╛ (56 + 69) / 2 = 62,5.

Q2 ╨╕╨╗╨╕ ╨╝╨╡╨┤╨╕╨░╨╜╨░ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 62,5.

╨з╤В╨╛ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 50% ╨╜╨░╤Б╨╡╨╗╨╡╨╜╨╕╤П.

╨Ф╨╕╨░╨┐╨░╨╖╨╛╨╜ ╨▓╨╛╨╖╨╜╨░╨│╤А╨░╨╢╨┤╨╡╨╜╨╕╤П ╨▒╤Г╨┤╨╡╤В ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝:

47.50 тАФ 62.50 тАФ 18 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓ ╨╖╨░ ╤В╨║╨░╨╜╤М.

> 62,50 тАФ 89 ╨┐╨╛╨╗╤Г╤З╨░╤В 20 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓ ╨╖╨░ ╤В╨║╨░╨╜╤М

> 89,00 ╨┐╨╛╨╗╤Г╤З╨╕╤В╨╡ 25 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓ ╨╖╨░ ╤В╨║╨░╨╜╤М

╨Х╤Б╨╗╨╕ ╤А╨░╨▒╨╛╤В╨╜╨╕╨║ ╨┐╤А╨╛╨╕╨╖╨▓╨╛╨┤╨╕╤В 76, ╨╛╨╜ ╨▒╤Г╨┤╨╡╤В ╨╗╨╡╨╢╨░╤В╤М ╨▓╤Л╤И╨╡ Q1. ╨б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М╨╜╨╛, ╨▒╤Г╨┤╨╡╤В ╨╕╨╝╨╡╤В╤М ╨┐╤А╨░╨▓╨╛ ╨╜╨░ ╨▒╨╛╨╜╤Г╤Б ╨▓ ╤А╨░╨╖╨╝╨╡╤А╨╡ 20 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓.

╨Я╤А╨╕╨╝╨╡╤А тДЦ3

╨Я╤А╨╡╨┐╨╛╨┤╨░╨▓╨░╨╜╨╕╨╡ ╤З╨░╤Б╤В╨╜╤Л╤Е ╨║╨╛╤Г╤З-╨║╨╗╨░╤Б╤Б╨╛╨▓ ╨┐╤А╨╡╨┤╨┐╨╛╨╗╨░╨│╨░╨╡╤В ╨▓╨╛╨╖╨╜╨░╨│╤А╨░╨╢╨┤╨╡╨╜╨╕╨╡ ╤Б╤В╤Г╨┤╨╡╨╜╤В╨╛╨▓ ╨╕╨╖ ╨▓╨╡╤А╤Е╨╜╨╕╤Е 25% ╨║╨▓╨░╤А╤В╨╕╨╗╨╕ ╤Б╨╛╨▓╨╡╤В╨░╨╝╨╕ ╨╝╨╡╨╢╨║╨▓╨░╤А╤В╨╕╨╗╤М╨╜╤Л╨╝ ╤Б╤В╤Г╨┤╨╡╨╜╤В╨░╨╝, ╨╜╨░╤Е╨╛╨┤╤П╤Й╨╕╨╝╤Б╤П ╨▓ ╤Н╤В╨╛╨╝ ╨┤╨╕╨░╨┐╨░╨╖╨╛╨╜╨╡, ╨╕ ╨┐╨╛╨▓╤В╨╛╤А╨╜╤Л╨╝ ╤Б╨┤╨░╤З╨╡╨╣ ╨╖╨░╨╜╤П╤В╨╕╨╣ ╨┤╨╗╤П ╤Б╤В╤Г╨┤╨╡╨╜╤В╨╛╨▓, ╨╜╨░╤Е╨╛╨┤╤П╤Й╨╕╤Е╤Б╤П ╨╜╨╕╨╢╨╡ Q1. ╨Ш╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╣╤В╨╡ ╤Д╨╛╤А╨╝╤Г╨╗╤Г ╨║╨▓╨░╤А╤В╨╕╨╗╤П, ╤З╤В╨╛╨▒╤Л ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╕╤В╤М, ╤Б ╨║╨░╨║╨╕╨╝╨╕ ╨┐╨╛╤Б╨╗╨╡╨┤╤Б╤В╨▓╨╕╤П╨╝╨╕ ╨╛╨╜ ╤Б╤В╨╛╨╗╨║╨╜╨╡╤В╤Б╤П, ╨╡╤Б╨╗╨╕ ╨╛╨╜ ╨╜╨░╨▒╨╡╤А╨╡╤В ╨▓ ╤Б╤А╨╡╨┤╨╜╨╡╨╝ 63 ╨▒╨░╨╗╨╗╨░. .

