Satz: Ungleichung der Mittelwerte

Für eine nichtnegative Stichprobe x, d.h. x i 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaaqaaaaaaaaaWdbiaadMgaa8aabeaak8qacqGHLjYScaaIWaaa aa@3AD7@ , gilt:

min i=1n x i x ¯ harm x ¯ geom x ¯ max i=1n x i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qadaWfqaqaaiGac2gacaGGPbGaaiOBaaWcbaGaamyAaiabg2da9iaa igdacqGHMacVcaWGUbaabeaakiaadIhapaWaaSbaaSqaa8qacaWGPb aapaqabaGccqGHKjYOceWG4bGbaebadaWgaaWcbaGaamiAaiaadgga caWGYbGaamyBaaqabaGccqGHKjYOceWG4bGbaebadaWgaaWcbaGaam 4zaiaadwgacaWGVbGaamyBaaqabaGccqGHKjYOceWG4bGbaebacqGH KjYOpeWaaCbeaeaaciGGTbGaaiyyaiaacIhaaSqaaiaadMgacqGH9a qpcaaIXaGaeyOjGWRaamOBaaqabaGccaWG4bWdamaaBaaaleaapeGa amyAaaWdaeqaaaaa@5D3D@