╨а╨╡╤И╨╡╨╜╨╕╨╡ :

╨Ш╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╣╤В╨╡ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╡ ╨┤╨░╨╜╨╜╤Л╨╡ ╨┤╨╗╤П ╤А╨░╤Б╤З╨╡╤В╨░ ╨║╨▓╨░╤А╤В╨╕╨╗╤П.

╨Ф╨░╨╜╨╜╤Л╨╡ ╨┤╨╗╤П 25 ╤Б╤В╤Г╨┤╨╡╨╜╤В╨╛╨▓.

╨Ъ╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣ ╨╖╨┤╨╡╤Б╤М ╤А╨░╨▓╨╜╨╛ 25, ╨╕ ╨╜╨░╤И╨╕╨╝ ╨┐╨╡╤А╨▓╤Л╨╝ ╤И╨░╨│╨╛╨╝ ╨▒╤Г╨┤╨╡╤В ╨┐╤А╨╡╨╛╨▒╤А╨░╨╖╨╛╨▓╨░╨╜╨╕╨╡ ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╜╨╜╤Л╤Е ╨▓╤Л╤И╨╡ ╨╜╨╡╨╛╨▒╤А╨░╨▒╨╛╤В╨░╨╜╨╜╤Л╤Е ╨┤╨░╨╜╨╜╤Л╤Е ╨▓ ╨┐╨╛╤А╤П╨┤╨║╨╡ ╨▓╨╛╨╖╤А╨░╤Б╤В╨░╨╜╨╕╤П.
╨а╨░╤Б╤З╨╡╤В ╨║╨▓╨░╤А╤В╨╕╨╗╤П Q1 ╨╝╨╛╨╢╨╡╤В ╨▒╤Л╤В╤М ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝:

Q1 = ┬╝ (n+1)-╨╣ ╤З╨╗╨╡╨╜

= ┬╝ (25+1)

= ┬╝ (26)

Q1 ╨▒╤Г╨┤╨╡╤В тАУ

Q1 «=» 6.5 ╨б╤А╨╛╨║

Q1 ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 56,00, ╤З╤В╨╛ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╨╜╨╕╨╢╨╜╨╕╨╡ 25%

╨а╨░╤Б╤З╨╡╤В ╨║╨▓╨░╤А╤В╨╕╨╗╤П Q3 ╨╝╨╛╨╢╨╜╨╛ ╨▓╤Л╨┐╨╛╨╗╨╜╨╕╤В╤М ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝:

Q3 = ┬╛ (n+1)-╨╣ ╤З╨╗╨╡╨╜

= ┬╛ (26)

Q3 ╨▒╤Г╨┤╨╡╤В тАУ

Q3 «=» 19.50 ╨б╤А╨╛╨║

╨Ч╨┤╨╡╤Б╤М ╨╜╨╡╨╛╨▒╤Е╨╛╨┤╨╕╨╝╨╛ ╨▓╨╖╤П╤В╤М ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ 19-╨│╨╛ ╨╕ 20-╨│╨╛ ╤З╨╗╨╡╨╜╨╛╨▓, ╤В╨╛ ╨╡╤Б╤В╤М 77 ╨╕ 77. ╨б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╤А╨░╨▓╨╜╨╛ (77+77)/2 = 77,00.

Q3 ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 77, ╤З╤В╨╛ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 25% ╨╗╤Г╤З╤И╨╕╤Е.

╨Ь╨╡╨┤╨╕╨░╨╜╨░ ╨╕╨╗╨╕ Q2 ╨▒╤Г╨┤╨╡╤В тАУ

╨Ь╨╡╨┤╨╕╨░╨╜╨░ ╨╕╨╗╨╕ Q2=19,50 тАУ 6,5

╨Ь╨╡╨┤╨╕╨░╨╜╨░ ╨╕╨╗╨╕ Q2 ╨▒╤Г╨┤╨╡╤В тАУ

╨Ь╨╡╨┤╨╕╨░╨╜╨░ ╨╕╨╗╨╕ Q2 «=» 13 ╨б╤А╨╛╨║

Q2 ╨╕╨╗╨╕ ╨╝╨╡╨┤╨╕╨░╨╜╨░ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 68,00.

╨з╤В╨╛ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 50% ╨╜╨░╤Б╨╡╨╗╨╡╨╜╨╕╤П.

╤А╨│╨╜╨╡╨▓ ╨▒╤Г╨┤╨╡╤В:

56.00 тАУ 68.00

>68.00 тАУ 77.00

77.00

╨Р╨║╤В╤Г╨░╨╗╤М╨╜╨╛╤Б╤В╤М ╨╕ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡ ╤Д╨╛╤А╨╝╤Г╨╗╤Л ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╣

╨Ъ╨▓╨░╤А╤В╨╕╨╗╨╕ ╨┐╨╛╨╖╨▓╨╛╨╗╤П╤О╤В ╨▒╤Л╤Б╤В╤А╨╛ ╤А╨░╨╖╨┤╨╡╨╗╨╕╤В╤М ╨╖╨░╨┤╨░╨╜╨╜╤Л╨╣ ╨╜╨░╨▒╨╛╤А ╨┤╨░╨╜╨╜╤Л╤Е ╨╕╨╗╨╕ ╨▓╤Л╨▒╨╛╤А╨║╤Г ╨╜╨░ ╤З╨╡╤В╤Л╤А╨╡ ╨╛╤Б╨╜╨╛╨▓╨╜╤Л╨╡ ╨│╤А╤Г╨┐╨┐╤Л, ╤Г╨┐╤А╨╛╤Й╨░╤П ╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╤В╨╡╨╗╤О ╨╛╤Ж╨╡╨╜╨║╤Г ╤В╨╛╨│╨╛, ╨║ ╨║╨░╨║╨╛╨╣ ╨╕╨╖ ╤З╨╡╤В╤Л╤А╨╡╤Е ╨│╤А╤Г╨┐╨┐ ╨╛╤В╨╜╨╛╤Б╨╕╤В╤Б╤П ╤В╨╛╤З╨║╨░ ╨┤╨░╨╜╨╜╤Л╤Е. ╨Т ╤В╨╛ ╨▓╤А╨╡╨╝╤П ╨║╨░╨║ ╨╝╨╡╨┤╨╕╨░╨╜╨░, ╨║╨╛╤В╨╛╤А╨░╤П ╨╕╨╖╨╝╨╡╤А╤П╨╡╤В ╤Ж╨╡╨╜╤В╤А╨░╨╗╤М╨╜╤Г╤О ╤В╨╛╤З╨║╤Г ╨╜╨░╨▒╨╛╤А╨░ ╨┤╨░╨╜╨╜╤Л╤Е, ╤П╨▓╨╗╤П╨╡╤В╤Б╤П ╨╜╨░╨┤╨╡╨╢╨╜╨╛╨╣ ╨╛╤Ж╨╡╨╜╨║╨╛╨╣ ╨╝╨╡╤Б╤В╨╛╨┐╨╛╨╗╨╛╨╢╨╡╨╜╨╕╤П. ╨Ю╨╜ ╨╜╨╡ ╨│╨╛╨▓╨╛╤А╨╕╤В, ╨╜╨░╤Б╨║╨╛╨╗╤М╨║╨╛ ╨┤╨░╨╜╨╜╤Л╨╡ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣ ╨╗╨╡╨╢╨░╤В ╨╜╨░ ╤В╨╛╨╣ ╨╕╨╗╨╕ ╨╕╨╜╨╛╨╣ ╤Б╤В╨╛╤А╨╛╨╜╨╡ ╨╕╨╗╨╕ ╤А╨░╤Б╤Б╨╡╤П╨╜╤Л ╨╕╨╗╨╕ ╤А╨░╨╖╨▒╤А╨╛╤Б╨░╨╜╤Л. ╨Ъ╨▓╨░╤А╤В╨╕╨╗╤М ╨╕╨╖╨╝╨╡╤А╤П╨╡╤В ╤А╨░╨╖╨▒╤А╨╛╤Б ╨╕╨╗╨╕ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╤О. ╨Т ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╤П (╨╕╨╗╨╕ ╤А╨░╨╖╨▒╤А╨╛╤Б) тАФ ╤Н╤В╨╛ ╤Б╤А╨╡╨┤╤Б╤В╨▓╨╛ ╨╛╨┐╨╕╤Б╨░╨╜╨╕╤П ╤Б╤В╨╡╨┐╨╡╨╜╨╕ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨┤╨░╨╜╨╜╤Л╤Е ╨▓╨╛╨║╤А╤Г╨│ ╤Ж╨╡╨╜╤В╤А╨░╨╗╤М╨╜╨╛╨│╨╛ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨╕╨╗╨╕ ╤В╨╛╤З╨║╨╕. ╨н╤В╨╛ ╨┐╨╛╨╝╨╛╨│╨░╨╡╤В ╨┐╨╛╨╜╤П╤В╤М ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╨┤╨░╨╜╨╜╤Л╤Е. ╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡ ╨╛ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П╤Е ╨▓╤Л╤И╨╡ ╨╕ ╨╜╨╕╨╢╨╡ ╤Б╤А╨╡╨┤╨╜╨╡╨│╨╛ ╨░╤А╨╕╤Д╨╝╨╡╤В╨╕╤З╨╡╤Б╨║╨╛╨│╨╛ ╨б╤А╨╡╨┤╨╜╨╡╨╡ ╨░╤А╨╕╤Д╨╝╨╡╤В╨╕╤З╨╡╤Б╨║╨╛╨╡ ╨б╤А╨╡╨┤╨╜╨╡╨╡ ╨░╤А╨╕╤Д╨╝╨╡╤В╨╕╤З╨╡╤Б╨║╨╛╨╡ ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╤В ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨▓╤Б╨╡╤Е ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣ ╤А╤П╨┤╨░ ╨┤╨░╨╜╨╜╤Л╤Е. ╨н╤В╨╛ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╤М ╨▓╤Б╨╡╤Е ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╣ ╨▓ ╨╜╨░╨▒╨╛╤А╨╡ ╨┤╨░╨╜╨╜╤Л╤Е, ╨┤╨╡╨╗╨╡╨╜╨╜╨░╤П ╨╜╨░ ╨╛╨▒╤Й╨╡╨╡ ╨║╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣ ╨╕╨╗╨╕ ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡, ╤А╨░╨╖╨┤╨╡╨╗╤П╤О╤Й╨╡╨╡ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╨╜╨░ ╤З╨╡╤В╤Л╤А╨╡ ╨╛╤Б╨╜╨╛╨▓╨╜╤Л╨╡ ╨│╤А╤Г╨┐╨┐╤Л, ╨╛╨┐╨╕╤Б╨░╨╜╨╜╤Л╨╡ ╨▓╤Л╤И╨╡.

╨а╨╡╨║╨╛╨╝╨╡╨╜╨┤╤Г╨╡╨╝╤Л╨╡ ╤Б╤В╨░╤В╤М╨╕

╨н╤В╨░ ╤Б╤В╨░╤В╤М╤П ╨▒╤Л╨╗╨░ ╤А╤Г╨║╨╛╨▓╨╛╨┤╤Б╤В╨▓╨╛╨╝ ╨┐╨╛ ╤Д╨╛╤А╨╝╤Г╨╗╨╡ ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╣. ╨Ч╨┤╨╡╤Б╤М ╨╝╤Л ╤Г╨╖╨╜╨░╨╡╨╝, ╨║╨░╨║ ╤А╨░╤Б╤Б╤З╨╕╤В╨░╤В╤М ╨║╨▓╨░╤А╤В╨╕╨╗╨╕ ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡, ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╤П ╨╡╨╡ ╤Д╨╛╤А╨╝╤Г╨╗╤Г, ╨┐╤А╨░╨║╤В╨╕╤З╨╡╤Б╨║╨╕╨╡ ╨┐╤А╨╕╨╝╨╡╤А╤Л ╨╕ ╨╖╨░╨│╤А╤Г╨╢╨░╨╡╨╝╤Л╨╣ ╤И╨░╨▒╨╗╨╛╨╜ Excel. ╨Т╤Л ╨╝╨╛╨╢╨╡╤В╨╡ ╤Г╨╖╨╜╨░╤В╤М ╨▒╨╛╨╗╤М╤И╨╡ ╨╛ ╨╝╨╛╨┤╨╡╨╗╨╕╤А╨╛╨▓╨░╨╜╨╕╨╕ ╨▓ Excel ╨╕╨╖ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╤Е ╤Б╤В╨░╤В╨╡╨╣:

• ╨Ю╤Ж╨╡╨╜╤Й╨╕╨║╨╕ ╨▒╨░╨╗╨╗╨╛╨▓
• ╨Ъ╨▓╨░╤А╤В╨╕╨╗╤М╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡╨Ъ╨▓╨░╤А╤В╨╕╨╗╤М╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡╨Ъ╨▓╨░╤А╤В╨╕╨╗╤М╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨╛╤Б╨╜╨╛╨▓╨░╨╜╨╛ ╨╜╨░ ╤А╨░╨╖╨╜╨╕╤Ж╨╡ ╨╝╨╡╨╢╨┤╤Г ╨┐╨╡╤А╨▓╤Л╨╝ ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╝ ╨╕ ╤В╤А╨╡╤В╤М╨╕╨╝ ╨║╨▓╨░╤А╤В╨╕╨╗╨╡╨╝ ╨▓ ╤З╨░╤Б╤В╨╛╤В╨╜╨╛╨╝ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╕, ╨╕ ╤Н╤В╨░ ╤А╨░╨╖╨╜╨╕╤Ж╨░ ╤В╨░╨║╨╢╨╡ ╨╕╨╖╨▓╨╡╤Б╤В╨╜╨░ ╨║╨░╨║ ╨╝╨╡╨╢╨║╨▓╨░╤А╤В╨╕╨╗╤М╨╜╤Л╨╣ ╤А╨░╨╖╨╝╨░╤Е, ╤А╨░╨╖╨╜╨╕╤Ж╨░, ╨┤╨╡╨╗╨╡╨╜╨╜╨░╤П ╨╜╨░ ╨┤╨▓╨░, ╨╕╨╖╨▓╨╡╤Б╤В╨╜╨░ ╨║╨░╨║ ╨║╨▓╨░╤А╤В╨╕╨╗╤М╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨╕╨╗╨╕ ╨┐╨╛╨╗╤Г╨╝╨╡╨╢╨║╨▓╨░╤А╤В╨╕╨╗╤М╨╜╤Л╨╣ ╤А╨░╨╖╨╝╨░╤Е.╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡
• ╨д╨╛╤А╨╝╤Г╨╗╨░ ╨║╨╛╤Н╤Д╤Д╨╕╤Ж╨╕╨╡╨╜╤В╨░ ╨▓╨░╤А╨╕╨░╤Ж╨╕╨╕╨д╨╛╤А╨╝╤Г╨╗╨░ ╨║╨╛╤Н╤Д╤Д╨╕╤Ж╨╕╨╡╨╜╤В╨░ ╨▓╨░╤А╨╕╨░╤Ж╨╕╨╕╨Ъ╨╛╤Н╤Д╤Д╨╕╤Ж╨╕╨╡╨╜╤В ╨▓╨░╤А╨╕╨░╤Ж╨╕╨╕ тАУ ╤Н╤В╨╛ ╤Б╨╕╤Б╤В╨╡╨╝╨░╤В╨╕╨╖╨╕╤А╨╛╨▓╨░╨╜╨╜╨░╤П ╨╝╨╡╤А╨░ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╕ ╨▓╨╡╤А╨╛╤П╤В╨╜╨╛╤Б╤В╨╜╨╛╨│╨╛ ╨╕╨╗╨╕ ╤З╨░╤Б╤В╨╛╤В╨╜╨╛╨│╨╛ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П. ╨Ю╨╜ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╤П╨╡╤В╤Б╤П ╨║╨░╨║ ╨╛╤В╨╜╨╛╤И╨╡╨╜╨╕╨╡ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨│╨╛ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╤П ╨║ ╤Б╤А╨╡╨┤╨╜╨╡╨╝╤Г. ╤З╨╕╤В╨░╤В╤М ╨┤╨░╨╗╨╡╨╡
• ╨Т╤Л╤З╨╕╤Б╨╗╨╕╤В╤М ╨║╨╛╤Н╤Д╤Д╨╕╤Ж╨╕╨╡╨╜╤В ╨║╨╛╤А╤А╨╡╨╗╤П╤Ж╨╕╨╕╨Т╤Л╤З╨╕╤Б╨╗╨╕╤В╤М ╨║╨╛╤Н╤Д╤Д╨╕╤Ж╨╕╨╡╨╜╤В ╨║╨╛╤А╤А╨╡╨╗╤П╤Ж╨╕╨╕╨Ъ╨╛╤Н╤Д╤Д╨╕╤Ж╨╕╨╡╨╜╤В ╨║╨╛╤А╤А╨╡╨╗╤П╤Ж╨╕╨╕, ╨╕╨╜╨╛╨│╨┤╨░ ╨╜╨░╨╖╤Л╨▓╨░╨╡╨╝╤Л╨╣ ╨║╨╛╤Н╤Д╤Д╨╕╤Ж╨╕╨╡╨╜╤В╨╛╨╝ ╨▓╨╖╨░╨╕╨╝╨╜╨╛╨╣ ╨║╨╛╤А╤А╨╡╨╗╤П╤Ж╨╕╨╕, ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤Б╨╛╨▒╨╛╨╣ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╤Г╤О ╨╝╨╡╤А╤Г, ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╨╝╤Г╤О ╨┤╨╗╤П ╨╛╤Ж╨╡╨╜╨║╨╕ ╤Б╨╕╨╗╤Л ╨▓╨╖╨░╨╕╨╝╨╛╤Б╨▓╤П╨╖╨╕ ╨╝╨╡╨╢╨┤╤Г ╨┤╨▓╤Г╨╝╤П ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Л╨╝╨╕. ╨Х╨│╨╛ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨▓╨░╤А╤М╨╕╤А╤Г╤О╤В╤Б╤П ╨╛╤В -1,0 (╨╛╤В╤А╨╕╤Ж╨░╤В╨╡╨╗╤М╨╜╨░╤П ╨║╨╛╤А╤А╨╡╨╗╤П╤Ж╨╕╤П) ╨┤╨╛ +1,0 (╨┐╨╛╨╗╨╛╨╢╨╕╤В╨╡╨╗╤М╨╜╨░╤П ╨║╨╛╤А╤А╨╡╨╗╤П╤Ж╨╕╤П). ╤З╨╕╤В╨░╤В╤М ╨┤╨░╨╗╨╡╨╡